Transient nonlinear optically-thick radiative–convective double-diffusive boundary layers in a Darcian porous medium adjacent to an impulsively started surface: Network simulation solutions

Abstract A boundary-layer model is described for the two-dimensional nonlinear transient thermal convection heat and mass transfer in an optically-thick fluid in a Darcian porous medium adjacent to an impulsively started vertical surface, in the presence of significant thermal radiation and buoyancy forces in an ( X ∗ , Y ∗ , t ∗ ) coordinate system. An algebraic approximation is employed to simplify the integro-differential equation of radiative transfer for unidirectional flux normal to the plate into the boundary-layer regime, by incorporating this flux term in the energy conservation equation. The conservation equations are non-dimensionalized into an ( X , Y , T ) coordinate system and solved using the Network Simulation Method (NSM), a robust numerical technique which demonstrates high efficiency and accuracy. The transient variation of non-dimensional streamwise velocity component ( u ) and temperature ( T ) and concentration ( C ) functions is computed for various selected values of Stark number (radiation–conduction interaction parameter) and Darcy number. Transient velocity ( u ) and steady-state local skin friction ( τ X ) are also studied for various thermal Grashof number (Gr), species Grashof number (Gm), Schmidt number (Sc) and Stark number ( N ) values. These computations for the infinite permeability case (Da → ∞) are compared with previous finite difference solutions [Prasad et al. Int J Therm Sci 2007;46(12):1251–8] and shown to be in excellent agreement. An increase in Darcy number is seen to accelerate the flow and boost velocity. A decrease in Stark number (corresponding to an increase in thermal radiation heat transfer contribution) is shown to increase the velocity values. Temperature function is observed to fall in value with a rise in Da and increase with decrease in N (corresponding to an increase in thermal radiation heat transfer contribution). Applications of the study include rocket combustion chambers, astrophysical flows, spacecraft thermal fluid dynamics in debris-laden environments (cosmic dust), heat transfer in forest fire spread, geochemical contamination and ceramic materials processing.