Abstract
This study proposes a mathematical model and the numerical scheme, with rigorous stability and convergence analyses, for a channel flow problem incorporating a nonstandard variable cross-diffusion (Soret-Dufour effects), an unconventional nonlinear radiative heat flux, and time-dependent wall velocity and wall temperature. This led to a system of highly coupled nonlinear partial differential equations. Backward difference scheme is considered for time derivatives, while conservative-type central scheme is adopted for spatial derivatives. The nonlinear terms are discretized by freezing coefficients in discrete time. This resulted in an implicit-explicit algorithm for each nondimensional equation. To investigate the stability, we adopt the discrete maximum principle and derive two-sided estimates for the numerical solution. To establish convergence, we consider a general scheme that encompasses all three schemes, and prove convergence in the grid L2 norm. A problem with nontrivial source terms is used to confirm the theoretical results. Finally, the flow is investigated and the results showed that the nonlinear radiation parameter increased the fluid temperature.
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