Unsteady boundary layer flow and heat transfer over a stretching sheet: heat flux case

Cornelia Revnic; Teodor Groşan; Ioan Pop

doi:10.33993/jnaat362-866

Authors

Cornelia Revnic Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Romania
Teodor Groşan Babeş-Bolyai University, Cluj-Napoca, Romania
Ioan Pop Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat362-866

Keywords:

heat transfer, unsteady flow, stretching surface, boundary layer, stagnation point flow, numerical results

Abstract views: 279

Abstract

Unsteady two-dimensional boundary layer flow and heat transfer over a stretching flat plate in a viscous and incompressible fluid of uniform ambient temperature is investigated in this paper. It is assumed that the velocity of the stretching sheet and the heat flux from the surface of the plate vary inverse proportionally with time. Two equal and opposite forces are impulsively applied along the plate so that the plate is stretched keeping the origin fixed. Using appropriate similarity variables, the basic partial differential equations are transformed into a set of two ordinary differential equations. These equations are solved numerically for some values of the governing parameters using the Runge-Kutta method of fourth order. Flow and heat transfer characteristics are determined and represented in some tables and figures. It is found that the structure of the boundary layer depends on the ratio of the velocity of the potential flow near the stagnation point to that of the velocity of the stretching surface. In addition, it is shown that the heat transfer from the plate increases when the Prandtl number increases. The present results include also the steady situation as a special case considered by other authors. Comparison with known results is very good.

Downloads

Download data is not yet available.

References

Ali, M. E. and Magyari, E., Unsteady fluid and heat flow induced by a submerged stretching surface while its steady motion is slowed down gradually, Int. J. Heat Mass Transfer, 50, pp. 188-195, 2007, https://doi.org/10.1016/j.ijheatmasstransfer.2006.06.021 DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2006.06.021

Crane, L. J., Flow past a stretching plate, J. Appl. Math. Phys, (ZAMP), 21, pp. 645-647, 1970, https://doi.org/10.1007/bf01587695 DOI: https://doi.org/10.1007/BF01587695

Elbashbeshy, E. M. A. and Bazid, M.A.A., Heat transfer over an unsteady stretching surface, Heat Mass Transfer, 41, pp. 1-4, 2004, https://doi.org/10.1007/s00231-004-0520-x DOI: https://doi.org/10.1007/s00231-004-0520-x

Lakshmisha, K. N., Venkateswaran, S. and Nath, G., Three-dimensional unsteady flow with heat and mass transfer over a continuous stretching surface, ASME J. Heat Transfer, 110, pp. 590-595, 1988, https://doi.org/10.1115/1.3250533 DOI: https://doi.org/10.1115/1.3250533

Lightill, M. J., The response of laminar skin friction and heat transfer to fluctuations in the free stream velocity, Proc. Roy. Soc., 224A, pp. 1-23, 1954, https://doi.org/10.1098/rspa.1954.0137 DOI: https://doi.org/10.1098/rspa.1954.0137

Lin, C. R. and Chen, C. K., Exact solution of heat transfer from a streatching surface with variable heat flux, Heat and Mass Trabsfer 33, pp. 477-480, 1998, https://doi.org/10.1007/s002310050218 DOI: https://doi.org/10.1007/s002310050218

Lin, C. C., Motion in the boundary layer with a rapidly oscillating external flow, Proc. 9th Int. Cong. Appl. Mech, 4, pp. 155-168, 1956.

Ludlow, D. K., Clarkson, P. A. and Bassomv A. P., New similarity solutions of the unsteady incompressible boundary-layer equations, Q. Jl. Mech. Appl. Math., 53, pp. 175-206, 2000, https://doi.org/10.1093/qjmam/53.2.175 DOI: https://doi.org/10.1093/qjmam/53.2.175

Ma, P. K. H. and Hui, W. H., Similarity solutions of the two-dimensional unsteady boundary layer equations, J. Fluid Mech, 216, pp. 537-559, 1990, https://doi.org/10.1017/s0022112090000520 DOI: https://doi.org/10.1017/S0022112090000520

Ray Mahapatra, T. and Gupta, A. S., Heat transfer in stagnation-point flow towards a stretching sheet, Heat Mass Transfer, 38, pp. 517-521, 2002, https://doi.org/10.1007/s002310100215 DOI: https://doi.org/10.1007/s002310100215

Ray Mahapatra, T. and Gupta, A. S., Stagnation-point flow of a viscoelastic fluid towards a stretching surface, Int. J. Non-Linear Mech, 39, pp. 811-820, 2004, https://doi.org/10.1016/s0020-7462(03)00044-1 DOI: https://doi.org/10.1016/S0020-7462(03)00044-1

Moore, F.K., Unsteady laminar boundary layer flow, NACA TN, 1951.

Pop, I. and Na, T. Y., Unsteady flow past a stretching sheet, Mech. Res. Comm., 23, pp. 413-422, 1996, https://doi.org/10.1016/0093-6413(96)00040-7 DOI: https://doi.org/10.1016/0093-6413(96)00040-7

Pop, I., Theory of Unsteady Boundary Layers (in Romanian), Ed. Ştiinţifică şi Enciclopedică, Bucureşti-Romania, 1983.

Riley, N., Unsteady laminar boundary layers, SIAM Review, 17, pp. 274-297, 1975, https://doi.org/10.1137/1017033 DOI: https://doi.org/10.1137/1017033

Sharidan, S., Mahmood, T., and Pop, I., Similarity solutions for the unsteady boundary layer flow and heat transfer due to a stretching sheet, Int. J. Appl. Mech. Engrg., 11, pp. 647-654, 2006.

Stuart, J. T., Unsteady boundary layers,In Recent Research of Unsteady Boundary Layers (E.-A. Eichelbrenner, ed.), 1, pp. 1-40, 1971.

Surma Devi, C. D., Takhar, H. S. and Nath, G., Unsteady, three-dimensional, boundary- layer flow due to a stretching surface, Int. J. Heat Mass Transfer, 29, pp. 1996-1999, 1986, https://doi.org/10.1016/0017-9310(86)90020-7 DOI: https://doi.org/10.1016/0017-9310(86)90020-7

Takhar, H. S., Chamkha A. J. and Nath, G., Unsteady three-dimensional MHD- boundary-layer flow due to the impulsive motion of a stretching surface, Acta Mechanica, 146, pp. 59-71, 2001, https://doi.org/10.1007/bf01178795 DOI: https://doi.org/10.1007/BF01178795

Wang, C. Y., Exact solutions of the steady-state Navier-Stokes equations, Annu. Re. Fluid Mech, 23, pp. 159-177, 1991, https://doi.org/10.1146/annurev.fl.23.010191.001111; https://doi.org/10.1146/annurev.fluid.23.1.159 DOI: https://doi.org/10.1146/annurev.fl.23.010191.001111

Wang, C. Y., Du, Q., Miklavčič , M. and Chang, C. C., Impulsive stretching of a surface in a viscous fluid, SIAM J. Appl. Math., 57, pp. 1-14, 1997, https://doi.org/10.1137/s0036139995282050 DOI: https://doi.org/10.1137/S0036139995282050

Telionis, D. P., Review-Unsteady boundary layers, separated and attached, J. Fluids Engng., 101, pp. 29-43, 1979, https://doi.org/10.1115/1.3448732 DOI: https://doi.org/10.1115/1.3448732

Telionis, D. P., Unsteady Viscous Flows, Springer, Berlin, 1981, https://doi.org/10.1007/978-3-642-88567-9_6 DOI: https://doi.org/10.1007/978-3-642-88567-9