Overlapping Multi-Domain Spectral Method for MHD Mixed Convection Slip Flow Over an Exponentially Decreasing Mainstream with Nonuniform Heat Source/Sink and Convective Boundary Conditions

Abstract

Overlapping multi-domain bivariate spectral quasilinearization method is applied on magnetohydrodynamic mixed convection slip flow over an exponentially decreasing mainstream with convective boundary conditions and nonuniform heat source/sink effects. The method is employed in solving the transformed flow equations. The convergence properties and accuracy of the method are determined. The method gives highly accurate results after few iterations and using few grid points in each space subinterval and the entire interval. The use of minimal numbers of grid points at each subinterval minimizes the effects of round-off errors that can lead to instabilities. The accuracy increases as the number of overlapping subintervals increases. The accuracy improvement is achieved through making the coefficient matrices less dense. The effects of controlling parameters on the flow fields and physical quantities of interest are studied. Results show that increasing Biot number and nonuniform heat source/sink enhances the flow fields while reducing skin friction and heat transfer rate. The fluid properties improve with injection whereas the flow characteristics augment with suction. The considered exponentially decreasing external flows have particular applications in diverging channel flows. This study has practical significance in various boundary layer problems such as in controlling and delaying boundary layer separation on control surfaces and in suppressing recirculating bubbles.

Irreversibility scrutinization on EMHD Darcy–Forchheimer slip flow of Carreau hybrid nanofluid through a stretchable surface in porous medium with temperature‐variant properties

“…According to Yang et al, 58 the method becomes very complicated if the number of collocation points is varied in each subdomain. Second, the length of each subdomain must fixed if linear transformation is used, which appears in many studies 53–56 as follows: $$${\mathscr{L}}=\frac{{\eta }_{\max }}{P+(1-P)\left(1-\cos \frac{\pi }{{M}_{\eta }}\right)\unicode{x02215}2}.$$$…”

“…Recently, researchers 14,[53][54][55][56][57] tried to circumvent these limitations by implementing the overlapping grid idea with spectral collocation methods to ensure accuracy, stability, and computational efficiency are maintained when solving differential equations defined on large computational domains. These techniques are very powerful methods for the numerical computation of solutions to nonlinear boundary value problems.…”

“…According to Yang et al, 58 the method becomes very complicated if the number of collocation points is varied in each subdomain. Second, the length of each subdomain must fixed if linear transformation is used, which appears in many studies [53][54][55][56] as follows:…”