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A NOVEL CONCEPT IN THEORY OF QUADRATIC EQUATION

Authors:

Prabir Chandra Bhattacharyya

DOI NO:

https://doi.org/10.26782/jmcms.2022.03.00006

admin March 29, 2022

Abstract:

The basic idea of a quadratic equation is one of the most important topics in algebra. The mathematical concept for the method of solution of a quadratic equation is dependent on the advancement of the theory of numbers. The author developed a new concept regarding the method of solution of the quadratic equation based on “Theory of Dynamics of Numbers”. The author determined the inherent nature of one unknown quantity (say x) from the quadratic expression ax²+bx+c of the quadratic equation ax²+bx+c=0 by keeping the structure of the second-degree expression intact and then finding the solution of the quadratic equation using the novel concept of the Theory of Dynamics of Numbers. The author solved any quadratic equation in one unknown number (say x) of the quadratic equation in the form of ax²+bx+c=0, whether the numerical value of the discriminant is b²-4ac≥0 or b²-4ac<0, is real numbers only without using any imaginary numbers. With these new inventive concepts, the author developed new theories in the theory of quadratic equation.

Keywords:

Bhattacharyya’s Co-ordinate System,Cartesian Co-ordinate System,Quadratic Equation,Theory of Dynamics of Numbers,Theory of Numbers,

Refference:

I. Bhattacharyya P. C. “AN INTRODUCTION TO RECTANGULAR BHATTACHARYYA’S CO-ORDINATES: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, November (2021). pp 76-86.
II. Bhattacharyya P. C.. “AN INTRODUCTION TO THEORY OF DYNAMICS OF NUMBERS: A NEW CONCEPT”. J. Mech. Cont. & Math. Sci., Vol.-16, No.-11, January (2022). pp 37-53
III. Boyer, C. B. & Merzbach, U. C. (2011). A history of mathematics. New York: John Wiley & Sons.
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VI. Datta, B. B., & Singh, A. N. (1938). History of Hindu Mathematics, A source book. Mumbai, Maharashtra: Asia Publishing House.
VII. Gandz, S. (1937). The origin and development of the quadratic equations in Babylonian, Greek, and Early Arabic algebra. History of Science Society, 3, 405-557.
VIII. Gandz, S. (1940). Studies in Babylonian mathematics III: Isoperimetric problems and the origin of the quadratic equations. Isis, 3(1), 103-115.
IX. Hardy G. H. and Wright E. M. “An Introduction to the Theory of Numbers”. Sixth Edition. P. 52.
X. Katz, V. J. (1997), Algebra and its teaching: An historical survey. Journal of Mathematical Behavior, 16(l), 25-36.
XI. Katz, V., J. (1998). A history of mathematics (2nd edition). Harlow, England: Addison Wesley Longman Inc.
XII. Katz Victor, (2007). The Mathematics of Egypt, Mesopotamia, China, India and Islam: A source book 1st ed., New Jersey, USA: Princeton University Press.
XIII. Kennedy, P. A., Warshauer, M. L. & Curtin, E. (1991). Factoring by grouping: Making the connection. Mathematics and Computer Education, 25(2), 118-123.
XIV. Ling, W. & Needham, J., (1955). Horner’s method in Chinese Mathematics: Its root in the root extraction procedures of the Han Dynasty, England: T’oung Pao.
XV. Nataraj, M. S., & Thomas, M. O. J. (2006). Expansion of binomials and factorisation of quadratic expressions: Exploring a vedic method. Australian Senior Mathematics Journal, 20(2), 8-17.
XVI. Rosen, Frederic (Ed. and Trans). (1831). The algebra of Mohumed Ben Muss. London: Oriental Translation Fund; reprinted Hildesheim: Olms, 1986, and Fuat Sezgin, Ed., Islamic Mathematics and Astronomy, Vol. 1. Frankfurt am Main: Institute for the History of Arabic-Islamic Science 1997.
XVII. Smith, D. (1951). History of mathematics, Vol. 1. New York: Dover. Smith, D. (1953). History of mathematics, Vol. 2. New York: Dover. Stols, H. G. (2004).
XVIII. Smith, D. (1953). History of mathematics, Vol. 2. New York: Dover.
XIX. Thapar, R., (2000). Cultural pasts: Essays in early Indian History, New Delhi: Oxford University Press.
XX. Yong, L. L. (1970). The geometrical basis of the ancient Chinese square-root method. The History of Science Society, 61(1), 92-102.
XXI. http://en. wikipedia.org/wiki/Shridhara

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Journal Vol – 17 No -3, March 2022

OPTICAL PARALLEL HALF ADDER USING SEMICONDUCTOR OPTICAL AMPLIFIER-ASSISTED SAGNAC GATES

Authors:

Dilip Kumar Gayen

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00001

admin April 24, 2022

Abstract:

Today communication needs huge operational speed. This will be accomplished in case the conventional carrier of data, i.e. electron is supplanted by a photon for gadgets based on switching and logic. Gates are the basic building pieces of advanced frameworks. Different logic and arithmetic operations can be done using this gate. Optical logic and arithmetic operations are exceptionally much anticipated in high-speed communication frameworks. In this paper, we have presented parallel models to perform the addition of two binary digits based on terahertz optical asymmetric demultiplexer (TOAD)/semiconductor optical amplifier (SOA)-assisted Sagnac gates. Using only two TOAD-based switches we have designed a parallel half adder. This optical circuit increases the speed of calculation and is also capable of synthesizing light as an input to form the output. The most advantage of this parallel circuit is that no synchronization is required for distinctive inputs. The circuit is hypothetically planned and confirmed by numerical simulations.

Keywords:

Terahertz optical asymmetric demultiplexer,semiconductor optical amplifier,half adder,optical logic,

Refference:

I. Bhattacharyya A, Gayen D. K and Chattopadhyay T, “Alternative All-optical Circuit of Binary to BCD Converter Using Terahertz Asymmetric Demultiplexer Based Interferometric Switch”, Proceedings of 1st International Conference on Computation and Communication Advancement, 2013.
II. Gayen D. K, Roy J. N, Taraphdar C, and Pal R. K, “All-optical reconfigurable logic operations with the help of terahertz optical asymmetric demultiplexer”, International Journal for Light and Electron Optics. vol. 122, pp: 711-718, 2011.
III. Gayen D. K, Chattopadhyay T, Das M. K, Roy J. N and Pal R. K, “All-optical binary to gray code and gray to binary code conversion scheme with the help of semiconductor optical amplifier -assisted sagnac switch”, IET Circuits, Devices & Systems. vol. 5, pp: 123-131, 2011.
IV. Ghosh P, Kumbhakar D, Mukherjee A. K and Mukherjee K, “An all-optical method of implementing a wavelength encoded simultaneous binary full-adder-full-subtractor unit exploiting nonlinear polarization rotation in semiconductor optical amplifier International”, Journal for Light and Electron Optics. vol. 122, pp: 1757-1763, 2011.
V. Kim J. H, Kim S. H, Son C. W, Ok S. H. Ok, Kim S. J, Choi J. W, Byun Y. T, Jhon Y. M Jhon, Lee S, Woo D. H and Kim S. H. Kim, “Realization of all-optical full-adder using cross-gain modulation”, Proceedings of the Conference on Semiconductor Lasers and Applications. SPIE. vol. 5628, pp: 333-340, 2005.
VI. Li P, Huang D, Zhang X and Zhu G, “Ultra-high speed all-optical half-adder based on four wave mixing in semiconductor optical amplifier” Optics Express. vo1.14, pp: 11839-47, 2006.
VII. Minh H. L., Ghassemlooy Z., and Ng W. P, “Characterization and performance analysis of a TOAD switch employing a dual control pulse scheme in high speed OTDM demultiplexer” IEEE Communications Letters. vol.12, pp: 316-318, 2008.
VIII. Mukhopadhyay S and Chakraborty B, “A method of developing optical half- and full-adders using optical phase encoding technique”, Proceedings of the Conference on Communications, Photonics and Exhibition (ACP). TuX6 1-2, 2009.
IX. Mukherjee K, “Method of implementation of frequency encoded all-optical half- adder, half-subtractor, and full-adder based on semiconductor optical amplifiers and add drop multiplexers”, International Journal for Light and Electron Optics. vol. 122, pp: 1188-1194, 2011.

X. Poustie A, Blow K. J, Kelly A. E and Manning R. J, “All-optical full-adder with bit differential delay”, Optics Communications. vol. 168, pp: 89-93, 1999.
XI. Sokoloff J. P, Prucnal P. R, Glesk I and Kane M, “A terahertz optical asymmetric demultiplexer (TOAD)”, IEEE Photonics Technology Letters. vol. 5, pp: 787-790, 1993.
XII. Suzuki M and H. Uenohara, “Invesigation of all-optical error detection circuitusing SOA-MZI based XOR gates at 10 Gbit/s”, Electronics Letters. vol. 45, pp: 224-225, 2009.
XIII. Wang B, Baby V, Tong W, Xu L, Friedman M, Runser R, Glesk I and Prucnal P, “A novel fast optical switch based on two cascaded terahertz optical asymmetric demultiplexers (TOAD)”, Optics Express. vol. 10 15-23, 2002.
XIV. Zoiros K. E, Vardakas J, Houbavlis T and Moyssidis M, “Investigation of SOA-assisted Sagnac recirculating shift register switching characteristics”, International Journal for Light and Electron Optics. vol. 116, pp: 527-541, 2005.
XV. Zoiros K. E, Avramidis P and Koukourlis C. S, “Performance investigation of semiconductor optical amplifier based ultra-fast nonlinear interferometer in nontrivial switching mode”, Optical Engineering. vol. 47, pp: 115006-11, 2008.

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Journal Vol – 17 No -4, April 2022

SOME PROPERTIES OF T₀ FUZZY SOFT TOPOLOGICAL SPACES IN QUASI-COINCIDENCE SENSE

Authors:

Ruhul Amin, Raihanul Islam, Sudipto Kumar Shaha, Saikh Shahjahan Miah

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00002

admin April 24, 2022

Abstract:

In this paper, we have introduced and studied some new notions of T₀ separation axiom in fuzzy soft topological spaces using quasi-coincident relation for fuzzy soft points. We have shown a relationship between ours and other counterparts and observed that all these notions satisfy good extension, hereditary, productive, and projective properties. Moreover, we have also shown that these notions are preserved under one-one, onto, and fuzzy soft continuous mappings. Finally, initial and final soft topologies are studied also.

Keywords:

Fuzzy soft set,Fuzzy Soft Topological Spaces,Quasi-coincidence,Fuzzy Soft T₀Topological Space,Initial and Final Fuzzy Soft Topology,

Refference:

I. A. Aygunglu, H. Aygun, Introduction to Fuzzy Soft Groups, Comput. Math. Appl., 58, (2009), pp 1279-1286.
II. A. S. Atmaca, I. Zorlutuna, On Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), (2013), pp 377-386.
III. Aziz-ul-Hakim, H. Khan, I. Ahmad, A. Khan, Fuzzy Bipolar Soft Semiprime Ideals in Ordered Semigroups, Heliyon, 7, (2021).
IV. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Hindawi Publishing Corporation, Advances in Fuzzy Systems Article ID 586507, (2009).
V. B. P. Varol, H. Aygun, Fuzzy Soft Topology, Hacettepe Journal of Mathematics and Statistics, 41 (3), (2012), pp 407-419.
VI. B. Tanay, M. B. Kandemir, Topological Structure of Fuzzy Soft Sets, Computer and Mathematics with Applications, 61, (2011), pp 2952-2957.
VII. D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parameterization Reduction of Soft Set and Its Application, Computers and Mathematics with Applications, 49, (2005), pp 757-763.
VIII. D. Molodtsov, Soft Set Theory First Results, Comput. Math. Appl., 37 (4-5), (1999), pp 19-31.
IX. H. Aktas, N. Cagman, Soft Sets and Soft Group, Information Science, 177 (2007), pp 2726-2735.
X. K. V. Babitha, J. J. Sunil, Soft Set Relations and Functions, Comput. Math. Appl., 60 (7), (2010), pp 1840-1849.
XI. M. I. Ali, M. Shabir, Comments on De Morgan’s Law in Fuzzy Soft Sets, Int. J. Fuzzy Math. 18, (2010), pp 679-686.
XII. M. R. Amin, M. S. Hossain, S. S. Miah, Fuzzy Pairwise Regular Bitopological Space in Quasi-coincidence Sence, J. Bangladesh Acad. Sci., 42 (2), (2020), pp 139-143.
XIII. M. Shabir, M. Naz, On Soft Topological Spaces, Comput. Math. Appl., 61, (2011), pp 1786-1799.
XIV. M. Terepeta, On Separating Axioms and Similarity of Soft Topological Spaces, Soft Comput., 23, (2019), pp 1049-1057.
XV. O. Gocur, A. Kopuzlu, On Soft Separation Axioms, Ann. Fuzzy Math. Inform., 9 (5), (2015), pp 817-822.
XVI. P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, J. Fuzzy Math., 9 (3), (2001), pp 589-602.
XVII. R. Amin, R. Islam, New Concepts on 𝑅1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math., 22 (2), (October 2021), pp 123-132.
XVIII. S. Al Ghour, A. B. Saadon, On Some Generated Soft Topological Spaces and Soft Homogeneity, Heliyon, 5 (2009).
XIX. S. Hussain, B. Ahmad, Soft Separation Axioms in Soft Topological Spaces, Hacettepe Journal of Mathematics and Statistics, 44 (3), (2015), pp 559-568.
XX. S. Mishra, R. Srivastava, Hausdorff Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 9 (2), (2015), pp 247-260.
XXI. S. Mishra, R. Srivastava, On 𝑇0 and 𝑇1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 10 (4), (2015), pp 591-605.
XXII. S. Nazmul, S. K. Samanta, Soft Topological Groups, Kochi J. Math., 5, (2010), pp 151-161.
XXIII. S. Roy, T. K. Samanta, A Note on Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), (2012), pp 305-311.
XXIV. S. S. Miah, M. R. Amin, Certain Properties on Fuzzy (𝑅0) Topological Spaces in Quasi-coincidence Sense, Annals of Pure and Applied Mathematics, 14 (1), (2007), pp 125-131.
XXV. S. S. Miah, M. R. Amin, M. Jahan, Mappings on Fuzzy (𝑇0) Topological Spaces in Quasi-coincidence Sense, J. Math. Comput. Sci., 7 (5), (2007), pp 883-894.
XXVI. S. S. Miah, M. R. Amin, M. Shahjala, Separation Axiom (𝑇0) on Fuzzy Bitopological Space in Quasi-coincidence Sense, GANIT J. Bangladesh Math. Soc., 40 (2), (2020), pp 156-162.
XXVII. S. Saleh, A. M. Abd El-Latif, A. Al-Salemi, On Separation Axioms in Fuzzy Soft Topological Spaces, South Asian Journal of Mathematics, 8 (2), (2018), pp 92-109.

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Journal Vol – 17 No -4, April 2022

ROTATED EMPIRICAL ORTHOGONAL FUNCTION ANALYSIS FOR SPATIO-TEMPORAL DATA ANALYSIS

Authors:

Shreyasi Debnath, Mourani Sinha

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00003

admin April 24, 2022

Abstract:

Given any space-time field, Empirical orthogonal function (EOF) analysis finds a set of orthogonal spatial patterns along with a set of associated uncorrelated time series or principal components (PCs). Spatial orthogonality and temporal uncorrelation of EOFs and PCs respectively impose limits on the physical interpretability of EOF patterns. This is because physical processes are not independent, and therefore physical modes are expected in general to be non-orthogonal. Rotated empirical orthogonal functions (REOF) were introduced to generate general localized structures by compromising some of the EOF properties such as orthogonality. EOF and REOF analysis are carried out for the significant wave height (SWH) data for the Bay of Bengal (BOB) region for the period 1958 to 2001. Separate experiments were conducted for all the months together and also for July and December representing the southwest and northeast monsoon periods. The first eigenmodes account for 84%, 68%, and 59% of the total variability for the above three cases respectively. The REOF proved to be more effective than EOF for the above region.

Keywords:

Rotated empirical orthogonal functions,Principal components,Data analysis,Significant wave height,Bay of Bengal,

Refference:

I. Craddock, J. M., 1973: Problems and prospects for eigenvector analysis in meteorology. The statistician, 22, 133-145.
II. Crommelin, D. T., and A. J. Majda, 2004: Strategies for model reduction: Comparing different optimal bases. J. Atmos. Sci., 61, 2206–2217.
III. Farrell, B. F., and P. J. Ioannou, 1996: Generalized stability theory. Part I: Autonomous operators. J. Atmos. Sci., 53, 2025–2040.
IV. Hannachi, A., I. Joliffe, and D. Stephenson, 2007: Empirical orthogonal functions and related techniques in atmospheric science: Areview. Int. J. Climatol., 27, 1119–1152, doi:10.1002/joc.1499.
V. Hotelling, H., 1933: Analysis of a complex of statistical variables into principal components. J. Educ. Psych,, 24, 417-520.
VI. Jolliffe, I. T., 2002: Principal Component Analysis. Springer-Verlag, 2nd Edition, New York.
VII. Kleeman, R., 2008: Stochastic theories for the irregularity of ENSO. Philos. Trans. Roy. Soc., 366A, 2509–2524, doi:10.1098/rsta.2008.0048.
VIII. Kutzbach, J. E., 1967: Empirical eigenvectors of sea-level pressure, surface temperature and precipitation complexes over North America. J. Appl.Meteor., 6, 791-802.
IX. Lo`eve, M., 1978: Probability theory, Vol II, 4’th ed., Springer-Verlag, 413pp.
X. Lorenz, E. N., 1956: Empirical orthogonal functions and statistical weather prediction. Technical report, Statistical Forecast Project Report 1, Dept. of Meteor., MIT, 1956. 49pp.
XI. Monahan, A. H., and A. Dai, 2004: The spatial and temporal structure of ENSO nonlinearity. J. Climate, 17, 3026–3036.
XII. North, G. R., T. L., Bell, R. F. Cahalan, and F. J. Moeng, 1982: Sampling errors in the estimation of empirical orthogonal functions. Mon.Weather Rev., 110, 699-706.
XIII. North, G. R., 1984: Empirical orthogonal functions and normal modes. J. Atmos. Sci., 41, 879–887.
XIV. Penland, C., 1996: A stochastic model of Indo-Pacific sea surface temperature anomalies. Physica D, 98, 534–558.
XV. von Storch, H., and F. W. Zwiers, 1999: Statistical Analysis in Climate research, Cambridge University Press, Cambridge.
XVI. Weare, B. C., and J. S. Nasstrom, 1982: Examples of extended empirical orthogonal function analysis. Mon. Weath. Rev., 110, 481-485.
XVII. Wilks, D. S., 1995: Statistical Methods in the Atmospheric Sciences. Academic Press, San Diego.

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Journal Vol – 17 No -4, April 2022

PARA-COMPACTNESS CONCEPT IN INTUITIONISTIC FUZZY TOPOLOGICAL SPACES

Authors:

Md. Aman Mahbub, Md. Sahadat Hossain, M. Altab Hossain

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00004

admin April 24, 2022

Abstract:

This paper aims to establish the para-compactness concept in intuitionistic fuzzy topological space. Here we give three new notions related to para-compactness and one new notion of IF--compactness in intuitionistic fuzzy topological space. Also, we discuss separation axioms in intuitionistic fuzzy para-compactness and some of its features. Furthermore, using some provisos we will find a relation among second countable, para-compactness, and IF--compactness in intuitionistic fuzzy topological spaces.

Keywords:

Fuzzy set,Intuitionistic fuzzy set,Intuitionistic fuzzy topological space,Intuitionistic fuzzy compactness,Intuitionistic fuzzy para-compactness,

Refference:

I. Ahmed, E., Hossain, M.S. and Ali, D.M. (2014). On Intuitionistic Fuzzy T0 Spaces, Journal of Bangladesh Academy of Sciences, 38(2) 197-207.
II. Ahmed, E., Hossain, M.S. and Ali, D.M. (2015). On Intuitionistic Fuzzy R0 Spaces, Annals of Pure and Applied Mathematics, 10(1), 7-14.
III. Ahmed, E., Hossain, M.S. and Ali, D.M. (2015). On Intuitionistic Fuzzy R1 Spaces, J. Math. Comput. Sci, 5(5), 681-693.
IV. Ahmed, E., Hossain, M.S. and Ali, D.M. (2014). On Intuitionistic Fuzzy T1 Spaces, Journal of Physical Sciences, 19, 59-66.
V. Ahmed, E., Hossain, M.S. and Ali, D.M. (2014). On Intuitionistic Fuzzy T2 Spaces, IOSR Journal of Mathematics (IOSR-JM), 10(6), 26-30.
VI. Ahmad, M.K., Salahuddin. (2013). Fuzzy Generalized Variational Like Inequality problems in Topological Vector Spaces, Journal of Fuzzy Set Valued Analysis Volume 2013, doi:10.5899/2013/jfsva-00134.
VII. Ali, A.M., Senthil, S., Chendralekha, T. (2016). Intuitionistic Fuzzy Sequences in Metric Space, International Journal of Mathematics and its Applications Volume 4, Issue 1–B, 155–159.
VIII. Ali, A.M., Kanna, G.R. (2017). Intuitionistic Fuzzy Cone Metric Spaces and Fixed Point Theorems, International Journal of Mathematics and its Applications Volume 5, Issue 1–A, 25–36.
IX. Atanassov, K.T. (1986) Intuitionistic fuzzy sets,Fuzzy Sets and Systems, 20(1), 87-96.
X. Atanassov, K.T., Stojanova D., Cartesian products over intuitionistic fuzzy sets, Methodology of Mathematical Modelling, vol.1, Sofia, 1990, No.1.
XI. Barile, M. To space, Retrived from http://mathworld.wolfarm.com/T0-space.html.
XII. Bayhan, S. and Coker, D. (1996).On fuzzy separation axioms in intuitionistic fuzzy topological space, BUSEFAL, 67, 77-87.
XIII. Bayhan, S., Coker, D. (2005). Pairwise Separation axioms in intuitionistic topological Spaces, Hacettepe Journal of Mathematics and Statistics, 34, 101-114.
XIV. Chang, C.L. (1968). Fuzzy Topological Space, J. of Mathematical Analysis and Application, 24, 182-90.
XV. Coker, D. (1996). A note on intuitionistic sets and intuitionistic points, Tr. J. of Mathematics, 20(3), 343-351.
XVI. Coker, D. (1997). An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 88(1), 81-89.
XVII. Coker, D. and Bayhan, S. (2001). On Separation Axioms in Intuitionistic Topological Space, Int. J. of Math. Sci., 27(10), 621-630.
XVIII. Coker, D. and Bayhan, S. (2003). On T1 and T2 Separation Axioms in Intuitionistic fuzzy Topological Space, Journal of Fuzzy Mathematics, 11(3), 581-592.
XIX. Das, S. (2013). Intuitionistic Fuzzy Topological Spaces (MS Thesis Paper), Dept. of Math, National Inst. of Tech.
XX. Fang, J. & Guo, Y. (2012). Quasi-coincident neighbourhood structure of relative I-fuzzy topology and its applications, Fuzzy Sets and Systems, 190, 105-117.
XXI. Hassan, Q.E. (2007).On some kinds of fuzzy connected spaces, Applications Of Mathematics, 52, N0.4, 353-361.
XXII. Immaculate, H.J., Arockiarani, I. (2015). A new class of connected spaces in intuitionistic topological spaces, Int. J. of Appl. Research, 1(9), 720-726.
XXIII. Islam, R., Hossain, M.S. and Hoque, M.F. (2020). A study on L-fuzzy T1 Spaces, Notes on Intuitionistic Fuzzy Set, 26(3), 33-42.
XXIV. Islam, M.S., Hossain, M.S. and Asaduzzaman, M. (2017). Level Seperation on Intuitionistic Fuzzy T0 spaces, Intern. J. of Fuzzy Mathematical Archive, 13(2),123-133.
XXV. Islam, M.S., Hossain, M.S. and Asaduzzaman, M. (2018). Level separation on Intuitionistic fuzzy T2 spaces; J. Math. Compu. Sci., 8(3), 353-372.
XXVI. Lee, S.J. and Lee, E.P. (2000). The Category of Intuitionistic Fuzzy Topological Space, Bull. Korean Math. Soc., 37(1), 63-76.
XXVII. Lee, S.J. and Lee, E.P. (2004). Intuitionistic Fuzzy Proximity Spaces, IJMMS, 49, 2617-2628.
XXVIII. Mahbub, M.A., Hossain, M.S. and Hossain, M.A. (2018). Some Properties of Compactness in Intuitionistic Fuzzy Topological Spaces, Intern. J. of Fuzzy Mathematical Archive, 16(1), 39-48.
XXIX. Mahbub, M.A., Hossain, M.S. and Hossain, M.A. (2019). Separation Axioms in Intuitionistic Fuzzy Compact Topological Spaces, ISPACS, 2019(1), 14-23.
XXX. Mahbub, M.A., Hossain, M.S. and Hossain, M.A. (2019). ON Q-COMPACTNESS IN INTUITIONISTIC FUZZY TOPOLOGICAL SPACES, J. of Bangladesh Acad. Sci., 43(2), 197-203.
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Journal Vol – 17 No -4, April 2022

NUMERICAL INVESTIGATION OF TURBULENT FLOW THROUGH 90⁰ MIXING ELBOW PIPE WITH DIFFERENT REYNOLDS NUMBER

Authors:

Samir Das, Dipankar De, Moloy K. Banerjee, Tarun Kanti Pal, Anirban Das

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00005

admin April 24, 2022

Abstract:

This work presents a computational investigation of turbulent flow inside a mixing elbow pipe and this study focus on the behaviour of fluid flow in a mixing elbow. Mixing elbow is a region where two types of fluid flow with different parameters and high Reynolds number is intensively mixed together and is among typical geometries exactly where velocity, as well as temperature fluctuation, happen. A CFD model of turbulent flow in the elbow pipes is implemented using the ANSYS tool. RANS turbulent models, the k-ε model are used for the simulation and the variation of axial velocity, wall shear stress, and turbulent intensity along the length of the elbow pipes are studied. The fluid used for this purpose is water. The simulations are carried out with different Reynolds numbers rangings from 2,500 to 10,000.

Keywords:

Turbulent Flow,Mixing Elbow,k-ε Model.,

Refference:

I. Bhatia, S. S., Nishad, R., Patil, S. R., Dewangan, M. K., et. al. [2015]. “Elbow Mixture Analysis”, “International Journal of Advances in Production and Mechanical Engineering (Ijapme)”, PP 2394-6210.
II. Dutta, P., Saha, S. K., Nandi, N., Pal, N., [2016]. “Numerical study on flow separation in 90° pipe bend under high Reynolds number by k-ε modeling” “Engineering Science and Technology, an International Journal”, PP 904–910.
III. Forney, L. J., and H. C., Lee,[1982] “Optimum Dimensions for Pipeline Mixing at a T Junction”, AIChE J., 28(6), 980-987.
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V. M. Nematollahi, B. Khonsha, [2012] “Comparison of T-junction flow pattern of water and sodium for different geometries of power plant piping systems”. Annals of Nuclear Energy 39, pp 83–93.
VI. Mazumder, H. Q., [2012]. “CFD Analysis of the Effect of Elbow Radius on Pressure Drop in Multiphase Flow”, Hindawi Publishing Corporation Modelling and Simulation in Engineering, Article ID 125405, PP 8. doi:10.1155/2012/125405.
VII. Nematollahi M., et al, [1985] “Effect of Bend Curvature Ratio on Flow Pattern at a Mixing Tee after a 90 Degree Bend”, “International Journal of Engineering (IJE)”, pp.478-487
VIII. Patankar S. V.,[1980] “Numerical heat transfer and fluid flow”. USA, McGRAW-HILL Book Company, 197 p.
IX. Seyed Mohammad Hosseini, Kazuhisa Yuki, Hidetoshi Hashizume, [2008] “Classification of turbulent jets in a T-junction area with a 90-deg bend upstream”, “International Journal of Heat and Mass Transfer 5”, pp 2444–2454.

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Journal Vol – 17 No -4, April 2022

NEW CONCEPTS ON R₁ FUZZY SOFT BITOPOLOGICAL SPACE IN QUASI-COINCIDENCE SENSE

Authors:

Saikh Shahjahan Miah, Ruhul Amin, Raihanul Islam, Muhammad Shahjalal, Rezaul Karim

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00006

admin April 24, 2022

Abstract:

In this paper, three notions of property in fuzzy soft bitopological spaces in the sense of quasi-coincidence for fuzzy soft points has been introduced and studied. Hereditary, productive, and projective properties are satisfied by these notions. Moreover, it is observed that all these concepts are preserved under one-one, onto, fuzzy open, and FSP continuous mappings.

Keywords:

Fuzzy soft set,Fuzzy soft bitopological Spaces,Quasi-coincidence,Fuzzy Soft R₁ bitopological Space,Mappings,

Refference:

I. D. Molodtsov, Soft Set Theory First Results, Comput. Math. Appl., 37 (4-5), (1999), pp 19-31.
II. P. K. Maji, R. Biswas, A. R. Roy, Fuzzy Soft Sets, J. Fuzzy Math., 9 (3), (2001), pp 589-602.
III. D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parameterization Reduction of Soft Set and Its Application, Computers and Mathematics with Applications, 49, (2005), pp 757-763.
IV. B. Ahmad, A. Kharal, On Fuzzy Soft Sets, Hindawi Publishing Corporation, Advances in Fuzzy Systems Article ID 586507, (2009).
V. S. Al Ghour, A. B. Saadon, On Some Generated Soft Topological Spaces and Soft Homogeneity, Heliyon, 5 (2009).
VI. H. Aktas, N. Cagman, Soft Sets and Soft Group, Information Science, 177 (2007), pp 2726-2735.
VII. Aziz-ul-Hakim, H. Khan, I. Ahmad, A. Khan, Fuzzy Bipolar Soft Semiprime Ideals in Ordered Semigroups, Heliyon, 7, (2021).
VIII. A. Aygunglu, H. Aygun, Introduction to Fuzzy Soft Groups, Comput. Math. Appl., 58, (2009), pp 1279-1286.
IX. S. Nazmul, S. K. Samanta, Soft Topological Groups, Kochi J. Math., 5, (2010), pp 151-161.
X. B. P. Varol, H. Aygun, Fuzzy Soft Topology, Hacettepe Journal of Mathematics and Statistics, 41 (3), (2012), pp 407-419.
XI. B. Tanay, M. B. Kandemir, Topological Structure of Fuzzy Soft Sets, Computer and Mathematics with Applications, 61, (2011), pp 2952-2957.
XII. S. S. Miah, M. R. Amin, M. Jahan, Mappings on Fuzzy (𝑇0) Topological Spaces in Quasi-coincidence Sense, J. Math. Comput. Sci., 7 (5), (2007), pp 883-894.
XIII. S. S. Miah, M. R. Amin, Certain Properties on Fuzzy (𝑅0) Topological Spaces in Quasi-coincidence Sense, Annals of Pure and Applied Mathematics, 14 (1), (2007), pp 125-131.
XIV. S. S. Miah, M. R. Amin, M. Shahjalal, Separation Axiom (𝑇0) on Fuzzy Bitopological Space in Quasi-coincidence Sense, GANIT J. Bangladesh Math. Soc., 40 (2), (2020), pp 156-162.
XV. M. R. Amin, M. S. Hossain, S. S. Miah, Fuzzy Pairwise Regular Bitopological Space in Quasi-coincidence Sence, J. Bangladesh Acad. Sci., 42 (2), (2020), pp 139-143.
XVI. S. Saleh, A. M. Abd El-Latif, A. Al-Salemi, On Separation Axioms in Fuzzy Soft Topological Spaces, South Asian Journal of Mathematics, 8 (2), (2018), pp 92-109.
XVII. M. Terepeta, On Separating Axioms and Similarity of Soft Topological Spaces, Soft Comput., 23, (2019), pp 1049-1057.
XVIII. M. Shabir, M. Naz, On Soft Topological Spaces, Comput. Math. Appl., 61, (2011), pp 1786-1799.
XIX. S. Hussain, B. Ahmad, Soft Separation Axioms in Soft Topological Spaces, Hacettepe Journal of Mathematics and Statistics, 44 (3), (2015), pp 559-568.
XX. O. Gocur, A. Kopuzlu, On Soft Separation Axioms, Ann. Fuzzy Math. Inform., 9 (5), (2015), pp 817-822.
XXI. S. Mishra, R. Srivastava, On 𝑇0 and 𝑇1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 10 (4), (2015), pp 591-605.
XXII. R. Amin, R. Islam, New Concepts on 𝑅1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math., 22 (2), (October 2021), pp 123-132.
XXIII. S. Mishra, R. Srivastava, Hausdorff Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 9 (2), (2015), pp 247-260.
XXIV. S. Roy, T. K. Samanta, A Note on Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), (2012), pp 305-311.
XXV. A. S. Atmaca, I. Zorlutuna, On Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), (2013), pp 377-386.
XXVI. K. V. Babitha, J. J. Sunil, Soft Set Relations and Functions, Comput. Math. Appl., 60 (7), (2010), pp 1840-1849.

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Journal Vol – 17 No -4, April 2022

VERIFICATION OF DISTRICT-LEVEL WEATHER FORECAST OF KOLKATA AND ITS SUBURBS DURING MONSOON ‘2019 & 2020 FOR COMPARATIVE STUDY OF THE PERFORMANCE OF MODEL BETWEEN PRE COVID NON-LOCKDOWN AND COVID LOCKDOWN PERIOD

Authors:

Sukumar Roy, Nabajit Chakraborty

DOI NO:

https://doi.org/10.26782/jmcms.2022.04.00007

admin April 24, 2022

Abstract:

India Meteorological Department has started issuing district-level weather forecasts for up to 5 days on an operational basis from 1st June 2008. The weather parameters related to agro, namely rainfall, maximum and minimum temperature, wind speed, and direction, relative humidity, and cloudiness were chosen for outputs from the model. The rainfall forecast is generated based on multi-model ensemble techniques ( MME ) and ECMWF forecasts ( presently IMDGFS) are used for forecasting other parameters. These forecast generated for the districts of West Bengal by the model is further moderated by State Agro Met. Centre, Kolkata, and forwarded to six Agro Met. Field Units ( created by six agro-climatic zones in West Bengal ) and seven District Agro Met. Unit ( DAMU ) for preparation of weather-based District as well as Block level Agromet advisory bulletin which benefits the farmers in their crop production. Thus forecast verification of the model as well as moderated value for the monsoon season of 2019 and 2020 has been done to make a comparative study of the model performance concerning Kolkata and its suburbs based on Probability of Detection, False alarm, Heidke Skill score, Missing rate, Critical Success Index, True Skill Score, Hanssen, and Kuipers Index, etc. The monsoon rainfall of 2019 and 2020 was chosen to study the performance of the model concerning the pre-covid non-lockdown and covid lockdown period so that the effect of pollutants on the performance of the model can be analyzed. The verification results show that the model forecast, as well as a moderated forecast of this region, has to be more refined by taking inputs of other parameters and index that has been computed by different recent research works on this region because this region is under the influence of tropical climate. Moreover, the comparative study between monsoon 2019 and monsoon 2020 reveals that there have been changes in the performance of the model.

Keywords:

Pre Covid period,Covid period,Probability of Detection,False alarm,Heidke Skill score,Missing rate,Critical Success Index,True Skill Score,Hanssen and Kuipers Index,

Refference:

I. Chattopadhyay , N., Roy Bhowmik , S.K. , Singh ,K.K., Ghosh ,K., and Malathi , K., 2016 , “ Verification of district level weather forecast “ , Mausam , 67, 4 , 829-840.

II. Krishnamurti , T. N ., Kishtawal , C.M., Larow , T., Bachiochi ,D., Zhang, Z., Willford,E.C., Gadgil,S. and Surendran , S.,1999, “Improved weather and seasonal climate forecasts from multimodel super ensemble “ , Science , 285 , 1548-1550.

III. Rajeevan , M .,Bhate,J.,Kale,J.D. and Lal,B.,2005, “ development of high resolution gridded rainfall data for Indian Region “,IMD Met. Monograph No. Climatology 22/2007.

IV. Rathore , L.S., Roy Bhowmik , S.K. and Chattopadhyay , N., 2011 , “Integrated Agro Advisory Services of India”, Challenges and opportunities of Agro-meteorology , 195-205 ( Spinger publication )

V. Roy Bhowmik , S.K. and Das, A.K., 2007 , “Rainfall Analysis for Indian monsoon region using the merged rain gauge observations and satellite estimates : Evaluation of monsoon rainfall features “. Journal of Earth System Science , 116 . 3 , 187-198.

VI. Roy Bhowmik , S.K. and Durai, V.R., 2012 , “Development of multi-model satellite ensemble based district level medium range rainfall forecast system for Indian region “, Journal of Earth System Science , 121 . 2 , 273 – 285.

VII. WMO Technical Circular No.- WMO /TO No. 1023 Guidelines on Performance Assessment of Public Weather Services.

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Journal Vol – 17 No -4, April 2022

TURBULENT FLOW CHARACTERISTICS OF DUAL JET INTERACTIONS USING DIFFERENT TURBULENCE MODELS

Authors:

Bouaraour Kamel, Lalmi Djemoui

DOI NO:

https://doi.org/10.26782/jmcms.2022.05.00001

admin May 29, 2022

Abstract:

This paper, reports the numerical results of the turbulent flow characteristics and turbulent quantities when a triangular object is placed at the exit of two nozzles. The fluid flow at the entrance of the nozzles is considered isothermal and incompressible. Three turbulence k-ε models are used to study the jets interaction and its resulting characteristics. The numerical method is first validated with the available experimental results for a configuration where no object is placed between nozzles. Numerical simulations are carried out for fixed turbulence intensity at the nozzles exit (3%), and for Reynolds numbers varied from 2.10³ to 10⁴. Results reveal that the existence of a solid object between the dual jets affects the location of the merge and combined points. The merge point is pushed downstream of the flow, and the corresponding axial velocity of the combined point is reduced for all Reynolds numbers. The turbulent kinetic energy field is also affected, either in the near field or in the far field for all Reynolds numbers. We have concluded also that the Realizable k-ε model overestimates velocity and turbulent kinetic energy fields compared to the other models.

Keywords:

flow interaction,merge point,combined point,turbulence model,

Refference:

I. Abbasalizadeh M., Jafarmadar S. and Shirvani H., “The effects of pressure difference in nozzle’s two phase flow on the quality of exhaust mixture”, International Journal of Engineering Transactions B: Applications, vol. 26, no. 5, pp: 553-562, 2013.
II. Anderson E. A. and Spall R. E., “Experimental and numerical investigation of two-dimensional parallel jets”, Transactions of ASME, Journal of Fluids Engineering, vol. 123, no. 2, pp: 401-406, 2001.
III. Azim M. A., “Characteristics of twin axisymmetric free jets”, Proceedings of the international Conference on Mechanical Engineering, Bangladesh, 2009.
IV. Boussoufi M., Sabeur-Bendehina A., El Ganaoui M., Morsli S. and Ouadha A., Numerical simulation of the flow field analysis in the mixing twin jets, Energy Procedia, vol. 139, pp: 161-166, 2017.
V. Elbanna H., Sabbagh J. A. and Rashed M. I. I, “Interception of two equal turbulent jets”, AIAA Journal, vol. 23, no. 7, pp: 985-986, 1985.
VI. Elbanna H., Gahin S. and Rashed M. I. I., “Investigation of two plane parallel jets”, AIAA Journal, vol. 21, no. 7, 986-991, 1983.
VII. Erdem D. and Ath V., “Interaction of two parallel rectangular jets”, 23rd International Congress of Aeronautical Sciences, Canada, 2002.
VIII. Gao J., Xu X. and Li X., “Numerical simulation of supersonic twin-jet noise with high-order finite difference scheme”, AIAA Journal, vol. 56, no. 1, pp: 290-300, 2018.
IX. Hnaien N., Marzouk Khairallah S., Ben Aissia H and Jay J, “Numerical study of interaction of two plane parallel jets”, International Journal of Engineering TRANSACTIONS A: Basics, vol. 29, no. 10, pp: 1421-1430, 2016.
X. Karnam A., Baier F., Gutmark E. J., Jeun J., Wu G. J. and Lele S. K., “An investigation into flow field interactions between twin supersonic rectangular jets”, AIAA Scitech forum, January 2021.
XI. Kwon S. J. and Seo I. W., “Reynolds number effects on the behavior of a non-buoyant round jet”, Experiments in Fluids, vol. 38, no. 6, pp: 801-812, 2005.
XII. Lin Y. F. and Sheu M. J., “Interaction of parallel turbulent plane jets”, AIAA Journal, vol. 29, no. 9, pp: 1372-1373, 1991.
XIII. Lin Y. F. and Sheu M. J., “Investigation of two plane parallel unventilated jets”, Experiments in Fluids, vol. 10, no. 1, pp: 17-22, 1990.
XIV. Mi J. and Nathan G. J., “Statistical properties of turbulent free jets issuing from nine differently-shaped nozzles”, Flow, Turbulence and Combustion, vol. 84, pp: 583-606, 2010.
XV. Naseri Oskouie R., Tachie M. F. and Wang B. C., “Effect of nozzle spacing on turbulent interaction of low-aspect-ratio twin rectangular jets”, Flow, Turbulence and Combustion, vol. 103, no. 2, pp: 323, 2019.
XVI. Nasr A. and Lai J. C. S., “Two parallel plane jets: mean flow and effects of acoustic excitation”, Experiments in Fluids, vol. 22, no. 3, pp: 251-260, 1997.
XVII. Pandey K. M. and Kumar V., “CFD analysis of four jet flow at Mach 1.74 with Fluent software”, International Journal of Environmental Science and Development, vol. 1, no. 5, pp: 423-428, 2010.
XVIII. Pandey K. M., Kumar V. and Srivastava P., “CFD analysis of twin jet supersonic flow with Fluent software”, Current Trends in Technology and Sciences, vol. 1, no. 2, pp: 84-91, 2012.
XIX. Patankar S. V., Numerical heat transfer and ﬂuid ﬂow, Mac Graw Hill, New York, 1980.
XX. Shih T. H., Liou W. W., Shabbir A., Yang Z. and Zhu J., A new k-ε eddy viscosity model for high Reynolds number turbulent flows, Computer and Fluids, vol. 24, no. 3, pp: 227-238, 1995.
XXI. Sourav S., Hossain Rifat A. and Taher Ali M. A., “Effects of Reynolds number on twin circular jets at a small space ratio”, International Journal of Research and Scientific Innovation, vol. 7, no. 8, pp: 248-252, 2020.
XXII. Spall R. E., Numerical study of buoyant plane parallel jets, Journal of Heat Transfer, vol. 124, no. 6, pp: 1210-1212, 2002.
XXIII. Tanaka E., “Experiments on the combined flow of dual jet: the interference of two-dimensional parallel jets”, Bulletin JSME, vol. 17, no. 109, pp: 920- 927, 1974.
XXIV. Tanaka E., “The interference of two dimensional parallel jets”, Bulletin JSME, vol. 13, no. 56, pp: 272-280, 1970.
XXV. Tenchine D. and Moro J. P., “Experimental and numerical study of coaxial jets”, Proceedings of the 8th Int topical meeting on nuclear reactor thermal-hydraulics, Japan, vol. 3, pp: 1381-1387, 1997.
XXVI. Wang C. S., Lin Y. F. and Sheu M. J., “Measurements of turbulent inclined plane dual jets”, Experiments in Fluids, vol. 16, no. 1, pp: 27-35, 1993.
XXVII. Zheng X., Jian X., Wei J. and Wenzheng D., “Numerical and experimental investigation of near-field mixing in parallel dual round jets”, International Journal of Aerospace Engineering, vol. 1, pp: 1-12, 2016.

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Journal Vol – 17 No -5, May 2022

INVESTIGATION BEHAVIOR OF POLYMER GEAR MATERIAL

Authors:

D. S. Jenaris, K. Hari Ram, D. S. Manoj Abraham, R. Rethan Raj, G. Satish Pandian, N. Ramanan

DOI NO:

https://doi.org/10.26782/jmcms.2022.05.00002

admin May 29, 2022

Abstract:

This work primarily focuses on the polymer matrix composite comprising Nylon 6 and Basalt fibre pooled together for the purpose of wear reduction in spur gear material. The method employed here using the Nylon 6 and Basalt fibre is employed through the Injection Moulding method, the fibres are combined in the ratio of (80:20) & (70:30). This project aims to focus on the mechanical properties such as tensile, compression, and impact test as per ASTM standards. Later Finite Element models were then developed to simulate the impact, tensile, and wear characteristics behavior of the tested material,

Keywords:

Compressive Strength,Split Tensile Strength,GGBS,Metakaoline,Regression Analysis,

Refference:

I. A. J. Mertens and S. Senthilvelan, “Effect of Mating Metal Gear Surface Texture on the Polymer Gear Surface Temperature,” Mater. Today Proc., vol. 2, no. 4–5, pp. 1763–1769, 2015.

II. K. Mao, W. Li, C. J. Hooke, and D. Walton, “Polymer gear surface thermal wear and its performance prediction,” Tribol. Int., vol. 43, no. 1–2, pp. 433–439, 2009.

III. K. Mao, W. Li, C. J. Hooke, and D. Walton, “Friction and wear behaviour of acetal and nylon gears,” Wear, vol. 267, no. 1–4, pp. 639–645, 2009.

IV. K. Mao, P. Langlois, Z. Hu, K. Alharbi, X. Xu, M. Milson, W. Li, C. J. Hooke, and D. Chetwynd, “The wear and thermal mechanical contact behaviour of machine cut polymer gears,” Wear, vol. 332–333, pp. 822–826, 2015

V. M. C. S. Ribeiro, S. P. B. Sousa, and P. R. O. Nóvoa, “An investigation on fire and flexural mechanical behaviors of nano and micro polyester composites filled with SiO 2 and Al 2 O 3 particles,” Mater. Today Proc., vol. 2, no. 1, pp. 8–19, 2015.

VI. S. Xue and I. Howard, “Dynamic modelling of flexibly supported gears using iterative convergence of tooth mesh stiffness,” Mech. Syst. Signal Process., pp. 1–22, 2016.

VII. S. Senthilvelan and R. Gnanamoorthy, “Effect of rotational speed on the performance of unreinforced and glass fiber reinforced Nylon 6 spur gears,” Mater. Des., vol. 28, no. 3, pp. 765–772, 2007.

VIII. V. Savaria, F. Bridier, and P. Bocher, “Predicting the effects of material properties gradient and residual stresses on the bending fatigue strength of induction hardened aeronautical gears,” Int. J. Fatigue, pp. 1–39, 2015.

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Journal Vol – 17 No -5, May 2022

NUMERICAL STUDY OF THE INFLUENCE OF TEMPERATURE-DEPENDENT VISCOSITY ON THE UNSTEADY LAMINAR FLOW AND HEAT TRANSFER OF A VISCOUS INCOMPRESSIBLE FLUID DUE TO A ROTATING DISC

Authors:

Akter Hossain, Sarder Firoz Ahmmed

DOI NO:

https://doi.org/10.26782/jmcms.2022.05.00003

admin May 29, 2022

Abstract:

In this article, the effect of temperature-dependent viscosity (TVD) on the unsteady laminar flow and heat transfer (HT) of a viscous incompressible fluid due to a rotating disc (RD) has been investigated numerically by exploiting an in-house numerical code. A set of time-dependent, axisymmetric, and non-linear partial differential equations which govern the fluid flows and heat transfer are reduced to non-linear local non-similarity ordinary differential equations by introducing a newly developed group of transformations for different time regimes. Three different solution methods, such as, (i) perturbation solution method for small t, (ii) asymptotic solution method for large t, and (iii) implicit finite difference method for the entire t regime, have been applied to solve the resulting equations treating t as the time-dependent rotating parameter. The local radial skin friction, tangential skin friction and the heat transfer are computed at the surface of the disc for different numerical parameters, such as, Prandtl number, Pr and the viscosity-variation parameter, e. Besides, the key dimensionless quantities such as velocity and temperature profiles, which are inherently linked with the boundary layer thickness, are presented graphically for different values of e while Pr = 0.72. It is found that the dimensionless radial, tangential and axial velocity profiles decrease as e increases, and consequently, the momentum boundary layer thickness is decreased. On the other hand, the non-dimensional temperature profiles are increased owing to the increasing values of e, and this effect eventually leads to a small increment in the thermal boundary layer thickness.

Keywords:

Unsteady flow,heat transfer (HT),temperature-dependent viscosity (TDV),laminar flow,rotating disc (RD),

Refference:

I. A. Mehmood, M. Usman, Heat transfer enhancement in rotating disk boundary-layer, Thermal Sciences, vol. 22 pp: 2467-248, 2018.

II. A. Nilankush, B. Raju, P. K. Kundu, Influence of hall current on radiative nanofluid flow over a spinning disk: a hybrid approach, Physica E: Low dimensional systems and nanostructures, vol. 111,
pp: 103-112, 2019.

III. E. R. Benton, On the flow due to a rotating disc, Journal of Fluid Mechanics, vol. 24, pp: 781- 800, 1966.

IV. E. M. Sparrow, J. L. Gregg, Heat transfers from a rotating disk to a fluid of any Prandtl number, ASME Journal of Heat Transfer, vol. 81, pp: 249-251, 1959.

V. F. Kreith, Convection heat transfer in rotating systems, Advances in Heat Transfer, vol. 5, pp:129–251, 1969.

VI. G. K. Batchelor, Note on a class of solutions of the Navier-Stokes equations representing steady non-rotationally symmetric flow, The Quarterly Journal of Mechanics and Applied Mathematics, vol. 4, pp. 29-41, 1951.

VII. H. Ockendon, An asymptotic solution for steady flow above an infinite rotating disc with suction, The Quarterly Journal of Mechanics and Applied Mathematics, vol. 25, pp: 291-301, 1972.

VIII. H. B. Keller, Numerical methods in the boundary layer theory, Annual Annual Review of Fluid Mechanics, vol. 10, pp: 417-433, 1978.

IX. I. V. Shevchuk, Convective heat and mass transfer in rotating disk systems, Lecture Notes in Applied and Computational Mechanics, vol. 45, Springer-Verlag Berlin Heidelberg, 2009.

X. J. P. Hartnett, Heat transfer from a non-isothermal rotating disc in still air, ASME Journal of Applied Mechanics, vol. 26, no. 4, pp: 672-673,
1959.

XI. J. T. Stuart, On the effect of uniform suction on the steady flow due to a rotating disc, The uarterly Journal of Mechanics and Applied Mathematics, vol. 7, pp: 446-457, 1954.

XII. J. C. Butcher, Implicit Rungee-Kutta process, Journal of Mathematics of Computation, vol. 18, no. 85, pp. 50-64,1964.

XIII. J. M. Owen, R. H. Rogers, Flow and heat transfer in rotating disc systems: Rotor-stator systems, Research Studies, Taunton, U.K. and John Wiley, NY, USA, 1989.

XIV. J. F. Brady, L. Durlofsky, On rotating disk flow, Journal of Fluid Mechanics, vol. 175, pp: 363-394, 1987.

XV. J. X. Ling, A. Dybbs, Forced convection flow over a flat plate submerged in a porous medium with variable viscosity case, Conference of ASME, paper no. 87- WA/TH-23, New York, 1987.

XVI. J. Herrero, J. A. C. Humphrey, F. Giralt, Comparative analysis of coupled flow and heat transfer between co-rotating discs in rotating and fixed cylindrical enclosures, ASME Heat Transfer Division, vol. 300, pp: 111-121, 1994.

XVII. M. G. Rogers, G. N. Lance, The rotationally symmetric flow of a viscous fluid in presence of infinite rotating disc, Journal of Fluid Mechics, vol. 7, pp: 617-631, 1960.

XVIII. M. A. Hossain, S. M. Munir, Mixed convection flow from a vertical flat plate with temperature dependent viscosity, International Journal of Thermal Sciences, vol. 39, no. 2, pp: 173-183, 2000.

XIX. M. A. Hossain, A. Hossain, M. Wilson, Unsteady flow of viscous incompressible fluid with temperature-dependent viscosity due to arotating disc in presence of transverse magnetic field and heat transfer,
International Journal of The rmal Sciences, vol. 40, no. 1, pp: 11-20, 2001.

XX. M. A. Hossain, S. Kabir, D. A. S. Rees, Natural convection of fluid with variable viscosity from a heated vertical wavy surface, Journal of Applied Mathematics and Physics, Vol. 53 pp: 48-52, 2002.

XXI. M. M. Awad, Heat transfer from a rotating disk to fluids for a wide range of Prandtl numbers using the asymptotic model, ASME Journal Heat Transfer, vol. 130, no.014505, pp: 1-4, 2008.

XXII MD. Shamshuddin, S. R. Mishra, O. A. Bég, A. Kadir, Numerical study of heat transfer and viscous flow in a dual rotating extendable disk system with a non‐Fourier heat flux model, Heat Transfer Asian
Research, vol. 48, pp: 1-25, 2018.

XXIII. M. Ibrahim, Numerical analysis of time-dependent flow of viscous fluid due to a stretchable rotating disk with heat and mass transfer, Results in Physics, vol. 18 , no. 103242, pp:1-6, 2020.

XXIV. M. Ramzan, N. S. Khan, P. Kumam, A numerical study of chemical reaction in a nanofluid flow due to rotating disk in the presence of magnetic field, Scientific Reports, vol. 11, no. 19399, pp:1-24, 2021.

XXV. N. G. Kafoussias, D. A. S. Rees, J. E. Daskalakis, Numerical study of the combined free and forced convective laminar boundary layer flow past a vertical isothermal flat plate with temperature dependent viscosity, Acta Mechanica, vol. 127, pp: 39-50, 1998.

XXVI. P. R. Nachtshiem, P. Swigert, Satisfaction of the asymptotic boundary conditions in numerical solution of the system of non-linear equations of boundary layer type, NASA TND-3004, 1965.

XXVII. P. R. N. Childs, Rotating flow, 1st Edition, Butterworth–Heinemann, UK, 2010.

XXVIII. S. Ostrach, P. R. Thorton, Compressible laminar flow and heat transfer about a rotating isothermal disc, NACA Technical Note 4320, 1958.

XXIX S. P. Anjali Devi1, R. Uma Devi, On hydromagnetic flow due to a rotating disk with radiation effect, Nonlinear Analysis: Modelling and Control, vol. 16, pp: 17–29, 2011.

XXX. S. Imayama, P. H. Alfredsson, R. J. Lingwood, Experimental study of rotating-disk boundary-layer flow with surface roughness,
Journal of Fluid Mechanics, vol. 786, no. 5, pp:5-28, 2016.

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4, pp: 233-252, 1921.

XXXII. T. Cebeci, P. Bradshaw, Physical and computational aspects of
convective heat transfer, Springer-Verlag, New-York, 1984.

XXXIII. T. Hayat, M. Ijaz Khan, A. Alsaedi, M. Imran Khan, Joule heating and
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197, 2017.

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XXXV. W. G. Cochran, The flow due to a rotating disc, Proceedings of the
Cambridge Philosophical Society, vol.30, pp.365-37, 1934.

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Journal Vol – 17 No -5, May 2022

HETEROGENEOUS TWO SERVER QUEUE WITH BREAKDOWN AND WITH VARIANT REPAIR POLICY

Authors:

Kalyanaraman. R

DOI NO:

https://doi.org/10.26782/jmcms.2022.05.00004

admin May 29, 2022

Abstract:

In this paper, we consider a system with two heterogeneous servers Markovian queue. In which the system breakdown occurs when the system is in busy mode. Immediately the system undergoes repair. After completion of the repair, the system either undergoes optional repair mode or becomes busy mode based on a Bernoulli schedule. It is assumed that the number of repairs follows the Poisson process and the repair periods follow an exponential distribution. The model has been solved in steady-state using the matrix analytic method. Some performance measures and numerical results are obtained.

Keywords:

Markovian queue,heterogeneous server,breakdown,repair,steady-state solution,matrix-Geometric method,

Refference:

I. Cheng, C.Y., and Liu, H.H., (2010) The-finite – time -period preventive maintenance policies with failiure rate reduction under a warranty consideration, Journal of the Chinese institute of industrial Engineers, v.27, 81-89.
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Journal Vol – 17 No -5, May 2022

CFD ANALYSIS FOR HEAT TRANSFER AND PRESSURE DROP IN TUBE BUNDLE OF CROSS-FLOW HEAT EXCHANGER

Authors:

Shrinjoy Sen, Tapas Kumar Nandi

DOI NO:

https://doi.org/10.26782/jmcms.2022.05.00005

admin May 29, 2022

Abstract:

In the present work, the preliminary finding of possibilities of heat transfer and pressure drop is reported across the shell and tube arrangement cross-flow heat exchanger. The heat exchanger consists of cold-water flows through the bundle of circular tubes and hot air across the shell. Like in the conventional arrangement, the flow in adjacent rows of tubes is normal to the fluid flow in the shell in the cross-flow arrangement. The three-dimensional turbulent flow region is modelled by employing ANSYS FLUENT 21.0. The standard k-ε model is used to model the turbulence flow. A SIMPLE algorithm scheme is applied to link the pressure and velocity fields inside the domain for air fluids. The heat transfer in the water inside the tubes is represented by a convective boundary condition. The tube flow Reynolds number was fixed at 2200 and the shell flow Reynolds number was varied from 6000 to 10000 in the turbulent zone. The purpose of this paper is to determine temperature reduction and pressure drop across the tube bundle. The simulation will predict the temperature of the airstream at the heat exchanger exit and the pressure drop. The results indicated that there is a significant amount of temperature drop in the air that releases the heat due to forced convection and temperature drop continues in the turbulent region of the incoming fluid.

Keywords:

Cross flow heat exchanger,Temperature drop,Pressure drop,Turbulent flow,

Refference:

I. Alok Vyas et al. (2013). An Experimental Analysis Study to Improve Performance of Tubular Heat Exchanger. Journal of Engineering Research and Applications, Vol. 3, Issue 6, pp.1804-1809.

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III. A.S. Krishnan, P. Gowtham. (2017). Computational study of the staggered and double cross flow heat exchanger, Defence Science Journal, Vol. 67, No. 4, pp. 396-400.
IV. A. Taufiq, P.S. Dhakar. (2020). CFD analysis of plate heat exchanger by using Ansys, International Journal of Research and Analytical Reviews (IJRAR), Volume 7, Issue 3.
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VI. W.M. Kays, A.L. London. (1984). Compact Heat Exchanger 3rd edition, McGraw-Hill Book Co.

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Journal Vol – 17 No -5, May 2022

A STUDY OF CONCRETE INCORPORATING STEEL MILL SCALE WASTE

Authors:

M. A. Khan, M. S. Khan, A. Jawad

DOI NO:

https://doi.org/10.26782/jmcms.2022.06.00001

admin June 28, 2022

Abstract:

This paper presents the effective utilization of industrial waste steel mill scale in concrete. Tests were performed on concrete specimens incorporating 10%, 20%, 30%, and 40% steel mill scale by weight of sand and a control specimen. Results were assessed in terms of workability, compressive strength, flexural strength, and durability. The compressive and flexural strength of concrete incorporating a 20% steel mill scale was recorded higher as opposed to control and other percent replacement specimens. It was also observed that the durability and resistance against sulphate attack of concrete enhanced as the replacement proportion of mill scale were increased. Furthermore, the higher specific gravity of mill scale waste makes it a suitable material for heavyweight concrete members and radiation shield structures.

Keywords:

Concrete,Steel Scale Waste,Durability,Compressive Strength,Flexural Strength.,

Refference:

I. A. AlKhatib, M. Maslehuddin and S. U. Al-Dulaijan, “Development of high performance concrete using industrial waste materials and nano-silica”, Journal of Materials Research and Technology, 9(3), 6696–6711, 2020. https://doi.org/10.1016/j.jmrt.2020.04.067
II. A. B. M. A. Kaish, T. C. Odimegwu, I. Zakaria and M. M. Abood, “Effects of different industrial waste materials as partial replacement of fine aggregate on strength and microstructure properties of concrete”, Journal of Building Engineering, 35, 2021. https://doi.org/10.1016/j.jobe.2020.102092
III. A. O. Oyelade, D. O. Odegbaro and C. A. Fapohunda, “Effect of elevated temperature on the compressive strength of concrete produced with pulverized steel mill scale”, Nigerian Journal of Technology, 36(4), 1030, 2018. https://doi.org/10.4314/njt.v36i4.6
IV. D. A. Iluiu-Varvara, C. Aciu, M. Tintelecan and I. M. Sas-Boca, “Assessment of recycling potential of the steel mill scale in the composition of mortars for sustainable manufacturing”, In Procedia Manufacturing, Vol. 46, pp. 131–135, 2020. Elsevier B.V. https://doi.org/10.1016/j.promfg.2020.03.020
V. D. C. K. Jagarapu and A. Eluru, “Strength and durability studies of lightweight fiber reinforced concrete with agriculture waste”, In Materials Today: Proceedings, Vol. 27, pp. 914–919, 2020. Elsevier Ltd. https://doi.org/10.1016/j.matpr.2020.01.257
VI. E. Furlani and S. Maschio, “Steel scale waste as component in mortars
production: An experimental study”, Case Studies in Construction
Materials, 4, 93–101, 2016. https://doi.org/10.1016/j.cscm.2016.02.001
VII. K. Arunkumar, M. Muthukannan, A. S. Kumar and A. C. Ganesh, “Mitigation of waste rubber tire and waste wood ash by the production of rubberized low calcium waste wood ash based geopolymer concrete and influence of waste rubber fibre in setting properties and mechanical behavior”, Environmental Research, 194, 2021. https://doi.org/10.1016/j.envres.2020.110661
VIII. K. L. Jain, G. Sancheti and L. K. Gupta, “Durability performance of waste granite and glass powder added concrete”, Construction and Building Materials, 252, 2020. https://doi.org/10.1016/j.conbuildmat.2020.119075
IX. M. Alwaeli, “Investigation of gamma radiation shielding and compressive strength properties of concrete containing scale and granulated lead-zinc slag wastes”, Journal of Cleaner Production, 166, 157–162, 2017. https://doi.org/10.1016/j.jclepro.2017.07.203
X. M. Alwaeli, “The implementation of scale and steel chips waste as a replacement for raw sand in concrete manufacturing”, Journal of Cleaner Production, 137, 1038–1044, 2016. https://doi.org/10.1016/j.jclepro.2016.07.211
XI. M. Alwaelim and J. Nadziakiewicz, “Recycling of scale and steel chips waste as a partial replacement of sand in concrete”, Construction and Building Materials, 28(1), 157–163, 2012. https://doi.org/10.1016/j.conbuildmat.2011.08.047
XII. M. Asish Rafieizonooz, J. Mirza, M. R. Salim, M. W. Hussin and E. Khankhaje, “Investigation of coal bottom ash and fly ash in concrete as replacement for sand and cement”, Construction and Building Materials, 116, 15–24, 2016. https://doi.org/10.1016/j.conbuildmat.2016.04.080
XIII. M. Ozturk, T. Depci, E. Bahceci, M. Karaaslan, O. Akgol and U. K. Sevim, “Production of new electromagnetic wave shielder mortar using waste mill scales”, Construction and Building Materials, 242, 2020. https://doi.org/10.1016/j.conbuildmat.2020.118028
XIV. M. S. Khan, F. Ali and M. A. Zaib, “A Study of Properties of Wheat Straw Ash as a Partial Cement Replacement in the Production of Green Concrete”, University of Wah Journal of Science and Technology (UWJST), 3, 61-68, 2019. Retrieved from https://uwjst.org.pk/index.php/uwjst/article/view/23
XV. N. H. Roslan, M. Ismail, N. H. A. Khalid and B. Muhammad, “Properties of concrete containing electric arc furnace steel slag and steel sludge”, Journal of Building Engineering, 28, 2020. https://doi.org/10.1016/j.jobe.2019.101060
XVI. N. Ma, J. B. Houser and L. A. Wood, “Production of cleaner mill scale by dynamic separation of the mill scale from the fast-moving flume water at a hot rolling mill”, Journal of Cleaner Production, 176, 889–894, 2018. https://doi.org/10.1016/j.jclepro.2017.12.039
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Journal Vol – 17 No -6, June 2022

THE FLOW OF DUSTY VISCO-ELASTIC FLUID BETWEEN TWO PARALLEL FLAT PLATES.

Authors:

Raju Kundu, Pradip Kumar Biswas, K. C. Nandy, R. K. Das

DOI NO:

https://doi.org/10.26782/jmcms.2022.06.00002

admin June 28, 2022

Abstract:

The flow of dusty visco-elastic fluid between two parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane is considered because of its growing importance in various technical problems in modern applied science. In this paper, we would like to consider the laminar flow of visco-elastic fluid containing uniformly small solid particles between two infinitely extended parallel plates when the lower plate is at rest and the upper one begins oscillating harmonically in its own plane. The analytical expressions for velocity fields of fluid and dust particles are obtained which are in elegant forms. The effects of elastic elements in the fluid, the mass concentration, and the relaxation time of dust particles on the velocity profiles are studied in detail. The skin friction at the lower plate wall and the total volume flow in between the plates are also obtained.

Keywords:

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Journal Vol – 17 No -6, June 2022