Flow, Heat and Mass Transfer past a Stretching Sheet with Temperature Dependent Fluid Properties in Porous Medium

Document Type : Full Length Research Article

Author

Kohima Science College, Jotsoma, NAGALAND, INDIA

Abstract

An investigation is carried out to study MHD boundary layer flow, heat and mass transfer of an incompressible viscous fluid past a continuously moving nonlinear stretching porous sheet in porous medium with temperature dependent fluid properties subject to heat source, viscous dissipation, chemical reaction and suction. The fluid viscosity and the thermal conductivity are assumed to vary as an inverse function and linear function of temperature respectively. The governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations by using similarity transformations and solved numerically by the Matlab’s built in solver bvp4c. The numerical results are presented graphically for velocity, temperature and concentration distributions. The skin friction, wall temperature and wall concentration gradients are tabulated for emerging parameters. It is arrived at a good agreement on comparing the present numerical results with previously published results. It is found that skin friction rises but wall temperature and wall concentration gradients fall with growing viscosity, magnetic field, stretching parameter and Darcy parameter respectively. The thermal conductivity parameter diminishes wall temperature gradient while the Schmidt number and chemical reaction parameter enhance wall concentration gradient.

Keywords

Main Subjects

References

[1]   Sakiadis,B.C., 1961. Boundary-layer behavior on continuous solid surfaces: I. The boundary layer equations for two dimensional and axisymmetric flow. AIChE Journal, 7, pp. 26-28.
[2]   Sakiadis,B.C., 1961. Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface. AIChE Journal, 7, pp. 221-225.
[3]   Erickson, L.E., Fan, L.T. and Fox, V.G., 1966. Heat and mass transfer on the moving continuous flat plate with suction or injection. Ind. Eng. Chem. Fundamen, 5(1), pp. 19-25.
[4]   Tsou, F.K., Sparrow, E.M. and Goldstein, R.J., 1967. Flow and heat transfer in the boundary layer on a continuous moving surface. Int. J. Heat Mass Transfer, 10(2), pp.219-235.
[5]   Crane, L.J., 1970. Flow past a stretching plane. J. Appl. Math. Phys. (ZAMP), 21, pp. 645-647.
[6]   Gupta, P.S. and Gupta, A.S., 1977. Heat and mass transfer on a stretching sheet with suction or blowing. The Canadian Journal of Chemical Engineering, 55(6), pp. 744-746.
[7]   Soundalgekar, V.M. and Murty, T.V.R., 1980. Heat transfer in flow past a continuous moving plate with variable temperature. Wärme-und Stoffübertragung, 14, pp. 91-93.
[8]   Grubka, L.J. and Bobba, K.M., 1985. Heat transfer characteristics of a continuous, stretching surface with variable temperature. J. Heat Transfer, 107(1), pp. 248-250.
[9]   Vajravelu, K., 1986. Hydromagnetic flow and heat transfer over a continuous, moving, porous, flat surface. Acta Mechanica, 64, pp. 179-185.
[10] Kumari, M., Takhar, H.S. and Nath, G., 1990. MHD flow and heat transfer over a stretching surface with prescribed wall temperature or heat flux. Wärme-und Stoffübertragung, 25, pp. 331-336.
[11] Gorla, R.S.R. and Sidawi, I., 1994. Free convection on a vertical stretching surface with suction and blowing. Applied Scientific Research, 52, pp. 247-257.
[12] Anjalidevi, S.P. and Kayalvizhi, M., 2013. Nonlinear hydromagnetic flow with radiation and heat source over a stretching surface with prescribed heat and mass flux embedded in a porous medium. Journal of Applied Fluid Mechanics, 6(2), pp. 157-165.
[13] Malvandi, A., Hedayati, F.M. and Nobari, R. H., 2014. An analytical study on boundary layer flow and heat transfer of nano fluid induced by a non-linearly stretching sheet. Journal of Applied Fluid Mechanics, 7(2), pp. 375-384.
[14] Pop,I., Seddighi, S., Bachok, N. and Ismail, F., 2014. Boundary layer flow beneath a uniform free stream permeable continuous moving surface in a nanofluid. Journal of Heat and Mass Transfer Research, 1(1), pp. 55-65.
[15] Herwig, H. and Wickern, G., 1986. The effect of variable properties on laminar boundary layer flow. Wärme-und Stoffübertragung, 20, pp. 47-57.
[16] Lai, F.C. and  Kulacki, F. A., 1990. The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium. International Journal of Heat and Mass Transfer, 33(5), pp. 1028-1031.
[17] Pop, I., Gorla, R.S.R. and Rashidi, M., 1992. The effect of variable viscosity on flow and heat transfer to a continuous moving flat plate. International Journal of Engineering Science, 30(1), pp. 1-6.
[18] Chiam, T.C., 1998. Heat transfer in a fluid with variable thermal conductivity over a linearly stretching sheet. Acta Mechanica, 129, pp. 63-72.
[19] Kumari, M., 2001. Effect of variable viscosity on non-darcy free or mixed convection flow on a horizontal surface in a saturated porous medium. International Communications in Heat and Mass Transfer, 28(5), pp. 723-732.
[20] Mukhopadhyay, S., Layek, G.C. and Samad, Sk. A., 2005. Study of MHD boundary layer flow over a heated stretching sheet with variable viscosity. International Journal of Heat and Mass Transfer, 48(21-22), pp. 4460-4466.
[21] El-Aziz, M.A., 2007. Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating. Meccanica, 42(4), pp. 375-386.
[22] Sharma, P.R. and Singh, G., 2009. Effects of varying viscosity and thermal conductivity on steady MHD free convective flow and heat transfer along an isothermal plate with internal heat generation. International Journal of Numerical Methods for Heat & Fluid Flow, 19(1), pp. 78-92.
[23] Prasad, K.V., Vajravelu, K. and Datti, P.S., 2010. The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet. International Journal of Thermal Sciences, 49(3), pp. 603-610.
[24] Anjali Devi, S.P. and Prakash, M., 2015. Temperature dependent viscosity and thermal conductivity effects on hydromagnetic flow over a slendering stretching sheet. Journal of the Nigerian Mathematical Society, 34(3), pp.318-330.
[25] Kays, W.M., 1966. Convective Heat and Mass Transfer. McGraw-Hill, New York.
[26] Cortell, R., 2005. Flow and heat transfer of a fluid through a porous medium over a stretching surface with internal heat generation/ absorption and suction/blowing. Fluid Dynamics Research, 37, pp. 231-245.
[27] Mukhopadhyay, S. and Layek, G.C., 2012. Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink. Meccanica, 47, pp. 863-876.
[28] Pop, I. and Ingham, D.B., 2002. Transport Phenomena in Porous Media II, Elsevier Ltd.
[29] Ingham, D.B. and Pop, I., 2005. Transport Phenomena in Porous Media III, Elsevier Ltd.
[30] Vafai, K., 2015. Handbook of Porous Media, 3rd Edition, CRC Press.
[31] Nield, D.A. and Bejan, A., 2017. Convection in Porous Media, Fifth Edition, Springer.
[32] Dessie, H. and Kishan, N., 2014. MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink. Ain Shams Engineering Journal, 5(3), pp. 967-977.
[33] Ojeagbase, P. O. and  Ajibade, A., 2020. Effect of viscous dissipation on seady natural convection heat and mass transfer in a vertical channel with variable viscosity and thermal conductivity. Journal of Heat and Mass Transfer Research, 7(2), pp.105-116.
[34] Damseh, R.A., Al-Odat, M. Q., Chamkha, A.J. and Shannak, B.A., 2009. Combined effect of heat generation or absorption and first-order chemical reaction on micropolar fluid flows over a uniformly stretched permeable surface. International Journal of Thermal Sciences, 48, pp. 1658-1663.
[35] Bhattacharyya, K., Mukhopadhyay, S. and Layek, G.C., 2012. Reactive solute transfer in Magnetohydrodynamic boundary layer stagnation-point flow over a stretching sheet with suction/blowing. Chemical Engineering Communications, 199(3), pp. 368-383.
[36] Patil, P.M. and Chamkha, A.J., 2013. Heat and mass transfer from mixed convection flow of polar fluid along a plate in porous media with chemical reaction. International Journal of Numerical Methods for Heat & Fluid Flow, 3(5), pp. 899-926.
[37] Mjankwi, M.A., Masanja, V.G., Mureithi, E.W. and James, M.G., 2019. Unsteady MHD flow of nanofluid with variable properties over a stretching sheet in the presence of thermal radiation and chemical reaction. International Journal of Mathematics and Mathematical Sciences, 2019, | Article ID 7392459 |, https: // doi.org / 10.1155 / 2019 / 7392459.
[38] Slattery, J.C., 1972. Momentum energy and mass transfer in continua, McGraw-Hill, New York.
[39] Schilichting, H., 1972. Boundary Layer Theory, McGraw-Hill, New York.
[40] Shampine, L.F., Kierzenka, J. and Reichelt, M.W., 2000. Solving boundary value problems for ordinary differential equations in Matlab with bvp4c.https://classes.engineering.wustl.edu/che512/bvp_paper.pdf.

Files

Cited by

History

  • Receive Date: 06 November 2021
  • Revise Date: 08 February 2022
  • Accept Date: 13 February 2022

Share

How to cite

Statistics