In this work, we investigate the two‐dimensional unsteady natural convective fluid flow problem in a porous‐corrugated enclosure with a fixed sinusoidal heated upper wall. The corrugations of the enclosure are discretely heated while vertical walls are maintained isothermally cold. Subject to where the heat sources are located, five different cases are taken into consideration. The vorticity–streamfunction equations are discretized using a transformation‐free higher order compact approach, and the hybrid BiCGSTAB technique is used to solve the system of algebraic equations that derives from the numerical discretization. To validate our findings, we first compare them to previously published numerical and experimental data. The numerically simulated outcomes are then examined over a variety of essential parameters, such as the Darcy (10−5 ≤ Da ≤ 10−1), Rayleigh (103 ≤ Ra ≤ 106), and Prandtl (0.1 ≤ Pr ≤ 10) numbers. Symmetric and asymmetric fluid flow phenomena are observed. Asymmetric flow phenomenon can be caused by miscible or non‐miscible movements of lighter fluids by heavier fluids, or almost exclusively by nonuniform buoyancy‐driven forces caused by density variations that have arisen because of variations in fluid temperature. The averaged Nusselt value for Case 1 and Case 5 exhibits the highest percentage ratio. The thermal boundary layer is strongly affected by compression, dispersion, suppression, the zone of stratification, and the outweighing of isotherms. The simulated results are visualized by stream functions, isotherms, local and averaged Nusselt number plots.

The purpose of this research work is to investigate two‐dimensional transient natural convective heat transfer and fluid flows in an undulated cavity by placing solid objects with isolated heated surfaces on the bottom wall. We discretize the coupled nonlinear transport equations using a higher‐order compact finite‐difference scheme. First, we test our scheme using existing experimental and numerical data. Then, we analyze the transient and steady‐state natural convective flow phenomena for distributed heat sources on corrugations on the lower wall for a range of the Rayleigh number MathClass-open(R a = 1 0 3 − 1 0 6 MathClass-close) $(Ra=1{0}^{3}-1{0}^{6})$ and Prandtl number MathClass-open(P r = 0.71 MathClass-close) $(Pr=0.71)$. These simulated outcomes are presented in the form of central‐line velocity MathClass-open(u , v MathClass-close) $(u,v)$, local MathClass-openfalse(N u h * , N u v * MathClass-closefalse) $(N{u}_{h}^{* },N{u}_{v}^{* })$ and averaged MathClass-openfalse(N u h * true¯ , N u v * true¯ MathClass-closefalse) $(\bar{N{u}_{h}^{* }},\bar{N{u}_{v}^{* }})$ Nusselt numbers, streamlines MathClass-open( ψ MathClass-close) $(\psi )$, dispersion of isotherms MathClass-open( T MathClass-close) $(T)$, and so forth. It is found that the transient fluid flow behavior is more magnificent than the steady‐state solutions and shows the dominant behavior of the prominent primary cells over secondary cells, where it influences the heat transfer rates inside the entire enclosure. In steady states, at high Rayleigh numbers; convection dominates, formation of thermal boundary layers, compression of isotherms, and stratification of isotherms are significantly observed. Our results show many interesting flow phenomena that have not been analyzed previously.

In this study, we numerically analyzed the unsteady two‐dimensional combined convection flow problem in a porous‐corrugated enclosure whose upper wall is moving with uniform velocity associated with sinusoidal temperature distribution. The vertical sidewalls of the porous‐corrugated enclosure are kept at constant cold temperature while square‐shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending on the discrete isothermal heating. In this paper, we have used the vorticity‐stream‐function formulation of the Brinkmann‐extended Darcy model to numerically simulate the momentum transfer in a porous‐corrugated enclosure. A transformation‐free higher‐order compact (HOC) scheme is used to discretize the nonlinear coupled transport equations, and an advanced iterative solver, like the hybrid‐bi‐conjugate‐gradient stabilized technique, is used to solve the system of algebraic equations generated from the numerical discretization. The present higher‐order compact scheme is fourth‐order accurate in space coordinates and second‐order accurate in the time variable. The numerically simulated results are analyzed over a range of key parameters, like Darcy number ( 1 0 − 4 ≤ D a ≤ 1 0 − 1 ), Reynolds Number ( 100 ≤ R e ≤ 1000 ), Prandtl number ( 0.015 ≤ P r ≤ 10 ), and with fixed high Grashof number ( G r = 1 0 6 ), to study the effects of these leading parameters on the characteristics of heat transfer, fluid flow and isothermal distributions in the porous‐corrugated enclosure. These numerically computed results are presented in the form of streamlines, isotherms, Nusselt number plots, and so forth. Our computed results show numerous flow features which have not been studied previously.

In this study, we numerically examine the unsteady two-dimensional natural convective heat transfer flow problem in a corrugated enclosure containing an electrically conducting fluid whose top wall is nonuniformly heated. The vertical sidewalls of the corrugated enclosure are kept isothermally cold, while square-shaped undulations at the bottom wall are discretely heated. Five different cases are considered depending upon the location of the heat sources. A higher-order compact scheme is used to discretize the governing equations, and an advanced iterative solver,