Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

doi:10.1007/s10483-012-1601-9

Abstract

Abstract:

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface. The study considers the effects of frictional heating (viscous dissipation) and internal heat generation or ab- sorption. The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method. An analysis is carried out for two different cases of heating processes, namely, variable wall temperature (VWT) and variable heat flux (VHF). The effects of various physical parameters such as the magnetic parameter, the fluid-particle interaction pa- rameter, the unsteady parameter, the Prandtl number, the Eckert number, the number density of dust particles, and the heat source/sink parameter on velocity and temperature profiles are shown in several plots. The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.

Key words: rational mapping function approach, edge crack problem, stress intensity factor, stretching surface, heat transfer, boundary layer flow, dusty fluid, numerical solution, non-uniform heat source, viscous dissipation

2010 MSC Number:

B. J. GIREESHA;G. S. ROOPA;C. S. BAGEWADI. Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet. Applied Mathematics and Mechanics (English Edition), 2012, 33(8): 1001-1014.

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References

[1] Sakiadis, B. C. Boundary layer behavior on continuous solid surfaces: I. boundary layer equationsfor two dimensional and axisymmetric flow. AIChE Journal, 7(1), 26-28 (1961)
[2] Sakiadis, B. C. Boundary layer behavior on continuous solid surfaces: II. boundary layer behavioron continuous flat surface. AIChE Journal, 7(2), 221-225 (1961)
[3] Crane, L. J. Flow past a stretching plate. Zeitschrift f╱r Angewandte Mathematik und Physik(ZAMP), 21(4), 645-647 (1970)
[4] Grubka, L. J. and Bobba, K. M. Heat transfer characteristics of a continuous stretching surfacewith variable temperature. Journal of Heat Transfer, 107(1), 248-250 (1985)
[5] Chen, C. H. Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heatand Mass Transfer, 33(5-6), 471-476 (1998)
[6] Elbashbeshy, E. M. A. and Bazid, M. A. A. Heat transfer over an unsteady stretching surface.Heat and Mass Transfer, 41(1), 1-4 (2004)
[7] Sharidan, S., Mahmood, T., and Pop, I. Similarity solutions for the unsteady boundary layerflow and heat transfer due to a stretching sheet. International Journal of Applied Mechanics andEngineering, 11(3), 647-654 (2006)
[8] Tsai, R., Huang, K. H., and Huang, J. S. Flow and heat transfer over an unsteady stretchingsurface with a non-uniform heat source. International Communications in Heat and Mass Transfer,35(10), 1340-1343 (2008)
[9] Ishak, A., Nazar, R., and Pop, I. Hydromagnetic flow and heat transfer adjacent to a stretchingvertical sheet. Heat and Mass Transfer, 44(8), 921-927 (2008)
[10] Aziz, A. A similarity solution for laminar thermal boundary layer over a flat plate with a convectivesurface boundary condition. Communications in Nonlinear Science and Numerical Simulation,14(4), 1064-1068 (2009)
[11] Vajravelu, K. and Roper, T. Flow and heat transfer in a second grade fluid over a stretching sheet.International Journal of Non-Linear Mechanics, 34(6), 1031-1036 (1999)
[12] Chen, C. H. Combined heat and mass transfer in MHD free convection from a vertical surfacewith Ohmic heating and viscous dissipation. International Journal of Engineering Science, 42(7),699-713 (2004)
[13] Pal, D. and Hiremath, P. S. Computational modelling of heat transfer over an unsteady stretchingsurface embedded in a porous medium. Meccanica, 45(3), 415-424 (2010)
[14] Vajravelu, K. and Hadjinicolaou, A. Heat transfer in a viscous fluid over a stretching sheet withviscous dissipation and internal heat generation. International Communications in Heat and MassTransfer, 20(3), 417-430 (1993)
[15] Veena, P. H., Subhas-Abel, M., Rajagopal, K., and Pravin, V. K. Heat transfer in a visco-elasticfluid past a stretching sheet with viscous dissipation and internal heat generation. Zeitschrift f╱rAngewandte Mathematik und Physik (ZAMP), 57(3), 447-463 (2006)
[16] Saffman, P. G. On the stability of laminar flow of a dusty gas. Journal of Fluid Mechanics, 13,120-128 (1962)
[17] Datta, N. and Mishra, S. K. Boundary layer flow of a dusty fluid over a semi-infinite flat plate.Acta Mechanica, 42, 71-83 (1982)
[18] Agranat, V. M. Effect of pressure gradient on friction and heat transfer in a dusty boundary layer.Fluid Dynamics, 23, 729-732 (1988)
[19] Vajravelu, K. and Nayfeh, J. Hydromagnetic flow of a dusty fluid over a stretching sheet. Inter-national Journal of Non-Linear Mechanics, 27(6), 937-945 (1992)
[20] Xie, M. L., Lin, J. Z., and Xing, F. T. On the hydrodynamic stability of a particle-laden flow ingrowing flat plate boundary layer. Journal of Zhejiang University SCIENCE A, 8, 275-284 (2007)
[21] Palani, G. and Ganesan, P. Heat transfer effects on dusty gas flow past a semi-infinite inclinedplate. Forsch Ingenieurwes, 71, 223-230 (2007)
[22] Gireesha, B. J., Ramesh, G. K., Subhas-Abel, M., and Bagewadi, C. S. Boundary layer flow andheat transfer of a dusty fluid flow over a stretching sheet with non-uniform heat source/sink.International Journal of Multiphase Flow, 37(8), 977-982 (2011)
[23] Schlichting, H. Boundary Layer Theory, McGraw-Hill, New York (1968)