Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption

Binil Thomas Sebastian; P. Nagarani

Korea-Australia Rheology Journal, Vol.30, No.4, 261-271, November, 2018

DOI10.1007/s13367-018-0025-7 Export Citation

Convection-diffusion in unsteady non-Newtonian fluid flow in an annulus with wall absorption

Binil Thomas Sebastian, and P. Nagarani^{1, †}

School of Mathematics and Statistics, University of Technology, Jamaica, Kingston, Jamaica
¹Department of Mathematics, The University of the West Indies, Mona Campus, Kingston 7, Jamaica

E-mail:

The present study investigates the combined effects of non-Newtonian rheology and unsteady nature of the fluid on dispersion of a soluble substance between two coaxial cylinders having wall permeability at the outer wall with the flowing fluid is modelled as Casson fluid. Generalized dispersion method in combination with a finite difference scheme is used to study the dispersion phenomenon. Using the generalized dispersion model, the entire process of dispersion is expressed in terms of three transport coefficients viz., absorption, convection, and dispersion (effective diffusion) coefficients. These transport coefficients are evaluated numerically using Crank-Nicolson finite difference method. The mean concentration is expressed in terms of these transport coefficients. Effects of annular gap, yield stress, Womersley frequency parameter, amplitude of the pressure pulsation, and the absorption parameter on the transport coefficients and mean concentration are studied. Flow unsteadiness is observed influencing the dispersion coefficient both quantitatively and qualitatively. It is observed that, as Womersley number increases the fluctuation of the dispersion coefficient increases and the magnitude of dispersion coefficient decreases for small values of time (< 0.5) and increases for later values of time.

Keywords:dispersion theory;convection-diffusion;generalized dispersion method;Casson fluid;oscillatory flow

[References]

Ananthakrishnan V, Gill WN, Barduhn AJ, AIChE J., 11, 1063 (1965)
Aris R, Proc. R. Soc. Lond. A, 235, 67 (1956)
Aroesty J, Gross JF, Microvasc. Res., 4, 1 (1972)
Caro CG, Pedley TJ, Schroter RC, Seed WA, The Mechanics of the Circulation, 1978.
Dash RK, Jayaraman G, Mehta KN, J. Biomech., 29, 917 (1996)
Gill WN, Proc. R. Soc. Lond. A, 298, 335 (1967)
Gill WN, Sankarasubramanian R, Proc. R. Soc. Lond. A, 316, 341 (1970)
Kaye SR, Kavafyan P, Schroter RC, J. Biomech. Eng. -Trans. ASME, 115, 125 (1993)
Mazumder BS, Mondal KK, Q. J. Mech. Appl. Math., 58, 349 (2005)
McDonald DA, Blood Flow in Arteries, 1974.
Nagarani P, Sebastian BT, Appl. Math. Inform., 35, 241 (2017)
Nagarani P, Sarojamma G, Jayaraman G, Acta Mech., 187, 189 (2006)
Nagarani P, Sarojamma G, Jayaraman G, Acta Mech., 202, 47 (2009)
Palma M, Giudici R, Chem. Eng. J., 94(3), 189 (2003)
Pedley TJ, Kamm RD, J. Fluid Mech., 193, 347 (1988)
Ramana B, Sarojamma G, Adv. Appl. Sci. Res., 3, 3878 (2012)
Rao AR, Deshikachar KS, ZAMM-Z. Angew. Math. Mech., 67, 189 (1987)
Sankarasubramanian R, Gill WN, Proc. R. Soc. Lond. A, 333, 115 (1973)
Sarkar A, Jayaraman G, Acta Mech., 158, 105 (2002)
Sarkar A, Jayaraman G, Acta Mech., 172, 151 (2004)
Taylor GI, Proc. R. Soc. Lond. A, 219, 186 (1953)
Truskey GA, Yuan F, Katz DF, Transport Phenomena in Biological Systems, 2009.

[Referenced By]

[1] Ananthakrishnan V, Gill WN, Barduhn AJ, AIChE J., 11, 1063 (1965)

[2] Aris R, Proc. R. Soc. Lond. A, 235, 67 (1956)

[3] Aroesty J, Gross JF, Microvasc. Res., 4, 1 (1972)

[4] Caro CG, Pedley TJ, Schroter RC, Seed WA, The Mechanics of the Circulation, 1978.

[5] Dash RK, Jayaraman G, Mehta KN, J. Biomech., 29, 917 (1996)

[6] Gill WN, Proc. R. Soc. Lond. A, 298, 335 (1967)

[7] Gill WN, Sankarasubramanian R, Proc. R. Soc. Lond. A, 316, 341 (1970)

[8] Kaye SR, Kavafyan P, Schroter RC, J. Biomech. Eng. -Trans. ASME, 115, 125 (1993)

[9] Mazumder BS, Mondal KK, Q. J. Mech. Appl. Math., 58, 349 (2005)

[10] McDonald DA, Blood Flow in Arteries, 1974.

[11] Nagarani P, Sebastian BT, Appl. Math. Inform., 35, 241 (2017)

[12] Nagarani P, Sarojamma G, Jayaraman G, Acta Mech., 187, 189 (2006)

[13] Nagarani P, Sarojamma G, Jayaraman G, Acta Mech., 202, 47 (2009)

[14] Palma M, Giudici R, Chem. Eng. J., 94(3), 189 (2003)

[15] Pedley TJ, Kamm RD, J. Fluid Mech., 193, 347 (1988)

[16] Ramana B, Sarojamma G, Adv. Appl. Sci. Res., 3, 3878 (2012)

[17] Rao AR, Deshikachar KS, ZAMM-Z. Angew. Math. Mech., 67, 189 (1987)

[18] Sankarasubramanian R, Gill WN, Proc. R. Soc. Lond. A, 333, 115 (1973)

[19] Sarkar A, Jayaraman G, Acta Mech., 158, 105 (2002)

[20] Sarkar A, Jayaraman G, Acta Mech., 172, 151 (2004)

[21] Taylor GI, Proc. R. Soc. Lond. A, 219, 186 (1953)

[22] Truskey GA, Yuan F, Katz DF, Transport Phenomena in Biological Systems, 2009.