Volume 51 | Number 5 | Year 2017 | Article Id. IJMTT-V51P541 | DOI : https://doi.org/10.14445/22315373/IJMTT-V51P541

In this paper, a theoretical analysis is carried out to study the visco-elastic effects on hydromagnetic heat and mass transfer in a vertical channel. The two vertical plates are in porous medium and non- uniform wall temperatures. A magnetic field of uniform strength is applied in the direction perpendicular to the plates. The visco-elastic fluid flow is characterized by second order fluid. The analytical solution to the coupled non-liear equations governing the motion are obtained by regular perturbation technique. The effects of different flow parameters on skin friction are analyzed and illustrated graphically.

[1] Coleman, B.D.and Noll, W. (1960). An approximation theorem for functional with applications in continuum mechanics, Archs ration, MechAnalysis. 6, 355.

[2] Coleman, B. D. and Markovitz, H. (1964). Incompressible second order fluid. Adv. Appl. Mech. 8, 69.

[3] Misra, J. C., and Adhikary, S. D., 2016, “MHD oscillatory channel flow, heat and mass transfer in a physiological fluid in presence of chemical reaction,” Alexandria Eng. J., 55, pp. 287–297.

[4] Muthucumaraswamy, R., and Manivannan, K., 2007, “Mass transfer effects on vertical oscillating plate with heat flux,” Theoret. Appl. Mech., 34(4), pp. 309–322.

[5] Prasad, V. R., and Reddy, N. B., 2008, “Radiation and mass transfer effects on an unsteady MHD free convection flow past a semi-infinite vertical permeable moving plate with viscous dissipation,” Indian J. of Pure Appl. Phys., 46, pp. 8192.

[6] Salawu, S.O., and Dada, M.S., 2016, “Radiative heat transfer of variable viscosity and thermal conductivity effects on inclined magnetic field with dissipation in a non-Darcy medium,” J. Nigerian Mathe. Society, 35, pp. 93–106.

[7] Ahmed, S., Batin, A., and Chamkha, A. J., 2015, “Numerical/Laplace transform analysis for MHD radiating heat/mass transport in a Darcian porous regime bounded by an oscillating vertical surface,” Alexandria Eng. J., 54, pp. 45–54.

[8] Chand, K., Singh, K. D., and Kumar, S., 2013, “Oscillatory free convective flow of viscous fluid through porous medium in a rotating vertical channel,” Proc. Ind. Natn. Sci. Acad. DOI. 10.1007/s40010-013-0095-3.

[9] Sharma, P. R., Sharma, K., and Mehta, T., 2014, “Radiative and free convective effects on MHD flow through a porous medium with periodic wall temperature and heat generation or absorption, Int. J. of Mathe. archive, 5(9), pp. 119–128.

[10] Cogley, A. C. L., Vincenti, W. G., and Giles E. S., 2007, “Differential approximation for radiative heat transfer in a non-linear equation grey gas near equilibrium,” AIAA Journal, 6, pp. 551–553.

[11] El-Hakien, M. A., 2000, “MHD oscillatory flow on free convection radiation through a porous medium with constant suction velocity,” J. of Magnetism & Magnetic Materials, 220(2), pp. 271–276.

[12] Hamza, M. M., Isah, B. Y., and Usman, H., 2011, “Unsteady heat transfer to MHD oscillatory flow through a porous medium under slip condition,” Int. J. Computer Appl., 33(4), pp. 12–17.

[13] Harisingh, Naik S., Rao, K. R., and Murthy, M. V. R., 2014, “Thermal radiation effect on an unsteady hydro-magnetic free convective oscillatory Couette flow of a viscous fluid embedded in a porous medium,” Int. J. of Emerging Trends & Tech. in Comp. Sci., 3(4), pp. 6–12.

[14] Makinde, O. D., and Mhone, P. Y., 2005, “Heat transfer to MHD oscillatory flow in a channel filled with porous medium,” Rom. J. Phys., 50, pp. 931–938.

[15] Balamurugan, K. S., Ramaprasad, J. L., and Kumar Varma, S. V., 2015, “Unsteady MHD free convective flow past a moving vertical plate with time dependent suction and chemical reaction in a slip flow regime,” Int. Conf. comp. heat mass transfer, proced. eng., 127, pp. 516–523.

[16] Ibrahim, F.S., Elaiw, A.M., and Bakr, A.A., 2008, “Effect of the chemical reaction and radiation absorption on the unsteady MHD free convection flow past a semi–infinite vertical permeable moving plate with heat source and suction,” Comm. Nonlinear Science and Numerical Simul., 13, pp. 1056–1066.

[17] Ibrahim, S. M., Gangadhar, K., and Reddy, N. B., 2015, “Radiation and mass transfer effects on MHD oscillatory flow in a channel filled with porous medium in the presence of chemical reaction,” J. Appl. Fluid Mechanics, 8(3), pp. 529–537.

[18] Kataria, H. R., and Patel, H. R., 2016, “Radiation and chemical reaction effects on MHD Casson fluid flow past an oscillating vertical plate embedded in porous medium,” Alexandria Eng. J., 55, pp. 583–595.

[19] Malapati, V., and Polarapu, P., 2015 “Unsteady MHD free convective heat and mass transfer in a boundary layer flow past a vertical permeable plate with thermal radiation and chemical reaction,” Int. conference on comp. heat and mass transfer, 127, pp. 791–799.

[20] Mansour, M. A., ElAnssary, N. F., and Aly, A. M., 2008 “Effects of chemical reaction and viscous dissipation on MHD natural convection flows saturated in porous media,” Int. J. Appl. Math. Mech., 4, 6076.

[21] Mohammed Ibrahim, S., Gangabhar, K., and Bhaskar Reddy., N., 2015 “Radiation and mass transfer effects on MHD oscillatory flow in a channel filled with porous medium in the presence of chemical reaction,” J. Appl. Fluid Mechanics, 8(3), pp. 529–537.

[22] Sekhar, D. V., and Reddy, G. V., 2012, “Effects of chemical reaction on MHD free convective oscillatory flow past a porous plate with viscous dissipation and heat sink,” Advances in Appl. Science Research, 3 (5), pp. 3206–3215.

[23] Kumari,K. and Goyal,M. “Viscous Dissipation and Mass transfer effects on MHD oscillatory flow in a vertical channel with porous medium” Advances in Dynamical Systems and Applications,12(2);pp205-216.

Hridi Ranjan Deb, "Hydromagnetic Heat and Mass Transfer on Oscillatory Flow of VISCO-Elastic Fluid in a Vertical Channel," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 51, no. 5, pp. 312-316, 2017. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V51P541