Unsteady Water Boundary Layer Flow with Non-Uniform Mass Transfer

Authors: G. Revathi, P. Saikrishnan

Abstract:

In the present analysis an unsteady laminar forced convection water boundary layer flow is considered. The fluid properties such as viscosity and Prandtl number are taken as variables such that those are inversely proportional to temperature. By using quasi-linearization technique the nonlinear coupled partial differential equations are linearized and the numerical solutions are obtained by using implicit finite difference scheme with the appropriate selection of step sizes. Non-similar solutions have been obtained from the starting point of the stream-wise coordinate to the point where skin friction value vanishes. The effect non-uniform mass transfer along the surface of the cylinder through slot is studied on the skin friction and heat transfer coefficients.

Keywords: Boundary layer, heat transfer, non-similar solution, non-uniform mass, unsteady flow.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075905

References:

[1] F. T. Smith, "Steady and unsteady boundary layer separation," Annu. Rev. Fluid Mech., 1986, pp. 197-220.
[2] F. M. White, Viscous Fluid Flow, second ed. ed. New York: McGraw- Hill, 1991.
[3] H. Schlichting, K. Gersten, Boundary Layer Theory, Eighth revised and enlarged ed. (English) ed. New York: Springer, 2000.
[4] D. K. Ludlow, P. A. Clarkson, A. P. Bassom, "New similarity solutions of the unsteady incompressible boundary layer equations," Q. J. Mech. Appl. Math, vol. 53, no. 2, 2000, pp. 175-206.
[5] P. H. Ma, W. H. Hui, "Similarity solutions of the two dimensional unsteady boundary layer equations," J. Fluid Mech, vol. 206, 1990, pp. 537-559.
[6] M. Kumari, G. Nath, "Simultaneous heat and mass transfer under unsteady mixed convection along a vertical slender cylinder embedded in a porous medium," Warme- und Stoffubertragung, vol. 28, 1993, pp. 97-105.
[7] S. Roy, D. Anilkumar, "Unsteady mixed convection from a moving vertical slender cylinder," Journal of Heat Transfer, vol. 128, 2006, pp. 368-373.
[8] C. D. Surma Devi, G. Nath, "Unsteady non similar laminar boundarylayer flows with heat and mass transfer," Acta Technica Csav, vol. 28, 1983, pp. 225-239.
[9] A.J. Chamkha, S.M.M. EL-Kabeir, A.M. Rashad, "Heat and mass transfer by non-Darcy free convection from a vertical cylinder embedded in porous media with a temperature-dependent viscosity," International Journal of Numerical Methods for Heat and Fluid Flow, vol. 21, no. 7, 2011, pp. 847-863.
[10] M Adekojo Waheed, "Temperature dependent fluid properties effects on the heat function formulation of natural convective flow and heat transfer," International Journal of Numerical Methods for Heat and Fluid Flow, vol. 16, no. 2, 2006, pp. 240-260.
[11] A. T. Eswara, G. Nath, "Unsteady nonsimilar two-dimensional and axisymmetric water boundary layers with variable viscosity and Prandtl number," Int. J. Engng. Sci., vol. 32, no. 2, 1994, pp. 267-279.
[12] W. J. Minkowycz, E. M. Sparrow, G. E. Schneider, R. H. Pletcher, Handbook of Numerical Heat Transfer. New York: Wiley, 1988.
[13] P. Saikrishnan, S. Roy, "Non-uniform slot injection (suction) into water boundary layers over (i) a cylinder and (ii) a sphere," International Journal of Engineering Science, vol. 41, 2003, pp. 1351-1365.
[14] S. Roy, "Non-uniform mass transfer or wall enthalpy into a compressible flow over yawed cylinder," International Journal of Heat and Mass Transfer, vol. 44, 2001, pp. 3017-3024.
[15] S.Roy, P. Saikrishnan, "Non-uniform slot injection (suction) into steady laminar water boundary layer flow over a rotating sphere," International Journal of Heat and Mass Transfer, vol. 46, 2003, pp. 3389-3396.
[16] S. Roy, P. Saikrishnan, "Non-uniform slot injection (suction) into water boundary layer flow past yawed cylinder," International Journal of Engineering Science, vol. 42, 2004, pp. 2147-2157.
[17] J. X. Ling, A. Dybbs, "Forced convection over a flat plate submerged in a porous medium: variable viscosity case," WA/HT- 23, vol. 87, 1987.
[18] I. Pop, R. S. R. Gorla, M. Rashidi, "Free convection about cylinders of elliptic cross section embedded in a porous medium," Int. J. Eng. Sci., vol. 30, no. 1, 1992.
[19] D. R.(Ed.) Lide, Handbook of Chemistry and Physics, 71st ed. Boca Raton, FL: CRC Press, 1990.
[20] C. F. Dewey, J. F. Gross, "Exact solutions of the laminar boundary-layer equations," Advances in Heat Transfer, vol. 4, no. 13, 1967, p. 317.
[21] K. Inouye, A. Tata, "Finite-Difference version of Quasi-Linearization Applied to Boundary-Layer Equations," vol. 12, no. 4, 1974, pp. 558- 560.