Unsteady mixed convection flow over stretching sheet in presence of chemical reaction and heat generation or absorption with non-uniform slot suction or injection

doi:10.1007/s10483-015-1982-9

Abstract

Abstract: The article examines the unsteady mixed convection flow over a vertical stretching sheet in the presence of chemical reaction and heat generation or absorption with non-uniform mass transfer. The unsteadiness is caused by the time dependent free stream velocity varying arbitrarily with time. Non-similar solutions are obtained numerically by solving the coupled nonlinear partial differential equations using the quasilinearization technique in combination with an implicit finite difference scheme. To reveal the tendency of the solutions, typical results for the local skin friction coefficient and the local Nusselt and Sherwood numbers are presented for different values of parameters. The effects of various parameters on the velocity, temperature, and concentration distributions are discussed here. The present numerical results are compared with the previously published work, and the results are found to be in excellent agreement.

Key words: chemical reaction, non-uniform slot suction, unsteady mixed convection, stretching sheet, heat generation, non-similar solution

2010 MSC Number:

R. RAVINDRAN, N. SAMYUKTHA. Unsteady mixed convection flow over stretching sheet in presence of chemical reaction and heat generation or absorption with non-uniform slot suction or injection. Applied Mathematics and Mechanics (English Edition), 2015, 36(10): 1253-1272.

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References

[1] Sakiadis, B. C. Boundary layer behavior on continuous solid surfaces:II, the boundary layer on a continuous flat surface. American Institute of Chemical Engineers Journal, 7, 221-225(1961)
[2] Tsou, F. K., Sparrow, E. M., and Goldstein, R. J. Flow and heat transfer in the boundary layer on a continuous moving surface. International Journal of Heat and Mass Transfer, 10, 219-235(1967)
[3] Abdelhafez, T. A. Skin friction and heat transfer on a continuous flat surface moving in a parallel free stream. International Journal of Heat and Mass Transfer, 28, 1234-1237(1985)
[4] Soundalgekar, V. M. and Murty, T. V. R. Heat transfer in flow past a continuous moving plate with variable temperature. Wärme-und Stoffübertragung, 14, 91-93(1980)
[5] Afzal, N. and Varshney, I. S. The cooling of a low heat resistance stretching sheet moving through a fluid. Wärme-und Stoffübertragung, 14, 289-293(1980)
[6] Chen, C. H. Laminar mixed convection adjacent to a vertical, continuously stretching sheets. Heat and Mass Transfer, 33, 471-476(1998)
[7] Ali, M. E. Heat transfer characteristics of a continuous stretching surface. Wärme-und Stoffübertragung, 29, 227-234(1994)
[8] Jacobi, A. M. A scale analysis approach to the correlation of continuous moving sheet (backward boundary layer) forced convective heat transfer. Journal of Heat Transfer, 115, 1058-1061(1993)
[9] Ali, M. E. On thermal boundary layer on a power-law stretched surface with suction or injection. International Journal of Heat and Fluid Flow, 16, 280-290(1995)
[10] Chen, T. S. and Strobel, F. A. Buoyancy effects in boundary layer adjacent to a continuous moving horizontal flat plate. Journal of Heat Transfer, 102, 170-172(1980)
[11] Moutsoglou, A. and Chen, T. S. Bouyancy effects in boundary layers on inclined continuous, moving sheets. Journal of Heat Transfer, 102, 371-373(1980)
[12] Afzal, N. Momentum transfer on power law stretching plate with free stream pressure gradient. International Journal of Engineering Science, 41, 1197-1207(2003)
[13] Grubka, L. J. and Bobba, K. M. Heat transfer characteristics of a continuous stretching surface with variable temperature. Journal of Heat Transfer, 107, 248-250(1985)
[14] Patil, P. M., Roy, S., and Chamkha, A. J. Mixed convection flow over a vertical power-law stretching sheet. International Journal of Numerical Methods for Heat and Fluid Flow, 20, 445-458(2010)
[15] Ravindran, R. and Ganapathirao, M. Non-uniform slot suction/injection into mixed convection boundary layer flow over vertical cone. Applied Mathematics and Mechanics (English Edition), 34(11), 1327-1338(2013) DOI 10.1007/s10483-013-1748-7
[16] Patil, P. M. Effects of surface mass transfer on steady mixed convection flow from vertical stretching sheet with variable wall temperature and concentration. International Journal of Numerical Methods for Heat and Fluid Flow, 22, 287-305(2012)
[17] Mansur, S., Ishak, A., and Pop, I. Flow and heat transfer of nanofluid past stretching/shrinking sheet with partial slip boundary conditions. Applied Mathematics and Mechanics (English Edition), 35(11), 1401-1410(2014) DOI 10.1007/s10483-014-1878-7
[18] Khader, M. M. and Megahed, A. M. Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity, and thermal radiation. Applied Mathematics and Mechanics (English Edition), 35(11), 1387-1400(2014) DOI 10.1007/s10483-014-1870-7
[19] Takhar, H. S. and Nath, G. Unsteady three dimensional flows due to a stretching surface. Mechanics Research Communication, 23, 325-333(1996)
[20] Devi Surma, C. D., Takhar, H. S., and Nath, G. Unsteady three dimensional boundary layer flow due to a stretching surface. International Journal of Heat and Mass Transfer, 29, 1996-1999(1986)
[21] Lakshmisha, K. N., Venkateshwaran, S., and Nath, G. Three dimensional unsteady flow with heat and mass transfer over a continuous stretching surface. Journal of Heat Transfer, 110, 590-595(1988)
[22] Pop, I. and Na, T. Y. Unsteady flow past a stretching sheet. Mechanics Research Communication, 23, 413-422(1996)
[23] Chamkha, A. J. and Issa, C. Mixed convection effects on unsteady flow and heat transfer over a stretched surface. International Communications in Heat and Mass Transfer, 26, 717-727(1999)
[24] Ishak, A., Nazar, R., and Pop, I. Boundary layer flow and heat transfer over an unsteady stretching vertical surface. Meccanica, 44, 369-375(2009)
[25] Mukhopadhyay, S. Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity. International Journal of Heat and Mass Transfer, 52, 5213-5217(2009)
[26] Patil, P. M., Pop, I., and Roy, S. Unsteady heat and mass transfer over a vertical stretching sheet in a parallel free stream with variable wall temperature and concentration. Numerical Methods for Partial Differential Equations, 28, 926-941(2012)
[27] Ganapathirao, M., Revathi, G., and Ravindran, R. Unsteady mixed convection boundary layer flow over a vertical cone with non-uniform slot suction (injection). Meccanica, 49, 673-686(2014)
[28] Ravindran, R., Ganapathirao, M., and Pop, I. Effects of chemical reaction and heat generation/absorption on unsteady mixed convection MHD flow over a vertical cone with non-uniform slot mass transfer. International Journal of Heat and Mass Transfer, 73, 743-751(2014)
[29] Ganapathirao, M., Ravindran, R., and Pop, I. Non-uniform slot suction(injection) on an unsteady mixed convection flow over a wedge with chemical reaction and heat generation. International Journal of Heat and Mass Transfer, 67, 1054-1061(2013)
[30] Inowe, K. and Tate, A. Finite-difference version quasi-linearization applied to boundary layer equations. American Institute of Aeronautics and Astronautics (AIAA) Journal, 12, 558-560(1974)
[31] Varga, R. S. Matrix Iterative Analysis, Springer, New York (2000)