The role of local thermal non-equilibrium on the instability analysis in the presence of variable gravity field with throughflow

Abstract

The influence of variable gravity on the stability analysis has been investigated in a horizontal porous region with throughflow under a local thermal non-equilibrium (LTNE) situation. Flow inside the porous region is considered to be followed by the Darcy model. Also, the linear varying gravity field with height and nonlinear (parabolic, cubic, and exponential) changing gravity field depth have been considered to address the investigation. The obtained eigenvalue problem for the perturbed state is solved via bvp4c technique in MATLAB. Finally, we investigated the convective boundaries of the system due to the governing parameters, such as gravity variation parameter (λ), porosity-modified conductivity ratio (γ), interphase heat transfer parameter (H), and throughflow parameter (Q). The outcomes assure that the interphase heat transfer parameter has a significant impact on the breakdown of the convection inside of its intermediate range, while the local thermal equilibrium (LTE) state occurred when H converges both the limiting cases, i.e. H→0 and H→∞. It has also been observed that the gravity variation parameter and throughflow parameter have a stabilizing effect, whereas the porosity-modified conductivity ratio destabilizes the flow. Further, it is distinguished that the instability boundaries are unchanged by H when γ≥10. In addition, the flow field is more delayed for exponential changing gravity field, whereas more advanced for cubic varying gravity field.