Unsteady Water Boundary Layer Flow with Non-Uniform Mass Transfer
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:59836", author = "G. Revathi and P. Saikrishnan", title = "Unsteady Water Boundary Layer Flow with Non-Uniform Mass Transfer", 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.", volume = "6", number = "10", pages = "1424-5", }
