Fault Detection technique of electronic gadgets using Fuzzy Petri net abduction method


Sudipta Ghosh ,Arpan Dutta ,



Fuzzy technique using Petri net is a formal tool for describing a Discrete event system model of an actual system. The advantage of this technique is that concurrent evolutions with various processes evolving simultaneously and partially independently can be easily represented and analyzed. In local control applications conditions /events are used to describe the control sequences of elementary devices. Petri nets are made up of places, transitions and tokens. A state is represented by distribution of tokens in places. Various approaches can be used to combine Petri nets and Fuzzy sets. In this paper the authors speak about the fault finding technique of electronic networks with different illustrations.


Fuzzy sets,Petri nets,control sequences,technique of electronic networks ,


I. Bugarin, A. J. and Barro, S., “Fuzzy reasoning supported by Petri nets”, IEEE Trans. on Fuzzy Systems, vol. 2, no.2, pp 135-150,1994.

II. Buchanan, B. G., and Shortliffe E. H., Rule Based Expert Systems: The MYCIN Experiment of the Stanford University, Addison-Wesley, Reading, MA, 1984.

III. Cao, T. and Sanderson, A. C., “A fuzzy Petri net approach to reasoning about uncertainty in robotic systems,” in Proc. IEEE Int. Conf. Robotics and Automation, Atlanta, GA, pp. 317-322, May 1993.

IV. Cao, T., “Variable reasoning and analysis about uncertainty with fuzzy Petri nets,” Lecture Notes in Computer Science, vol. 691, Marson, M. A., Ed., Springer-Verlag, New York, pp. 126-145, 1993.

V. Cao, T. and Sanderson, A. C., “Task sequence planing using fuzzy Petri nets,” IEEE Trans. on Systems, Man and Cybernetics, vol. 25, no.5, pp. 755-769, May 1995.

VI.Cardoso, J., Valette, R., and Dubois, D., “Petri nets with uncertain markings”, in Advances in Petri nets, Lecture Notes in Computer Science, Rozenberg, G., Ed., vol.483, Springer-Verlag, New York, pp. 65-78, 1990.

VII. Chen, S. M., Ke, J. S. and Chang, J. F., “Knowledge representation using fuzzy Petri nets,” IEEE Trans. on Knowledge and Data Engineering, vol. 2 , no. 3, pp. 311-319, Sept. 1990.

VIII. Chen, S. M., “A new approach to inexact reasoning for rule-based systems,” Cybernetic Systems, vol. 23, pp. 561-582, 1992.

IX. Daltrini, A., “Modeling and knowledge processing based on the extended fuzzy Petri nets,” M. Sc. degree thesis, UNICAMP-FEE0DCA, May 1993.

X. Doyle, J., “Truth maintenance systems,” Artificial Intelligence, vol. 12, 1979.

XI. Garg, M. L., Ashon, S. I., and Gupta, P. V., “A fuzzy Petri net for knowledge representation and reasoning”, Information Processing Letters, vol. 39, pp.165-171,1991.

XII. Graham, I. and Jones, P. L., Expert Systems: Knowledge, Uncertainty and Decision, Chapman and Hall, London, 1988.

13) Hirota, K. and Pedrycz, W., ” OR-AND neuron in modeling fuzzy set connectives,” IEEE Trans. on Fuzzy systems, vol. 2 , no. 2 , May 1994.

XIV. Hutchinson, S. A. and Kak, A. C., “Planning sensing strategies in a robot workcell with multisensor capabilities,” IEEE Trans. Robotics and Automation, vol. 5, no. 6, pp.765-783, 1989.

XV. Jackson, P., Introduction to Expert Systems, Addison-Wesley, Reading, MA, 1988.

XVI. Konar, A. and Mandal, A. K., “Uncertainty management in expert systems using fuzzy Petri nets ,” IEEE Trans. on Knowledge and Data Engineering, vol. 8, no. 1, pp. 96-105, February 1996.

XVII. Konar, A. and Mandal, A. K., “Stability analysis of a non-monotonic Petrinet for diagnostic systems using fuzzy logic,” Proc. of 33rd Midwest Symp. on Circuits, and Systems, Canada, 1991.

XVIII.Konar, A. and Mandal, A. K., “Non-monotonic reasoning in expert systems using fuzzy Petri nets,” Advances in Modeling & Analysis, B, AMSE Press, vol. 23, no. 1, pp. 51-63, 1992.

XIX. Konar, S., Konar, A. and Mandal, A. K., “Analysis of fuzzy Petri net models for reasoning with inexact data and knowledge-base,” Proc. of Int. Conf. on Control, Automation, Robotics and Computer Vision, Singapore, 1994.

XX. Konar, A., “Uncertainty Management in Expert System using Fuzzy Petri Nets,” Ph. D. dissertation , Jadavpur University, India, 1994.

XXI. Konar, A. and Pal, S., Modeling cognition with fuzzy neural nets, in Fuzzy Theory Systems: Techniques and Applications, Leondes, C. T., Ed., Academic Press, New York, 1999.

XXII. Kosko, B., Neural Networks and Fuzzy Systems, Prentice-Hall, Englewood Cliffs, NJ, 1994.

XXIII. Lipp, H. P. and Gunther, G., “A fuzzy Petri net concept for complex decision making process in production control,” in Proc. First European congress on fuzzy and intelligent technology (EUFIT ’93), Aachen, Germany, vol. I, pp. 290 – 294, 1993.

XXIV. Looney, C. G., “Fuzzy Petri nets for rule-based decision making,” IEEE Trans. on Systems, Man, and Cybernetics, vol. 18, no.1, pp.178-183, 1988.

XXV. McDermott, V. and Doyle, J., “Non-monotonic logic I,” Artificial Intelligence, vol. 13 (1-2), pp. 41-72, 1980.

XXVI. Murata, T., “Petri nets: properties, analysis and applications”, Proceedings of the IEEE, vol. 77, no.4, pp. 541-580,1989.

XXVII. Pal, S. and Konar, A., “Cognitive reasoning using fuzzy neural nets,” IEEE Trans. on Systems , Man and Cybernetics, August, 1996.

XXVIII. Peral, J., “Distributed revision of composite beliefs,” Artificial Intelligence, vol. 33, 1987.

XXIX. Pedrycz, W. and Gomide, F., “A generalized fuzzy Petri net model,” IEEE Trans. on Fuzzy systems, vol . 2, no.4, pp 295-301, Nov 1994.

XXX. Pedrycz, W, Fuzzy Sets Engineering, CRC Press, Boca Raton, FL, 1995.

XXXI. Pedrycz, W., “Fuzzy relational equations with generalized connectives and their applications,” Fuzzy Sets and Systems, vol. 10, pp. 185-201, 1983.

XXXII. Pedrycz, W. and Gomide, F., An Introduction to Fuzzy Sets: Analysis and Design, MIT Press, Cambridge, MA, pp. 85-126, 1998.

View Download

Pressure-Driven Flow Instability with Convective Heat Transfer through a Rotating Curved Channel with Rectangular Cross-section: The Case of Negative Rotation


Md. Zohurul Islam,Md. Sirajul Islam,Muhammad Minarul Islam,



Due to engineering applications and its intricacy, the flow in a rotating curved duct has become one of the most challenging research fields of fluid mechanics. A comprehensive numerical study is presented for the fully developed two-dimensional thermal flow of viscous incompressible fluid through a rotating curved rectangular duct of constant curvature1.0=δ. Numerical calculations are carried out by using a spectral method and covering a wide range of the Taylor number 02000<≤−Trand the Dean number 1000100≤≤Dn for the constant Grashof number100=Gr. A temperature difference is applied, that is the outer wall of the duct is heated while the inner wall is cooled. The rotation of the duct about the center of curvature is imposed, and the effects of rotation (Coriolis force) on the unsteady flow characteristics are investigated. Flow characteristics are investigated for the case of negative duct rotation. We investigate the unsteady flow characteristics for the Taylor number02000<≤−Tr and it is found that the unsteady flow undergoes in the scenario ‘steady-state→ periodic→ multi-periodic → steady-state’, if Tr is increased in the negative direction. Contours of secondary flow patterns and temperature profiles are also obtained at several values of Tr, and it is found that there exist two- and multi-vortex solutions if the duct rotation is involved in the negative direction.


thermal flow,viscous incompressible fluid ,duct rotation,Taylor number,Grashof number,


I. Nandakumar, K. and Masliyah, J. H. (1986). Swirling Flow and Heat Transfer in Coiled and Twisted Pipes, Adv. Transport Process., Vol. 4, pp. 49-112.

II. Ito, H (1987). Flow in curved pipes. JSME International Journal, 30, pp. 543–552.

III. Yanase, S., Kaga, Y. and Daikai, R. (2002). Laminar flow through a curved rectangular duct over a wide range of the aspect ratio, Fluid Dynamics Research, Vol. 31, pp. 151-183.

IV. Selmi, M. and Namdakumar, K. and Finlay W. H., 1994. A bifurcation study of viscous flow through a rotating curved duct, J. Fluid Mech. Vol. 262, pp. 353-375.

V. Wang, L. Q. and Cheng, K.C., 1996. Flow Transitions and combined Free and Forced Convective Heat Transfer in Rotating Curved Channels: the Case of Positive Rotation Physics of Fluids, Vol. 8, pp.1553-1573.

VI. Selmi, M. and Namdakumar, K. (1999). Bifurcation Study of the Flow through Rotating Curved Ducts, Physics of Fluids, Vol. 11, pp. 2030-2043.

VII. Yamamoto, K., Yanase, S. and Alam, M. M. (1999). Flow through a Rotating Curved Duct with Square Cross-section, J. Phys. Soc. Japan, Vol. 68, pp. 1173-1184.

VIII. Mondal, R. N., Alam M. M. and Yanase, S. (2007). Numerical prediction of non- isothermal flows through a rotating curved duct with square cross section, Thommasat Int. J. Sci and Tech., Vol. 12, No. 3, pp. 24-43.

IX. Mondal, R. N., Datta, A. K. and Uddin, M. K. (2012). A Bifurcation Study of Laminar Thermal Flow through a Rotating Curved Duct with Square Cross-section, Int. J. Appl. Mech. and Engg. Vol. 17 (2). (In Press).

X. Mondal, R. N., Islam, M. S., Uddin, M. K. and Hossain, M. A. (2013). “Effects of Aspect Ratio on Unsteady Solutions through a Curved Duct Flow”, Appl. Math. & Mech. (Springer), Vol. 34(9), pp. 1-16

XI. Mondal, R. N., Islam, Md. Zohurul., and Md. saidul Islam, Editors. Transient Heat and Fluid Flow through a Rotating Curved Rectangular Duct: The Case of Positive and Negative Rotation. Proceedings of the 5th BSME International Conference on Thermal Engineering, (2012),December 21-23; IUT, Dhaka.

View Download

State Space Analysis of a Solar Power Array Taking a Higher Degree Of Non-Linearity into Account


Adhir Baran Chattopadhyay,Sunil Thomas,Aliakbar Eski,Ruchira Chatterjee ,



This paper develops a mathematical technique for the solution of a non linear state variable model of a solar array power system powering a non linear load. The significance of the technique lies in the fact that experimental complexities can be avoided to reach a desired conclusion regarding the design of the controller associated with a solar power array system. An iterative method has been used in which the initiating assumption has been made to consider the system to depend entirely upon its initial values at the instant t = 0 and taking the forcing function to be zero at that instant. In the next step we use the solution at t = 0 and plug it into the equation iteratively while having a non zero value of the forcing equation during the second iteration. The non linearity lies in the fact that the forcing function is a function of the state variable itself. We have applied the Maclaurin series to find the laplace transform of certain mathematical functions containing a singularity at the zero time instant. The time response is obtained and then it is plotted by using MATLAB and various graphs have been obtained.


solar array power system ,non linear state variable model, forcing function,laplace transform,time response,


I. Bae, H. S., J.H. Lee, S.H. Park and B.H. Cho, 2008. “Large-Signal Stability Analysis of Solar Array Power System”. IEEE Transactions on Aerospace and Electronic Systems, 44 Issue-2: 538-547. DOI: 10.1109/TAES.2008.4560205.

II. A. B. Chattopadhyay, A Choudhury, A. Nargund, 2011, “State Variable Model of a Solar Power System”, Trends in Applied Sciences Research, 563-579, DOI : 10.3923/tasr.2011.563.579

III. Bondar, D., D. Budimir and B. Shelkovnikov, 2008. “A new approach for non-linear analysis of power amplifiers”. In: 18th International Crimean Conference Microwave & Telecommunication Technology, 2008. Sevastopol, Crimea, 8-12 September 2008. IEEE, pp: 125 – 128.

IV. Bouchafaa, F., D. Beriber and M.S. Boucherit, 2010. “Modeling and control of a gird connected PV generation system”. In: 18th Mediterranean Conference on Control & Automation (MED), 2010. Marrakech. 23-25 June 2010. IEEE, pp: 315 – 320.

V. Chattopadhyay, A.B., S.S. Dubei and A. Bhattacharjee, 2005. “Modelling of DC-DC boost converter analysis of capacitor voltage dynamics”. A.M.S.E Journal, France, 78 no.6: 15-24.

VI. Chattopadhyay, A.B., S.S. Dubei, A. Bhattacharjee and K. Raman, 2009. “Modelling of DC-DC Boost converter state variable modeling and error analysis”. A.M.S.E Journal, France, Modelling Measurement & Control, 82 Issue-4: 1-16.

VII. Cho, B.H., J.R. Lee and F.C.Y. Lee, 1990. “Large-Signal Stability Analysis of Spacecraft Power Processing System”. IEEE Transactions on Power Electronics, 5 Issue-1: 110 – 116. DOI: 10.1109/63.46005.

VIII. Cho, Y.J. and B.H. Cho, 2001. “Analysis and design of the inductor-current-sensing peak-power-tracking solar array regulator”. AIAA Journal of Propulsion and Power, 17: 467—471.

IX. Hua, C. and C. Shen, 1998. “Comparative Study of Peak Power Tracking Techniques for Solar Storage System”. In: Thirteenth Annual Applied Power Electronics Conference and Exposition 1998. Anaheim, CA, USA. 15-19 February 1998. IEEE, pp: 679 – 685.

X. Huynh, P. and B. H. Cho, 1996. “Design and Analysis of a Microprocessor-Controlled Peak-Power-Tracking System”. IEEE Transactions on Aerospace and Electronic Systems, 32 Issue-1: 182-190. DOI: 10.1109/7.481260.

XI. Jensen, Michael, Russell Louie, Mehdi Etezadi-Amoli and M. Sami Fadali, 2010. “Model and Simulation of a 75kW PV Solar Array”. In: IEEE PES Transmission and Distribution Conference and Exposition 2010. New Orleans, LA, USA. 19-22 April 2010. IEEE, pp: 1 – 5.

XII. Mourra, O., A. Fernandez and F. Tonicello, 2010. “Buck Boost Regulator (B2R) for Spacecraft Solar Array Power conversion”. In: Twenty-Fifth Annual IEEE Applied Power Electronics Conference and Exposition (APEC), 2010. Palm Springs, CA, USA. 21-25 February 2010. IEEE, pp: 1313 – 1319.

XIII. Paulkovich, John, 1967. “Solar Array Regulators of Explorer Satellites XII, XIV, XV, XVIII, XXI, XXVI, XXVIII and Ariel I”. NASA Technical Note: 1 – 15.

XVI. Ramaprabha, R., B.L. Mathur and M. Sharanya, 2009. “Solar Array Modeling and Simulation of MPPT using Neural Network”. In: International Conference on Control, Automation, Communication and Energy Conservation, 2009. Perundurai, Tamil Nadu, India. 4-6 June 2009. IEEE, pp: 1 – 5.

XV.Siri, K. and K.A. Conner, 2002. “Parallel-Connected Converters with Maximum Power Tracking.” In: Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition 2002. Dallas, TX, USA. 10-14 March 2002. IEEE, pp: 419 – 425.

XVI. Siri, K., 2000a. “Study of System Instability in Solar-Array-Based Power Systems”. IEEE Transactions on Aerospace and Electronics Systems, 36 Issue-3: 957 – 964. DOI: 10.1109/7.869515.

XVII. Siri, K., 2000b. “Study of System Instability in Current-Mode Converter Power Systems Operating in Solar Array Voltage Regulation Mode”. In: Fifteenth Annual IEEE Applied Power Electronics Conference and Exposition 2000. New Orleans, LA, USA. 06-10 February 2000. IEEE, pp: 228—234.

XVIII. Wang, Xiaolei, Pan Yan and Liang Yang, 2010a. “An Engineering Design Model of Multi-cell Series-parallel Photovoltaic Array and MPPT control”. In: The 2010 International Conference on Modelling, Identification and Control (ICMIC). Okayama City, Japan. 17-19 July 2010. Okayama University, Japan, pp: 140 – 144.

XIX. Wang, Xiaolei, Liang Yang and Pan Yan, 2010b. “An Engineering Design Model of Multi-cell Series-parallel Solar Array”. In: 2nd International Conference on Future Computer and Communication (ICFCC), 2010. Wuhan, China. 21-24 May 2010. IEEE, pp: 498 – 502.

XX. Yuen-Haw Chang, 2011, “Design and Analysis of Multistage Multiphase Switched-Capacitor Boost DC–AC Inverter”, Circuits and Systems I: Regular Papers, IEEE Transactions on Volume: 58 , Issue: 1 , Page(s): 205 – 218

XXI. Gu, B.; Dominic, J.; Lai, J.-S.; Zhao, Z.; Liu, C., 2013, “High Boost Ratio Hybrid Transformer DC–DC Converter for Photovoltaic Module Applications”, Power Electronics, IEEE Transactions on Volume: 28 , Issue: 4 Page(s): 2048 – 2058

XXII. Yan Ping Jiao; Fang Lin Luo, 2009,” An improved sliding mode controller for boostconverter in solar energy system”, Industrial Electronics and Applications, 2009. ICIEA 2009. 4th IEEE Conference on, Page(s): 805 – 810

XXIII. Yuncong Jiang; Abu Qahouq, J.A., 2011, “Study and evaluation of load current based MPPT control for PV solar systems”, Energy Conversion Congress and Exposition (ECCE), 2011 IEEE, Page(s): 205 – 210

XXIV.Carvalho, C.; Paulino, N., 2010, A MOSFET only, “Step-up DC-DC micro powerconverter, for solar energy harvesting applications”, Mixed Design of Integrated Circuits and Systems (MIXDES), 2010 Proceedings of the 17th International Conference , Page(s): 499 – 504

XXV. Jianwu Zeng; Wei Qiao; Liyan Qu, 2012, “A single-switch isolated DC-DC converter for photovoltaic systems”, Energy Conversion Congress and Exposition (ECCE), 2012 IEEE, Page(s): 3446 – 3452

View Download

Some Results on Normal meet Semilattices


Momtaz Begum,A.S.A.Noor,



In this paper we introduce the concept of normal semilattices in presence of 0-distributivity and include a nice characterization of normal semilattices. We also study the p-ideals in pseudo complemented meet semilattices. Then we give the notion of S-semilattices and prove that every S-semilattice is comaximal, although its converse in not true. Finally, we prove that every S-semilattice is normal, but the converse need not be true.


normal semilattices,0-distributivity, ideals,meet semilattices,


I. P. Balasubramani and P. V. Venkatanarasimhan, Characterizations of the 0-Distributive Lattices, Indian J. Pure appl.Math. 32(3) 315-324, (2001).

II. H.S.Chakraborty and M.R.Talukder, Some characterizations of 0-distributive semilattices, Accepted in the Bulletin of Malaysian Math. Sci.Soc.

III. Cornish, W.H. Normal lattices, J. Austral Math. Soc. 14 (1972), 200-215.

IV. R.M. Hafizur Rahizur Rahman, M. Ayub Ali and A.S.A . Noor, On semi prime ideals in lattices, ISSN 0973-8975, J. Mech. Cont. & Math. Sci., Vol.-7, No.-2, January (2013) Pages 1094-1102.

V.Momtaz Begum and A.S.A. Noor, Semi prime ideals in meet semilattices, Annals of Pure & appl.Math.Vol.1, No.2, 2012, 149-157. Nag , C. Begum S.N. and Taluhder, M.R. Some characterizations of subclasses of P-algebras. Manuscript.

VI. A.S.A. Noor and Momtaz Begum, Some Properties of 0-distributive Meet Semilattices, Annals of Pure & appl. Math.Vol.2, No.1, 2012, 60-66.

VII. Y. S. Powar and N. K. Thakare, 0-Distributive semilattices, Canad. Math. Bull. Vol. 21(4) (1978), 469-475.

VIII. Y. Rav, Semi prime ideals in general lattices, Journal of pure and Applied Algebra, 56(1989) 105- 118.

IX. J. C. Varlet, A generalization of the notion of pseudo-complementedness, Bull.Soc.Sci.Liege, 37(1968), 149-158.

View Download



M. A. M. Talukder ,D. M. Ali ,



In this paper , we introduce the concept of partially α– shading ( resp. partially *α– shading ), in ahort, αp– shading ( resp. *αp– shading ) and partially α– compact ( resp. partially *α– compact ), in short, αp– compact ( resp. *αp– compact ) fuzzy sets and study their several features in fuzzy topological spaces.


fuzzy sets,compact fuzzy sets,fuzzy topological spaces,


I. D. M. Ali, On Certain Separation and Connectedness Concepts in Fuzzy Topology, Ph. D. Thesis, Banaras Hindu University; 1990.

II.K. K. Azad , On Fuzzy semi – continuity , Fuzzy almost continuity and Fuzzy weakly continuity , J. Math. Anal. Appl., 82(1) (1981), 14 – 32.

III. C. L. Chang, Fuzzy Topological Spaces, J. Math. Anal. Appl., 24(1968), 182 – 190.

IV. David. H. Foster, Fuzzy Topological Groups, J. Math. Anal. Appl., 67(1979), 549- 564.

V. T. E. Gantner, R. C. Steinlage and R. H. Warren, Compactness in Fuzzy Topological Spaces, J. Math. Anal. Appl., 62(1978), 547 – 562.

VI. M. Hanafy, Fuzzy β – Compactness and Fuzzy β – Closed Spaces, Turk J Math, 28(2004), 281 – 293.

VII. A. K. Katsaras, Ordered fuzzy topological spaces, J. Math. Anal. Appl., 84(1981), 44 – 58.

VIII. Lipschutz, Theory and problems of general topology, Schaum’s outline series, McGraw-Hill book publication company, Singapore; 1965.

IX. S. R. Malghan and S. S. Benchali, On Fuzzy Topological Spaces, Glasnik Mat., 16(36) (1981), 313 – 325.

X. Ming, Pu.Pao ; Ming, Liu Ying : Fuzzy topology I. Neighborhood Structure of a fuzzy point and Moore – Smith Convergence ; J. Math. Anal. Appl.,76(1980), 571- 599.

XI. R. Srivastava, S. N. Lal, and A K. Srivastava, Fuzzy 1T topological Spaces, J. Math. Anal. Appl., 102(1984), 442 – 448.

XII. P. Wuyts and R. Lowen, On separation axioms in fuzzy topological spaces, fuzzy neighbourhood spaces and fuzzy uniform spaces, J. Math. Anal. Appl., 93(1983), 27 – 41.

XIII. L. A. Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338 – 353.


View Download

Relation Between Lattice and Semiring


Kanak Ray Chowdhury,Abeda Sultana ,Nirmal Kanti Mitra ,A F M Khodadad Khan,



In this paper, connection between lattice and semiring are investigated. This is done by introducing some examples of lattice and semirings. Examples and results are illustrated. In some cases we have used MATLAB.


lattice,semiring, MATLAB,


I. Reutenauer C.and Straubing, H. Inversion of matrices over a commutative semiring, J. Algebra, 88(1984) 350-360.

II. Rutherford, D.E. Inverses of Boolean matrices, Proc Glasgow Math Asssoc., 6 (1963) 49-53.

III. Birkhoff, G. Lattice theory, rev. ed., Colloquium Publication No. 25, Amer. Math. Soc., Newyork 1948

IV. Goodearl, K. R. Von Neumann Regular Rings, Pitman, London, 1979.

V. Fang, Li Regularity of semigroup rings, Semigroup Forum, 53 (1996) 72-81.

VI.Petrich, M Introduction to Semiring, Charles E Merrill Publishing Company, Ohio, 1973.

VII. Sen M. K. and Maity, S. K. Reglar additively inverse semirings, Acta Math. Univ. Comenianae, LXXV, 1 (2006) 137-146

VIII. Karvellas, P.H. Inversive semirings, J. Austral. Math Soc., 18 (1974) 277-288.

IX. R.D Luce, A note on Boolean matrix theory, Proc Amer. Math Soc., 3(1952) 382-388.

X. R. M. Hafizur Rahman, Some properties of standard sublattices of a lattice, J. Mech. Cont. and Math. Sci., 6(1) (2011) 769-779

XI. Ghosh, S. The least lattice congruence on semirings, Soochow Journal of Mathematics, 20(3) (1994) 365-367.

XII. Ghosh, S. Another note on the least lattice congruence on semirings, Soochow Journal of Mathematics, 22(3) (1996) 357-362.

XIII. Vasanthi T. and Amala, M. Some special classes of semirings and ordered semirings, Annals of Pure and Applied Mathematics, 4(2) (2013) 145-159.

XIV. Vasanthi T. and Solochona, N. On the additive and multiplicative structure on semirings, Annals of Pure and Applied Mathematics, 3(1) (2013) 78-84.

View Download

Free Convective Mass Transfer Flow Through A Porous Medium In A Rotating System


M. M. Haque,M. Samsuzzoha,M. H. Uddin ,A. A. Masud,



An analytical investigation on a free convective mass transfer steady flow along a semi-infinite vertical plate bounded by a porous medium with large suction is completed in a rotating system. A mathematical model related to the problem is developed from the basis of studying Fluid Dynamics(FD). Non-dimensional system of equations is obtained by the usual similarity transformation with the help of similar variables. The perturbation technique is used to solve the momentum wiith concentration equations. The chief physical interest of the problem as shear stress and Sherwood number are also calculated here. The numerical values of velocities, concentration, shear stress and Sherwood number are plotted in figures. In order to observe the effects of various parameters on the flow variables, the results are discussed in detailed with the help of graphs. Last of all, some important findings of the problem are concluded in this study.


convective mass transfer,steady flow,shear stress ,Sherwood number ,


I.Callahan G.D. and Marner W.J. “Transient free convection with mass transfer on an isothermal vertical flat plate”. Int. J. Heat Mass Trans. Vol. 19, No. 2, pp 165 – 174 (1976).

II.Soundalgekar V.M. and Wavre P.D. “Unsteady free convective flow past an infinite vertical plate with constant suction and mass transfer”. Int. J. Heat Mass Trans. Vol. 20, No. 12, pp 1363 – 1373 (1977).

III.Soundalgekar V.M. and Ganesan P. “Transient free convection flow past a semi-infinite vertical plate with mass transfer”. Reg. J. Energy Heat and Mass Trans. Vol. 2, No. 1, pp 83 (1980).

IV.Raptis A. Tzivanidis G. and Kafousias N. “Free convection and mass transfer flow through a porous medium bounded by an infinite vertical limiting surface with constant suction”. L. Heat Mass Trans. Vol. 8, No. 5, pp 417- 424 (1981). V.Yamamoto K. and Iwamura N. “Flow with convective acceleration through a porous medium”. J. Engng. Math. Vol. 10, No. 1, pp 41 – 54 (1976).

VI.Kim S.J. and Vafai K. “Analysis of natural convection about a vertical plate embedded in a porous medium”. Int. J. Heat Mass Trans. Vol. 32, No. 4, pp 665 – 677 (1989).

VII.Magyari E. Pop I. and Keller B. “Analytic solutions for unsteady free convection in porous media”. J. Eng. Math. Vol. 48, No. 2, pp 93 – 104 (2004).

VIII.H.P.Greenspan: The theory of rotating fluids, Cambridge University Press, Cambridge, England (1968).

IX.Raptis A.A. and Perdikis C.P. “Effects of mass transfer and free convection currents on the flow past an infinite porous plate in a rotating fluid’. Astrophysics and Space Sci. Vol. 84, No. 2, pp 457 – 461 (1982).

View Download