# Archive

## A COMPARATIVE EXPLORATION ON DIFFERENT NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

#### Authors:

Mohammad Asif Arefin, Biswajit Gain, Rezaul Karim, Saddam Hossain

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00001

#### Abstract:

In this paper, the initial value problem of Ordinary Differential Equations has been solved by using different Numerical Methods namely Euler’s method, Modified Euler method, and Runge-Kutta method. Here all of the three proposed methods have to be analyzed to determine the accuracy level of each method. By using MATLAB Programming language first we find out the approximate numerical solution of some ordinary differential equations and then to determine the accuracy level of the proposed methods we compare all these solutions with the exact solution. It is observed that numerical solutions are in good agreement with the exact solutions and numerical solutions become more accurate when taken step sizes are very much small. Lastly, the error of each proposed method is determined and represents them graphically which reveals the superiority among all the three methods. We fund that, among the proposed methods Runge-Kutta 4th order method gives the accurate result and minimum amount of error.

#### Keywords:

Initial Value Problems (IVP),Euler’s Method,Modified Euler Method,Fourth-order Runge-Kutta Method,Error Estimation,

#### Refference:

I. Akanbi, M. A. (2010). Propagation of Errors in Euler Method, Scholars Research Library. Archives of Applied Science Research, 2, 457-469.

II. Hahn, G. D. (1991). A modified Euler method for dynamic analyses. International Journal for Numerical Methods in Engineering, 32(5), 943-955.

III. Hamed, A. B., Yuosif, I., Alrhaman, I. A., & Sani, I. (2017). The accuracy of Euler and modified Euler technique for first order ordinary differential equations with initial condition. Am. J. Eng. Res., 6, 334-338.

IV. Hong-Yi, L. (2000). The calculation of global error for initial value problem of ordinary differential equations. International journal of computer mathematics, 74(2), 237-245.

V. Hossain, M. B., Hossain, M. J., Miah, M. M., & Alam, M. S. (2017). A comparative study on fourth order and butcher’s fifth order runge-kutta methods with third order initial value problem (IVP). Applied and Computational Mathematics, 6(6), 243-253.

VI. Hossain, M. J., Alam, M. S., & Hossain, M. B. (2017). A study on the Numerical Solutions of Second Order Initial Value Problems (IVP) for Ordinary Differential Equations with Fourth Order and Butcher’s Fifth Order Runge-Kutta Mthods. American Journal of Computational and Applied Mathematics, 7(5), 129-137.

VII. Islam, M. A. (2015). Accuracy Analysis of Numerical solutions of initial value problems (IVP) for ordinary differential equations (ODE). IOSR Journal of Mathematics, 11(3), 18-23.

VIII. Islam, M. A. (2015). Accurate solutions of initial value problems for ordinary differential equations with the fourth order Runge Kutta method. Journal of Mathematics Research, 7(3), 41.

IX. Islam, M. A. (2015). A Comparative Study on Numerical Solutions of Initial Value Problems (IVP) for Ordinary Differential Equations (ODE) with Euler and Runge Kutta Methods. American Journal of Computational Mathematics, 5(03), 393.

X. Kockler, N. (1994). Numerical Method for Ordinary Systems of Initial Value Problems.

XI. Lambert, J. D. (1973). Computational methods in ordinary differential equations.

XII. Mathews, J.H. (2005) Numerical Methods for Mathematics, Science and Engineering. Prentice-Hall, India. [9]

XIII. Ntouyas, S. K., & Tsamatos, P. C. (1997). Global existence for semilinear evolution integrodifferential equations with delay and nonlocal conditions. Applicable Analysis, 64(1-2), 99-105.

XIV. Ogunrinde, R. B., Fadugba, S. E., & Okunlola, J. T. (2012). On some numerical methods for solving initial value problems in ordinary differential equations. IOSR Journal of Mathematics, 1(3), 25-31.

XV. Samsudin, N., Yusop, N. M. M., Fahmy, S., & binti Mokhtar, A. S. N. (2018). Cube Arithmetic: Improving Euler Method for Ordinary Differential Equation Using Cube Mean. Indonesian Journal of Electrical Engineering and Computer Science, 11(3), 1109-1113.

XVI. Shampine, L. F., & Watts, H. A. (1971). Comparing error estimators for Runge-Kutta methods. Mathematics of computation, 25(115), 445-455.

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## SYNERGISTIC EFFECT OF SUGARCANE BAGASSE ASH AND MARBLE SLUDGE POWDER AS A PARTIAL REPLACEMENT OF CEMENT IN CONCRETE

#### Authors:

Zeeshan Ullah, Khan Shahzada, Syed Azmat Ali Shah, Nauman Wahab, Sajjad Wali Khan, Akhtar Gul, Samiullah Qazi, Malik Hammad Naseer

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00002

#### Abstract:

Marble sludge powder is produced as a by-product during the cutting and polishing of marble. Similarly, sugarcane bagasse ash is produced during the burning operation of sugarcane bagasse. Improper disposal of these waste materials poses a severe threat to the environment. The objective of this research study was to partially substitute cement with a binary mixture of SBA and MSP to reduce the environmental and health issues by adequately utilizing the waste material in the production of low-cost and eco-friendly concrete. For this purpose, a total of 174 concrete cylinders were tested. Apart from this, XRF and EDX tests were performed to determine the chemical composition of waste. Ordinary Portland cement was replaced with a binary mix of SBA and MSP from 0 to 40% by weight to achieve the synergistic effect. Various tests were performed, including compressive and splitting tensile strength and material tests, i.e. specific gravity, absorption capacity, sieve analysis, dry rodded unit weight, and moisture content. The tested specimens were compared with the control samples. The results showed that the difference between compressive and tensile strength up to 15% replacement is within targeted strength and slump. The optimized sample by partial substitution with a negligible effect on properties of concrete was SB10-MP5 and SB5-MP10. The increase in partial replacement above 15% will lead to a decrease in compressive and tensile strength. The cost per cubic meter of concrete was reduced by 8% as per MRS2019.

#### Keywords:

Sugarcane bagasse ash,marble sludge powder,EDX,XRF,

#### Refference:

I. Adeed Khan, Muhammad Tehseen Khan, Muhammad Zeeshan Ahad, Mohammad Adil, Mazhar Ali Shah, Syed Khaliq Shah, : STRENGTH ASSESSMENT OF GREEN CONCRETE FOR STRUCTURAL USE, J. Mech. Cont. & Math. Sci., Vol.-15, No.-9, September (2020) pp 294-305
II. Azmatullah, Adil Afridi, Atif Afridi, Inayatullah Khan, : USE OF SUGARCANE BAGASSE ASH AS A PARTIAL REPLACEMENT OF CEMENT IN CONCRETE, J. Mech. Cont. & Math. Sci., Vol.-14, No.2, March-April (2019) pp 72-86
III. Arshad A., Shahid I., Anwar U.H.C., Baig M.N., Khan S., and Shakir K., “The Wastes Utility in Concrete”, International Journal of Environmental Research, vol. 8(4), pp: 1323-1328, 2014.
IV. Corinaldesi V., Moriconi G., and Naik T.R., “Characterization of marble powder for its use in mortar and concrete”, Construction and Building Materials, vol. 24(1), pp: 113-117, 2010.
V. Choudhary R., Gupta R., and Nagar R., “Impact on fresh, mechanical, and microstructural properties of high strength self-compacting concrete by marble cutting slurry waste, fly ash, and silica fume”, Construction and Building Materials, vol. 239, pp: 1178-88, 2020.
VI. Cinar M., Karpuzcu M., and Canakci H., “The measurement of fresh properties of cement-based grout containing waste marble powder”, Measurement, vol. 150, 106833, 2020.
VII. Ganesan K., Rajagopal K., and Thangavel K., “Evaluation of bagasse ash as supplementary cementitious material”, Cement and Concrete Composites, vol. 29(6), pp: 515-524, 2007.
VIII. Hendriks C.A.W.E., deJager D., Block K., and Riemer P., “Emission reduction of greenhouse gases from the cement industry, IEA Greenhouse gas R&D Programme. Retrieved December 25, 2019, from http://www.ieagreen.org.uk/prghgt42.htm.
IX. Jamil M., Khan M.N., Karim M.R., Kaish A.B.M.A., and Zain M.F., “Physical and chemical contributions of Rice Husk Ash on the properties of mortar”, Construction and Building Materials, vol. 128, pp: 185-198, 2016.
X. Jagadesh P., Ramachandramurthy A., and Murugesan R., “Evaluation of mechanical properties of Sugar Cane Bagasse Ash concrete”, Construction and Building Materials, vol. 176, pp: 608-617, 2018.
XI. Koushkbaghi M., Kazemi M.J., Mosavi H., and Mohseni E.,“Acid resistance and durability properties of steel fiber-reinforced concrete incorporating rice husk ash and recycled aggregate“, Construction and Building Materials, vol. 202, pp: 266-275, 2019.
XII. Khan W., Shehzada K., Bibi T., Ul Islam S., and Wali K.S., “Performance evaluation of Khyber Pakhtunkhwa Rice Husk Ash (RHA) in improving mechanical behavior of cement”, Construction and Building Materials, vol. 176, pp: 89-102, 2018.
XIII. Khan M.A., Khan B., Shahzada K., Khan S.W., Wahab N., and Ahmad M.I., “Conversion of Waste Marble Powder into a Binding Material”, Civil Engineering Journal, vol. 6(3), pp: 431-445, 2020.
XIV. Khan R.A., and Ganesh A., “The effect of coal bottom ash (CBA) on
mechanical and durability characteristics of concrete”, Journal of Building
Materials and Structures, vol. 3(1), pp: 31-42, 2016.
XV. Mangi S.A., Wan Ibrahim M.H., Abdullah A.H., Abdul Awal A.S.M., Sohu S., and Ali N., “Utilization of sugarcane bagasse ash in concrete as partial replacement of cement”, IOP Conference Series: Materials Science and Engineering, vol. 271, pp: 1-8, 2017.
XVI. Muthukrishnan S., Gupta S., and Kua H. W., “Application of rice husk biochar and thermally treated low silica rice husk ash to improve physical properties of cement mortar”, Theoretical and Applied Fracture Mechanics, vol. pp: 104, 1023-76, 2019.
XVII. Mangi S.A., Wan Ibrahim M.H., Jamaluddin N., Arshad M.F., and Ramadhansyah P.J., “Effects of Ground Ash on the Properties of Concrete”, Journal of Engineering Science and Technology, vol. 14 (1), pp: 338-350, 2019.
XVIII. Omar O.M., Elhameed G.D., Sherif M.A., and Mohamadien H.A., “Influence of limestone waste as partial replacement material for sand and marble powder in concrete properties”, HBRC Journal, vol. 8(3), pp: 193-203, 2019.

XIX. Qudoos A., Kim H.G., Attaur R., and Ryou J.S., “Effect of mechanical processing on the pozzolanic efficiency and the microstructure development of wheat straw ash blended cement composites”, Construction and Building Materials, vol. 193, pp: 481-490, 2018.
XX. Rajasekar A., Arunachalam K., Kottaisamy M., and Saraswathy V., “Durability characteristics of Ultra High Strength Concrete with treated sugarcane bagasse ash”, Construction and Building Materials, vol. 171, pp: 350-356, 2018.
XXI. Sasanipour H., Aslani F., and Taherinezhad J., “Effect of silica fume on durability of self-compacting concrete made with waste recycled concrete aggregates”, Construction and Building Materials, vol. 227, pp: 1165-98, 2019.
XXII. Salvador R.P., Rambo D.A.S., Bueno R.M., Silva K.T., and Figueiredo A.D., “On the use of blast-furnace slag in sprayed concrete applications”, Construction and Building Materials, vol. 218, pp: 543-555, 2019.
XXIII. Singh M., Srivastava A., and Bhunia D., “Long term strength and durability parameters of hardened concrete on partially replacing cement by dried waste marble powder slurry”, Construction and Building Materials, vol. 198, pp: 553-569, 2019.
XXIV. Tekle B.H., “Bagasse ash as a partial replacement of cement”, 2011.
XXV. Ulubeyli G.C., and Artir R., “Properties of Hardened Concrete Produced by Waste Marble Powder”, Social and Behavioral Sciences, vol. 195, pp: 2181-2190, 2015.
XXVI. Wu Z., Khayat K.H., and Shi C., “Changes in rheology and mechanical properties of ultra-high performance concrete with silica fume content”, Cement and Concrete Research, vol. 123, pp: 1057-86, 2019.
XXVII. Wan Ibrahim M.H., Hamzah A.F., Jamaluddin N., Ramadhansyah P.J., and Fadzil A.M., “Split tensile strength on self-compacting concrete containing coal bottom ash”, Social Behavioral Science, vol. 195, pp: 2280-2289, 2015.
XXVIII. Zareei S.A., Ameri F., Bahrami N., Shoaei P., Moosaei H.R., and Salemi N., “Performance of sustainable high strength concrete with basic oxygen steel-making (BOS) slag and nano-silica“, Journal of Building Engineering, vol. 25, pp: 1007-91, 2019.

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## EVALUATE THE INFLUENCE OF STEEL FIBERS ON THE STRENGTH OF CONCRETE USING PLASTIC WASTE AS FINE AGGREGATES

#### Authors:

Samiullah Qazi, , Attaul Haq, Sajjad Wali Khan, Fasih Ahmad Khan, Rana Faisal Tufail

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00003

#### Abstract:

The plastic existence in abundance and its low biodegradability affect the environment. In recent years, researchers have tested numerous recycling techniques. However, each has its demerits. One such technique is recycling plastic as aggregates in concrete. It improves the concrete thermal insulation but depreciates its compressive and tensile strength, which is its core property in the construction industry. The objective of this research work is to efficiently utilize the plastic aggregate in concrete without deteriorating its strength with the use of steel fibers. In total eight concrete mix configurations were studied in this research. The result discussion includes compressive strength, split tensile test, and toughness index. The steel fiber used in the concrete mix with recycled plastic as fine aggregates improved the concrete strength. Its effects increase with an increase in % vol replacement of plastic aggregates with fine aggregates from 5 to 20.

#### Keywords:

Concrete,compressive strength,tensile strength,recycled plastic granules,steel fibers,

#### Refference:

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XII. Foti D. Use of recycled waste pet bottles fibers for the reinforcement of concrete. Composite Structures 2013;96:396–404.
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XVII. Mustafa MAT, Hanafi I, Mahmoud R, Tayeh BA. Effect of partial replacement of sand by plastic waste on impact resistance of concrete: experiment and simulation. Structures 2019;20:519–26.
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XIX. Parker L. A whopping 91% of plastic isn’t recycled. National Geographic 2017. https://www.nationalgeographic.com/news/2017/07/plastic-produced-recycling-waste-ocean-trash-debris-environment/ (accessed November 28, 2019).
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XXI. Rai B, Rushad ST, Kr B, Duggal SK. Study of Waste Plastic Mix Concrete with Plasticizer. ISRN Civil Engineering 2012;2012:1–5.
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XXIII. Saikia N, De Brito J. Use of plastic waste as aggregate in cement mortar and concrete preparation: A review. Construction and Building Materials 2012;34:385–401.
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XXV. Saqib Muhammad, Qazi Sami Ullah, Hamza Mustafa, Yaseen Mahmood, Usama Ali, Abdul Farhan, : TO EVALUATE THE MECHANICAL PROPERTIES OF SELF-HEALING CONCRETE STRENGTHENED WITH STEEL FIBERS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-1, January (2020) pp 303-311
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XXVIII. Thorneycroft J, Orr J, Savoikar P, Ball RJ. Performance of structural concrete with recycled plastic waste as a partial replacement for sand. Construction and Building Materials 2018;161:63–9.

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## SOME RESULTS RELATED TO CONVEXIFIABLE FUNCTIONS

#### Authors:

Faraz Mehmood, , Asif R. Khan, M. Azeem Ullah Siddique

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00004

#### Abstract:

The present article is devoted to the class of convexiﬁable functions and related results. In this way, we would recapture the result of authors L. Maligranda et. al. and we would obtain new majorization type results for weighted convexiﬁable function. This article also recaptures similar results for convex function as well as for concave function

#### Keywords:

Convex Function,Convexiﬁable Function,Majorization,Karamata’s inequality,

#### Refference:

I. Adil Khan, Majorization theorem for convexiﬁable functions, Math. Commun., 18 (2013), 61–65.
II. Asif R. Khan, General inequalities for generalized convex functions, (Unpublished doctoral dissertation), Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan, 2014.
III. Asif R. Khan and Faraz Mehmood, Some Remarks on Functions with Non-decreasing Increments, Journal of Mathematical Analysis, 11(1)(2020), 1–16.
IV. Asif R. Khan, Faraz Mehmood, Faisal Nawaz and Aamna Nazir, Some Remarks on Results Related to ∇−Convex Function, J. Math. Fund. Sci., to appear.
V. C. Hermite, Sur deux limites d’une inte ́grale de ́ﬁnie, Mathesis, 3 (1883), 82.
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VII. Faraz Mehmood, On Functions with Nondecreasing Increments, (Unpublished doctoral dissertation), Department of Mathematics, University of Karachi, Karachi, Pakistan, 2019.
VIII. Faraz Mehmood, Asif R. Khan, M. Azeem Ullah Siddique, Concave and Concavifiable Functions and some Related Results, J. Mech. Cont. & Math. Sci., 15 (6) (2020), 268–279.
IX. Faraz Mehmood, Ghulam Mujtaba Khan, Kashif Saleem, Faisal Nawaz, Zehra Akhter Naveed and Abdul Rahman, Majorization Theorem for Concaviﬁable Functions, Global Journal of Pure and Applied Mathematics, 16 (4) (2020), 569–575.
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## INVESTIGATION OF CLIMATE CHANGE VARIABILITY UNDER CLIMATE CHANGE CONDITIONS OVER THE SEMI-ARID REGION

#### Authors:

Hareef Ahmed Keerio, Sallahuddin Panhwar, Sabab Ali Shah, Abdul Muntaqim Naji, Asim Ali, Adnan Aftab

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00005

#### Abstract:

The purpose of the study was to investigate the variation in climatic parameters and possible climate effects in the Hyderabad region. The least-square regression method was used to find a linear change in climatic parameters (Temperature and Precipitation). The maximum, minimum, and mean temperatures; annual, and monsoon precipitations were considered under the study. In the last 100 years, the global temperature has been increased by 0.6 or 0.74 0C. In Hyderabad city, we predicted that the minimum temperature (Tmin), maximum temperature (Tmax), and mean temperature (Tmean) are varied in the range of 0.00490C/year to -0.01330C/year. The variability in the precipitation was observed in the last 30 years. Yearly and monsoon precipitation was decreasing with the rate of 1.24mm/year, and 1.34mm/year. The maximum precipitation occurs in July, August, and September; in the rest of the months, no or little precipitation occurred which may lead to a shortage of fresh water.

#### Keywords:

Meteorology,Climate change variance,Least Square Regression analysis,Hyderabad region,Temperature and precipitation variance ,

#### Refference:

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II. Ali Muhammad, Syed Asif Ali, Imtiaz Hussain, Faisal Nawaz, : RETURN LEVEL ESTIMATES OF MAXIMUM TEMPERATURE FOR DIFFERENT RETURN PERIOD, J. Mech. Cont.& Math. Sci., Vol.-15, No.-8, August (2020) pp 73-86
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XIX. Hussain, M., et al., A comprehensive review of climate change impacts, adaptation, and mitigation on environmental and natural calamities in Pakistan. Environmental monitoring and assessment, 2020. 192(1): p. 48.
XX. Israr, M., et al., Farming community perceptions about climate change in Khyber Pakhtunkhwa Pakistan. World Journal of Agricultural Research, 2016. 4(3): p. 70-76.
XXI. Khan, J.A., The climate of Pakistan. 1993: Rehbar Publishers.
XXII. Lysenko, S.A. and V.F. Loginov, Current Changes in Winter Air Temperature in the Middleand High Latitudes of the Northern Hemisphere. Russian Meteorology and Hydrology, 2020. 45(4): p. 219-226.
XXIII. Lawson, E.T., et al., Dealing with climate change in semi-arid Ghana: understanding intersectional perceptions and adaptation strategies of women farmers. GeoJournal, 2019: p. 1-14.
XXIV. Mahmood, R. and S. Jia, Analysis of causes of decreasing inflow to the Lake Chad due to climate variability and human activities. Hydrology and Earth System Sciences Discussions, 2018: p. 1-42.
XXV. Mustafa, Z. Climate change and its impact with special focus in Pakistan. in Pakistan Engineering Congress, Symposium. 2011. Lahore.
XXVI. Miller, S.J., The method of least squares. Mathematics Department Brown University, 2006. 114.
XXVII. Rasul, G. and B. Ahmad, Climate change in Pakistan. Pakistan Meteorological Department, 2012.
XXVIII. Sadiq, N. and M.S. Qureshi, Climatic variability and linear trend models for the five major cities of Pakistan. Journal of Geography and Geology, 2010. 2(1): p. 83.
XXIX. Tishchenko, V.A., et al., Monthly and Seasonal Prediction of Precipitation and Air Temperature in the Amur River Basin. Russian Meteorology and Hydrology, 2019. 44(3): p. 169-179.

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## NUMERICAL INVESTIGATION OF DEVELOPING LAMINAR FLUID FLOW THROUGH RECTANGULAR ANNULUS DUCT

#### Authors:

Takwah Talib Hasan, Dr. Raed G. Saihood

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00006

#### Abstract:

The laminar fluid flow of water through the annulus duct was investigated numerically by ANSYS fluent version 15.0 with height (2.5, 5, 7.5) cm and constant length (L=60cm). With constant heat flux applied to the outer duct. The heat flux at the range (500,1000,1500,2000) w/m2 and Reynolds number values were ≤ 2300. The problem was 2-D investigated. Results revealed that Nusselt number decrease and the wall temperature increase with the increase of heat flux. Also, the average Nusselt number increase as Re increases. And as the height of the annulus increase, the values of the temperature and the local and average Nusselt number increase.

#### Keywords:

Forced convection,Laminar flow,annulus ducts, developing flow,entrance region,

#### Refference:

I. Ahmed F. Khudhereyer, Ali Jawad Obaid and Mazin Y. Abdul-Kareem ,”An Experimental study of mixed convection heat transfer in an inclined rectangular duct exposed to uniform heat flux from upper surface”, International Journal of Scintific & Engineering Research Vol. 4, Issue 2, ISSN 2229-5518. February2013.
II. Akeel A., Mustafa A. M., “Combined convection heat transfer at the entrance region of horizontal semicircular duct”. International Journal of engineering and applied Sciences.Vol.5, 2394-3661, January 2018.

III. Asish Mitra, : NUMERICAL SIMULATION ON LAMINAR FREE-CONVECTION FLOW AND HEAT TRANSFER OVER A VERTICAL PLATE WITH CONSTANT HEAT FLUX, J. Mech.Cont. & Math. Sci., Vol.-10, No.-2, January (2016) Pages 1487-1499
IV. Cotta, R. M., Ozisik,M. N., “Laminar forced convection to non-newtonian fluids in ducts with prescribed wall heat-flux”, International Communications in Heat and Mass Transfer, 13, No.3, 325, 1986.
V. Daotong Ch., Jiping L., Junjie Y, “Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section” International Journal in Heat and Mass Transfer.43(12):1238-1291.October 2007. DOI:10.1007/s00231-006-0214-7
VI. Emery, A. F., Neighbors, P. K. and Gessner, F. B., “The Numerical Prediction of Developing Turbulent Flow and Heat Transfer in Square Duct”, Trans. ASME, Vol.102, PP. 51-57, 1980.
VII. Etemad S.Gh., Mujumdar A.s. and R. Nassef, “Viscous non Newtonian forced convection heat transfer in semicircular and equilateral triangular ducts an experimental study”, Int. Comm. Heat Mass Transfer, Vol. 24, No.5, PP. 609-620, 1997.
VIII. Javeri, V., “Laminar Heat Transfer in Rectangular Channel for the Temperature Boundary Condition of the Third Kind”, Int. J. Heat Mass Transfer, Vol.21, p.p. 1029-1034, 1977.
IX. Kandasamy, A., Nadiminti, S. R. “Entrance region flow in concentric annuli with rotating inner wall for Herschel-Bulkley fluids.” International Journal of Applied and Computational Mathematics. 1(2), PP. 235-249.2015. DOI: 10.1007/s40819-015-0029-7
X. Maia, M. C., Gasparetto, C. A., “A numerical solution for entrance region of non-newtonian flow in annili.” Brazilian Journal of Chemical Engineering. 20(2), PP. 201-211. 2003.
XI. Rajamohan G., R. N., K. P., “Experimental study on mixed convection heat transfer in a square duct with varying inclination angles”, Pertanika Journal of Scince and Technology, 23(1): 141-151. January 2015.
XII. Soh, W. Y., “Developing fluid flow in curved duct of square cross-section and its fully developed dual solutions”, J. Fl. Mech. 188, PP. 337-361. 1988. DOI=https://doi.org/10.1017/S0022112088000758.

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## SEISMIC RETROFITTING OF REINFORCED CONCRETE SHEAR WALL USING CARBON FIBER REINFORCED POLYMERS (CFRP)

#### Authors:

Shahzad Khan, Samiullah Qazi, Ali Siddique, Muhammad Rizwan, Muhammad Saqib

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00007

#### Abstract:

In this paper, the experimental results of a partially retrofitted non-compliant with code concrete shear wall using uni-directional carbon fibre reinforced polymer (CFRP) are introduced. The common deficiencies in the wall were insufficient reinforcement, un-confinement at boundary zone, the lake of in-plane stiffness, and ductility. The adopted retrofitting technique consists of the CFRP strips bonded to both wall face with mesh anchors installed in the wall panel and foundation to avoid debonding. The wall was tested before and after retrofitting under a constant axial load, and the displacement control lateral cyclic load was applied to the head beam level. The retrofitted wall showed satisfactory results in terms of drift and shear strength. The test results include the failure pattern, load-displacement behaviours, and deflected shape.

#### Keywords:

Reinforced concrete,Deficient wall,partial retrofit,CFRP fabric,cyclic loading ,

#### Refference:

I. ACI Committee 318 (2005) Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (318R-05). Farmington Hills, MI.
II. A.E. Fiorato and W.G. Corley, R. G. O. (no date) ‘Behavior of Earthquake Resistant Structural Walls Before and After Repair,’ ACI Journal Proceedings, 80(5). DOI: 10.14359/10864.
III. Building Code of Pakistan (BCP): Seismic Provisions (2007). Islamabad, Pakistan: Ministry of Housing & Works.
IV. Babak Mansoori, Ashkan Torabi, Arash Totonchi, : NUMERICAL INVESTIGATION OF STRENGTHENING THE REINFORCED CONCRETE BEAMS USING CFRP REBAR, STEEL SHEETS AND GFRP, J. Mech. Cont.& Math. Sci., Vol.-15, No.-3, March (2020) pp 195-204
V. Durga Chaitanya Kumar Jagarapu, Arunakanthi Eluru, : DURABILITY STUDIES ON LIGHTWEIGHT FIBER REINFORCED CONCRETE BY INCORPORATING PALM OIL SHELLS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-1, January (2020) pp 19-30
VI. Effendy, E. et al. (2006) ‘Seismic behaviour of low-rise shear walls with SMA bars,’ Earth and Space 2006 – Proceedings of the 10th Biennial International Conference on Engineering, Construction, and Operations in Challenging Environments, 2006, p. 137. DOI: 10.1061/40830(188)137.
VII. Elnashai and Pinho (1997) ‘Repair and retrofitting of RC walls using selective Techniques,’ 2(4), pp. 525–568.
VIII. Khalid M. Mosalam and Michael Rojansky, S. A. M. (no date) ‘Evaluation of Seismic Performance and Retrofit of Lightweight Reinforced Concrete Shearwalls,’ ACI Structural Journal, 100(6). DOI: 10.14359/12835.
IX. Lombard, J., Lau, D. and Humar, J. (2000) ‘Seismic strengthening and repair of reinforced concrete shear walls,’ Proc., 12th World Conf. on …, pp. 1–8.
X. Pakravan, H. R. and Ozbakkaloglu, T. (2019) ‘Synthetic fibres for cementitious composites: A critical and in-depth review of recent advances’, Construction
XI. Qazi, S., Michel, L. and Ferrier, E. (2013) ‘Experimental investigation of CFRP anchorage systems used for strengthening RC joints,’ Composite Structures, 99, pp. 453–461. DOI: 10.1016/j.compstruct.2012.10.036.
XII. Raza, S. et al. (2019) ‘Strengthening and repair of reinforced concrete columns by jacketing: State-of-the-art review,’ Sustainability (Switzerland), 11(11). DOI: 10.3390/su11113208.
XIII. Sezen H.Whittaker A.S.Elwood K.J.and Mosalam K.M. (2003). Performance of reinforced concrete buildings during August 17, 1999, Kocaeli, Turkey earthquake and seismic design and construction practice in Turkey. Engineering Structures 25, 103–114
XIV. Taghdi et al. (2000) ‘SEISMIC RETROFITTING OF LOW-RISE MASONRY AND CONCRETE WALLS USING STEEL STRIPS,’ Taghdi et al., (September), pp. 1017–1025.
XV. UBC-97 (1997) ‘Uniform building code: Structural design requirement’, in.

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## EIGENVALUE METHOD AND LINEARIZATION FOR THE STEADY STATE STABILITY ANALYSIS OF JAMSHORO THERMAL POWER PLANT (JTPP)

#### Authors:

Zulfiqar Ali Shahani , Muhammad Mujtaba Shaikh, Ashfaque Ahmed Hashmani

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00008

#### Abstract:

Electrical power system without interruption is the need of every consumer. Therefore, supplying electrical power which must be efficient, reliable and secure from any disturbance is the priority of power supply companies. But, due to changes in weather conditions and continuous load variations, small disturbances arise which may lead to severe disturbance. All electrical generating stations are interconnected, so a failure in any one unit can affect other generating units, therefore analysis is compulsory to solve the problem in the least time, and avoid a further big loss. Analysis of steady-state stability or transient stability plays a key role in a power system which helps to understand the behavior of a dynamic system. The stability problem is concerned with the behavior of the generating station when the system puts on either small or large disturbance. In this work, the steady-state stability (SSS) analysis of the Jamshoro thermal power plant (JTPP) is analyzed by using the eigenvalue method and linearization technique at four different reheat gain values. We develop a nonlinear mathematical model of JTPP and discuss its linearized form, and examine the behavior of the system stability using eigenvalues. The eigenvalue method analyzes the behavior of synchronous machine when system load varies continually.   Numerical values of eigenvalues consist of either real part or real as well as imaginary parts. These eigenvalues help to understand the stability of the system, as to whether the system is stable or not.

#### Keywords:

Eigenvalue,Steady-state,Power system,Nonlinear model,Synchronous machine,

#### Refference:

I. Amin, M., & Molinas, M. (2017). Small-signal stability assessment of power electronics based power systems: A discussion of impedance-and eigenvalue-based methods. IEEE Transactions on Industry Applications, 53(5), 5014-5030.
II. Azizipanah-Abarghooee, et al (2018, October). Small Signal Based Frequency Response Analysis for Power Systems. In 2018 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe) (pp. 1-6). IEEE.
III. Balu, Neal, et al. “On-line power system security analysis.” Proceedings of the IEEE 80.2 (1992): 262-282.
IV. Banakar, H., Luo, C., & Ooi, B. T. (2006). Steady-state stability analysis of doubly-fed induction generators under decoupled P–Q control. IEE Proceedings-Electric Power Applications, 153(2), 300-306.
V. Bhan, V., Hashmani, A. A., & Shaikh, M. M. (2019). A new computing perturb-and-observe-type algorithm for MPPT in solar photovoltaic systems and evaluation of its performance against other variants by experimental validation. Scientia Iranica, 26(Special Issue on machine learning, data analytics, and advanced optimization techniques in modern power systems [Transactions on Computer Science & Engineering and Electrical Engineering (D)]), 3656-3671.
VI. Biswas, M. M., et al (2011). Steady State Stability Analysis of Power System under Various Fault Conditions. Global Journal of Research in Engineering, 11(6-F).
VII. Choo, Y. C, et al. (2006). Assessment of small disturbance stability of a power system. In Australasian Universities Power Engineering Conference (AUPEC) (pp. 1-
VIII. Himaja K., et al. (2012). Steady State Stability Analysis of a single machine power system by using MATLAB SOFTWARE. International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181
IX. Khoso, A. H., Shaikh, M. M., & Hashmani, A. A. (2020). A New and Efficient Nonlinear Solver for Load Flow Problems. Engineering, Technology & Applied Science Research, 10(3), 5851-5856.
X. Liverpool, T. B. (2020). Steady-state distributions and nonsteady dynamics in nonequilibrium systems. Physical Review E, 101(4), 042107.
XI. Martins, N. (1986). Efficient eigenvalue and frequency response methods applied to power system small-signal stability studies. IEEE Transactions on Power Systems, 1(1), 217-224.
XII. M. A. Huda, Md. Harun-or-Roshid, A. Islam and Mst. Mumtahinah, : SENSITIVITY AND ACCUARACY OF EIGENVALUES RELATIVE TO THEIR PERTURBATION, J. Mech. Cont. & Math. Sci., Vol.-6, No.-1, July (2011) Pages 780-796
XIII. Muhammad Aamir Aman, Muhammad Zulqarnain Abbasi, Murad Ali, Akhtar Khan, : To Negate the influences of Un-deterministic Dispersed Generation on Interconnection to the Distributed System considering Power Losses of the system, J.Mech.Cont.& Math. Sci., Vol.-13, No.-3, July-August (2018) Pages 117-132
XIV. Pruski, P., and Paszek, S. (2011). Analysis of calculation accuracy of power system electromechanical eigenvalues based on instantaneous power disturbance waveforms.
XV. Shahani, Z. A., Hashmani, A. A., & Shaikh, M. M. (2020). Steady state stability analysis and improvement using eigenvalues and PSS. Engineering, Technology & Applied Science Research, 10(1), 5301-5306.
XVI. Sidhu, T. S., et al. “Protection issues during system restoration.” IEEE Transactions on Power Delivery 20.1 (2005): 47-56.
XVII. Singh, Bindeshwar. “Applications of FACTS controllers in power systems for enhance the power system stability: a state-of-the-art.” International Journal of Reviews in Computing 6 (2011)
XVIII. Slootweg, J. G., et al. “A study of the eigenvalue analysis capabilities of power system dynamics simulation software.” Proc. 14th Power Systems Computation Conference. 2002.
XIX. Song, Y., & Wang, B. (2013). Survey on reliability of power electronic systems. IEEE Transactions on Power Electronics, 28(1), 591-604

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## THERMAL AWARE LINK ENERGY EFFICIENT SCHEME FOR BODY AREA NETWORKS

#### Authors:

M. Javed, Asim Zeb, M.Shahzad, Asif Nawaz, Ahmed Ali Shah, Zeeshan Rasheed, Naveed Jan, Atif Ishtiaq, Sheeraz Ahmed

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00009

#### Abstract:

A daunting task in Wireless Body Area Networks (WBANs) is still to develop Effective routing techniques. Small-sized nodes are installed on or within the human body to monitor human health conditions which then deliver the data to servers for analysis. During sensing and data transfer, biomedical sensors work continuously and the temperature of the nodes may rise beyond the threshold limit. This temperature rise may damage the human body tissues as well as the routing mechanism in terms of path losses. To keep the temperature at its normal working value, a priority-based selection of routes is required to prevent data loss during transmission. This will ensure safe and accurate data delivery at the destination. A protocol called "Thermal Aware Link Energy Efficient Scheme for WBANs” (TALEEBA) for workers is proposed to monitor the health of workers in factories. One of the four sinks will collect the data of the nearest worker in the field. As the body temperature of any worker is detected to rise, an alarm will be generated and the supervisor of the workplace will ask the worker to be replaced by some other worker. The same mechanism will continue till the task ends. Our proposed TALEEBA (Thermal Aware Link Energy Efficient Scheme for WBANs) scheme is aligned with current LAEEBA and THE-FAME WBAN schemes. In simulations, we analyze our protocol in terms of stability period, network lifetime, residual energy, a packet sent, packet dropped, and throughput. Hence, the results show stability and network life 50%, a packet sent 20% and throughput 23% are improved in comparison with LABEEA and THE-FAME protocols.

#### Keywords:

Wireless Body Area Networks,Delay,Thermal aware,

#### Refference:

I. Abidi, Bahae, Abdelillah Jilbab, and El Haziti Mohamed. “Wireless body area networks: a comprehensive survey.” Journal of Medical Engineering & Technology: 1-11. 2020.
II. Ahmad, Ashfaq, Nadeem Javaid, Umar Qasim, Mohammad Ishfaq, Zahoor Ali Khan, and Turki Ali Alghamdi. “RE-ATTEMPT: a new energy-efficient routing protocol for wireless body area sensor networks.” International Journal of Distributed Sensor Networks 10, no. (4)): 464010. 2014.

III. Ahmed, S., Nadeem Javaid, Mariam Akbar, Adeel Iqbal, Zahoor Ali Khan, and U. Qasim. “LAEEBA: Link aware and energy efficient scheme for body area networks.” In 2014 IEEE 28th International Conference on Advanced Information Networking and Applications, pp. 435-440. IEEE, 2014.
IV. Akram, Sana, Nadeem Javaid, Anum Tauqir, Areeba Rao, and Saad Noor Mohammad. “The-fame: Threshold-based energy-efficient fatigue measurement for wireless body area sensor networks using multiple sinks.” In 2013 Eighth International Conference on Broadband and Wireless Computing, Communication and Applications, pp. 214-220. IEEE, 2013.
V. Amin, Bahrul, Najeeb Ullah, Sheeraz Ahmed, Muhammad Taqi, and Abdul Hanan. “Path-Loss and Energy Efficient Model (PLEEM) for wireless body area networks (WBANs).” In 2017 International Symposium on Wireless Systems and Networks (ISWSN), pp. 1-6. IEEE, 2017.
VI. Bilandi, Naveen, Harsh K. Verma, and Renu Dhir. “AHP–neutrosophic decision model for selection of relay node in wireless body area network.” CAAI Transactions on Intelligence Technology 5, no. (3): 222-229. 2020.
VII. Brix, Gunnar, Martin Seebass, Gesine Hellwig, and Jürgen Griebel. “Estimation of heat transfer and temperature rise in partial-body regions during MR procedures: an analytical approach with respect to safety considerations.” Magnetic resonance imaging 20, no. (1): 65-76. 2002.
VIII. Chen, Min, Sergio Gonzalez, Athanasios Vasilakos, Huasong Cao, and Victor CM Leung. “Body area networks: A survey.” Mobile networks and applications 16, no. (20): 171-193. 2011.
IX. de Oliveira Brante, Glauber Gomes, Marcos Tomio Kakitani, and Richard Demo Souza. “On the energy efficiency of some cooperative and non-cooperative transmission schemes in WSNs.” In 2011 45th Annual Conference on Information Sciences and Systems, pp. 1-6. IEEE, 2011.
X. Gupta, Sandeep KS, Suresh Lalwani, Yashwanth Prakash, E. Elsharawy, and Loren Schwiebert. “Towards a propagation model for wireless biomedical applications.” In IEEE International Conference on Communications, 2003. ICC’03., vol. 3, pp. 1993-1997. IEEE, 2003.
XI. Hasan, Khalid, Kamanashis Biswas, Khandakar Ahmed, Nazmus S. Nafi, and Md Saiful Islam. “A comprehensive review of wireless body area network.” Journal of Network and Computer Applications (143): 178-198. 2019.

XII. Ilyas Khan, Majid Ashraf, Asif Nawaz, Rehan Ali Khan, M.Habib Ullah, Wisal Khan, Sheeraz Ahmed, : DUAL SINK BASED ROUTING SCHEME FOR RELIABLE DATA DELIVERY AND LOS COMMUNICATION IN WBANS, J. Mech. Cont.& Math. Sci., Vol.-15, No.-6, June (2020) pp 449-467
XIII. Javaid, Nadeem, Z. Abbas, M. S. Fareed, Zahoor Ali Khan, and N. Alrajeh. “M-ATTEMPT: A new energy-efficient routing protocol for wireless body area sensor networks.” Procedia Computer Science (19): 224-231. 2013.
XIV. Katayama, Norihiko, Kenichi Takizawa, Takahiro Aoyagi, Jun-ichi Takada, Huan-Bang Li, and Ryuji Kohno. “Channel model on various frequency bands for wearable body area network.” IEICE transactions on communications 92, no. (2): 418-424. 2009.
XV. Khan, Naveed A., Nadeem Javaid, Zahoor Ali Khan, M. Jaffar, U. Rafiq, and Ayesha Bibi. “Ubiquitous healthcare in wireless body area networks.” In 2012 IEEE 11th International Conference on Trust, Security and Privacy in Computing and Communications, pp. 1960-1967. IEEE, 2012.
XVI. Kim, Beom-Su, Kyong Hoon Kim, and Ki-Il Kim. “A survey on mobility support in wireless body area networks.” Sensors 17, no. (4)): 797. 2017.
XVII. Muhammad Aadil, Sheeraz Ahmed, Muhammad Zubair, M.Saeed Hussain kakar, Muhammad Junaid, Ata-ur-Rehman, : iBTTA: IMPROVED BODY TISSUES TEMPERATURE AWARE ROUTING SCHEME FOR WBANs, J.Mech.Cont.& Math. Sci., Vol.-14, No.-1, January-February (2019) pp 37-52.
XVIII. Nadeem, Qaisar, Nadeem Javaid, Saad Noor Mohammad, M. Y. Khan, Sohab Sarfraz, and M. Gull. “Simple: Stable increased-throughput multi-hop protocol for link efficiency in wireless body area networks.” In 2013 Eighth International Conference on Broadband and Wireless Computing, Communication and Applications, pp. 221-226. IEEE, 2013.
XIX. Shahbazi, Zeinab, and Yung-Cheol Byun. “Towards a secure thermal-energy aware routing protocol in Wireless Body Area Network based on blockchain technology.” Sensors 20, no. (12): 3604. 2020
XX. Taha, Mustafa Sabah, Mohd Shafry Mohd Rahim, Mohammed Mahdi Hashim, and Fadil Abass Johi. “Wireless body area network revisited.” International Journal of Engineering & Technology 7, no. (4) : 3494-3504. 2018.
XXI. Tang, Qinghui, Naveen Tummala, Sandeep KS Gupta, and Loren Schwiebert. “TARA: thermal-aware routing algorithm for implanted sensor networks.” In International conference on distributed computing in sensor systems, pp. 206-217. Springer, Berlin, Heidelberg, 2005.
XXII. Tauqir, Anum, Nadeem Javaid, Sana Akram, Areeba Rao, and Saad Noor Mohammad. “Distance aware relaying energy-efficient: Dare to monitor patients in multi-hop body area sensor networks.” In 2013 Eighth International Conference on Broadband and Wireless Computing, Communication and Applications, pp. 206-213. IEEE, 2013.
XXIII. Ullah, Sana, Henry Higgins, Bart Braem, Benoit Latre, Chris Blondia, Ingrid Moerman, Shahnaz Saleem, Ziaur Rahman, and Kyung Sup Kwak. “A comprehensive survey of wireless body area networks.” Journal of medical systems 36, no. (3): 1065-1094. 2012.
XXIV. Zang, Weilin, Fen Miao, Raffaele Gravina, Fangmin Sun, Giancarlo Fortino, and Ye Li. “CMDP-based intelligent transmission for wireless body area network in remote health monitoring.” Neural computing and applications 32, no. (3): 829-837. 2020.

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## CHARACTERIZATION OF THE NONLINEAR BEHAVIOR OF FLEXIBLE ROAD PAVEMENTS

#### Authors:

Irfan Ullah, Dr. Rawid Khan, Manzoor Elahi, Ajab Khurshid

#### DOI NO:

https://doi.org/10.26782/jmcms.2020.12.00010

#### Abstract:

In this paper, the Asphalt Concrete is analyzed by finite element modeling in Abaqus. The nonlinear viscoelastic behavior of Asphalt Concrete is simulated in Finite Element Analysis (FEA). The X-Ray Computed Tomography scans of the laboratory specimen are converted to a 3D virtual model in image processing software (Simpleware Scan IP). The 3D model is used in FEA by applying boundary conditions and giving mechanical properties, considering the Asphalt Concrete as a viscoelastic material. The mechanical properties of the Asphalt Concrete were determined from the laboratory test performed on the same sample. Three different types of model were analyzed. The representative 3D meshed model and Abaqus meshed model were analyzed for recovery of stress under constant strain and compared. It was concluded that the analysis on a model without considering the actual geometry of the Asphalt Concrete, gives a similar pattern of results but differ by 18% than a laboratory test.  The actual 3D geometry of Asphalt Concrete specimen can be obtained by converting 2D X-ray CT scans. It was also found that the nonlinear viscoelastic analysis on a 3D virtual model of Asphalt Concrete gives 96% similar results to the laboratory tests.

#### Keywords:

Micromechanical Modeling,asphalt concrete,finite element,discrete element,X-ray CT,

#### Refference:

I. Abdul Farhan, Nadeem Anwar Qureshi, Arshad Hussain, M. Bilal Khurshid, Hassan Farooq Afridi, : Field Investigation of Modified Asphalt Mix in Pakistan, J.Mech.Cont.& Math. Sci., Vol.-13, No.-4, September-October (2018) Pages 90-99
II. A. Abbas, E. Masad, T. Papagiannakis, and T. Harman, Micromechanical modeling of the viscoelastic behavior of asphalt mixtures using the discrete-element method, vol. 7, no. 2. 2007.
III. C. W. Huang, E. Masad, A. H. Muliana, and H. Bahia, “Nonlinearly viscoelastic analysis of asphalt mixes subjected to shear loading,” Mech. Time-Dependent Mater., vol. 11, no. 2, pp. 91–110, 2007, doi: 10.1007/s11043-007-9034-5.
IV. F. T. S. Aragão, Y.-R. Kim, J. Lee, and D. H. Allen, “Micromechanical Model for Heterogeneous Asphalt Concrete Mixtures Subjected to Fracture Failure,” J. Mater. Civ. Eng., vol. 23, no. 1, pp. 30–38, 2011, doi: 10.1061/(asce)mt.1943-5533.0000004.
V. H. M. Zelelew and A. T. Papagiannakis, “Micromechanical Modeling of Asphalt Concrete Uniaxial Creep Using the Discrete Element Method,” Road Mater. Pavement Des., vol. 11, no. 3, pp. 613–632, 2010, doi: 10.1080/14680629.2010.9690296.
VI. M. H. Sadd and D. Ph, “SIMULATION OF ASPHALT MATERIALS USING A FINITE ELEMENT,” 2003.
VII. Z. You and Q. Dai, “Dynamic complex modulus predictions of hot-mix asphalt using a micromechanical-based finite element model,” Can. J. Civ. Eng., vol. 34, no. 12, pp. 1519–1528, 2007, doi: 10.1139/L07-064.
VIII. Y. R. Kim, D. N. Little, and R. L. Lytton, “Effect of moisture damage on material properties and fatigue resistance of asphalt mixtures,” Transp. Res. Rec., no. 1891, pp. 48–54, 2004, doi: 10.3141/1891-07.

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