Heat generation/absorption effects on magnetohydrodynamic natural convection flow over a sphere in a non-Darcian porous medium

Abstract

In this article, the magnetohydrodynamic natural convection boundary-layer flow on a sphere in a porous medium is studied numerically. The porous medium is saturated with an electrically conducting fluid and the fluid is subject to heat generation/absorption. A viscous flow model is presented using boundary-layer theory comprising the momentum and energy conservation equations. The governing boundary-layer equations are transformed into non-dimensional form using appropriate reference quantities. The resulting coupled non-linear system of partial differential equations is solved numerically using the differential quadrature method (DQM). The advantage of DQM, which was introduced as a promising method two decades ago, is that the solution is converged with a few grid points and hence the computational costs are reduced. Comparison is made between the results obtained by the DQM method and those obtained using the finite-difference method for the same operating conditions. A validation test is carried out for the case of infinite permeability (i.e. infinite Darcy number). The results of the present study were compared with the results of a similar investigation available in the literature. Close agreement between the two sets of results was noticed. A parametric study was performed in which the effect of various parameters on temperature and velocity fields, local Nusselt numbers, and wall friction coefficient were investigated.

Keywords

natural convection porous medium heat generation magnetohydrodynamic differential quadrature method sphere

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References

Geoola

Cornish

A. R. H.

, ‘Numerical solution of steady-state free convective heat transfer from a solid sphere’ Int. J. Heat Mass Transf. 24 (1981): 1369–1379.

Huang

M. J.

Chen

C. K.

, ‘Laminar free convection from a sphere with blowing and suction’ ASME J. Heat Transf. 109 (1981): 529–532.

Nazar

Amin

Grosan

Pop

, ‘Free convection boundary layer on an isothermal sphere in a micropolar fluid’ Int. Commun. Heat Mass Transf. 29(3) (2002): 377–386.

Molla

Hossain

, ‘Effects of chemical reaction, heat and mass diffusion in natural convection flow from an isothermal sphere with temperature dependent viscosity’ Int. J. Comput. Aided Engng Softw. 23(6) (2006): 840–857.

Rossow

V. J.

, ‘On flow of electrically conducting fluids over a flat plate in the presence of a transverse magnetic field’ (South Carolina, USA: NACA 1957) Technical report TN 3971.

Vajravelu

Hadjinicolaou

, ‘Convective heat transfer in an electrically conducting fluid at a stretching surface with uniform free stream’ Int. J. Eng. 35 (1991): 1237–1244.

Bég

O. A.

Takhar

H. S.

Nath

Chamkha

A. J.

, ‘Mathematical modeling of hydromagnetic convection from a rotating sphere with impulsive motion and buoyancy effects’ Nonlinear Anal.: Model. Control 12(1) (2007): 227–245.

Bég

O. A.

Zueco

Bhargava

Takhar

H. S.

, ‘Magnetohydrodynamic convection flow from a sphere to a non-Darcian porous medium with heat generation or absorption effects: network simulation’ Int. J. Therm. Sci. 48 (2002): 913–921.

Vajravelu

Hadjinicolaou

, ‘Heat transfer in a viscous fluid over a stretching sheet with viscous dissipation and internal heat generation, international communication’ Heat Mass Transf. 20 (1991): 417–430.

10.

Molla

M. A.

Taher

M. A.

Chowdhury

M. M. K.

Hossain

M. A.

, ‘Magnetohydrodynamic natural convection flow on a sphere in presence of heat generation’ Nonlinear Anal.: Model. Control 10(4) (2005): 349–363.

11.

Molla

Hossain

Taher

, ‘Magnetohydrodynamic natural convection flow on a sphere with uniform heat flux in presence of heat generation’ Acta Mech. 186(1–4) (2006): 75–86.

12.

Alam

Alim

M. A.

Chowdhury

M. K.

, ‘Viscous dissipation effects on MHD natural convection flow along a sphere’ J. Mech. Eng. 36 (2002): 44–50.

13.

Forchheimer

, ‘Wasserbewegung durch Boden’ ForschHft. Ver Dt. Ing. 45 (1901): 1782–1788.

14.

Niranjan

S. S.

Soundalgekar

V. M.

Takhar

H. S.

, ‘Free convection effects on MHD horizontal channel flow with Hall currents’ IEEE Trans. Plasma Sci. 18(2) (1990): 177–183.

15.

Hossain

M. A.

Vafai

Khanafer

K. M. N.

, ‘Non-Darcy natural convection heat and mass transfer along a vertical permeable cylinder embedded in a porous medium’ Int. J. Therm. Sci. 38 (1991): 854–862.

16.

Yih

K. A.

, ‘Viscous and Joule heating effects on non-Darcy MHD natural convection flow over a permeable sphere in porous media with internal heat generation’ Int. Commun. Heat Mass Transf. 27(4) (2000): 591–600.

17.

Saeif

, ‘Analysis of free convection about a horizontal cylinder in a porous media using a thermal non-equilibrium model’ Int. Commun. Heat Mass Transf. 33 (2002): 158–165.

18.

Katagiri

Pop

, ‘Transient free convection from an isothermal horizontal circular cylinder’ Wirme and Stofffibertragung 12 (1971): 73–81.

19.

Gebhart

, Buoyancy-induced flows and transport (USA: Hemisphere Publishing Corporation 1988).

20.

Fujii

Matsunaga

, ‘A numerical analysis of laminar free convection around an isothermal horizontal circular cylinder’ Numer. Heat Transf. 2 (1971): 329–344.

21.

Fujii

Honda

, ‘A numerical analysis of laminar free convection around an isothermal sphere’ Numer. Heat Transf. 4 (1981): 69–84.

22.

Shu

, Differential quadrature and its application in engineering (Berlin: Springer 2000).