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In this paper, we study steady‐state conjugate heat transfer over a backward‐facing step flow using a combination of a compact finite difference scheme for the ψ ‐ v form of the Navier–Stokes equations and a higher‐order compact scheme for the temperature equations on nonuniform grids. We investigate the effect of Reynolds number ( 200 ≤ R e ≤ 800 ), conductivity ratio ( 1 ≤ k ≤ 1000 ), Prandtl number ( 0.1 ≤ P r ≤ 15 ), and slab thickness ( h ≤ b ≤ 6 h ) on the heat transfer characteristics. Isotherms remain clustered near the reattachment point in the fluid, while the temperature in the solid decreases vertically, with the minima at the reattachment point. Heat transfer rate (HTR) increases with Re, the maximum at the reattachment point. The HTR increases with k till k = 100 after, which it becomes invariant as k → ∞ . Isotherms at the inlet become more disorderly with increasing Pr, and progressively clustered near the interface, indicating an increase in HTR, while the temperature in the solid region decreases with Pr. Increasing b decreases the HTR. In addition to obtaining an excellent match with results previously reported in the literature, we offer more comprehensive and previously unreported insights on flow physics.

In this paper, we apply a reconstructed higher-order compact scheme on nonuniform grids to the problem of double-diffusive natural convection in a vertical porous annulus. The Darcy model is adopted for the fluid flow h c h c ). Furthermore, the top and bottom boundaries of the cavity are adiabatic and impermeable.The following assumptions hold for this study:(i) Darcy's law is applicable in the porous medium.(ii) The porous matrix is uniform and in equilibrium with the fluid.

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