HFF 10,1 116 International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 10 No. 1, 2000, pp. 116-133. # MCB University Press, 0961-5539 Received January 1999 Revised June 1999 Accepted August 1999 The Stokes problem for a dusty fluid in the presence of magnetic field, heat generation and wall suction effects Ali J. Chamkha Department of Mechanical and Industrial Engineering, Kuwait University, Safat, Kuwait Keywords Buoyancy, Magnetic fields, Finite differences, Fluids Abstract This work focuses on the laminar flow of a two-phase particulate suspension induced by a suddenly accelerated infinite vertical permeable surface in the presence of fluid buoyancy, magnetic field, heat generation or absorption, and surface suction or blowing effects. The governing equations for this modified Stokes problem are developed based on the continuum representation of both the fluid and the particle cloud. Appropriate dimensionless variables are introduced. The resulting dimensionless equations are solved numerically by an accurate implicit finite-difference method for two situations. The first case corresponds to an impulsive start of the surface from rest while the second case corresponds to a uniformly accelerated surface. The numerical results for these cases are illustrated graphically. Comparisons with previously published work are performed and the results are found to be in good agreement. Typical fluid- and particle-phase velocity and temperature distributions as well as wall shear stress and heat transfer results are reported for various values of the particle loading, Hartmann number, wall mass transfer coefficient and the heat generation or absorption coefficient. Nomenclature B 0 = Magnetic field strength c = Fluid-phase specific heat at constant pressure C = Fluid-phase skin-friction coefficient (C = ± qF/qZ(t,0)) F = Dimensionless fluid-phase tangential velocity (F = u/v 0 ) g = Acceleration due to gravity G = Numerical growth factor Gr = Grashof number (Gr = gb*n(T w ± T ? )/U 3 0 ) Ha = Hartmann number (Ha = B 0 /U 0 (sn/ r) 1/2 ) k = Stokes drag coefficient (k = 6pmr) K = Fluid-phase thermal conductivity m = Particle mass n = Wall velocity exponent N 0 = Particle number density p = Fluid-phase pressure Pr = Fluid-phase Prandtl number (Pr = mc/K) q w = Wall heat transfer coefficient Q 0 = Dimensional heat generation or absorption coefficient r = Particle radius r v = Dimensionless wall mass transfer (r v =v 0 /U 0 ) t = Time T = Dimensional fluid-phase temperature u = Dimensional x-component (vertical) of velocity U 0 = Surface velocity v = Dimensional y-component (horizontal) of velocity v 0 = Wall suction or injection velocity x, y = Cartesian coordinates Greek symbols a = Inverse Stokes number (a = n/(t p U 2 0 )) b* = Thermal expansion coefficient Z = Dimensionless normal distance f = Dimensionless heat generation or absorption coefficient (f = Q 0 n/ (rcU 2 0 )) The current issue and full text archive of this journal is available at http://www.emerald-library.com