Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and the Beavers-Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail.
In the present study, the commencement of double-diffusive convection with an internal heat source is studied using a linear instability analysis. The system consists of a fluid layer on top of a porous layer saturated with the same fluid. The boundaries are insulating to temperature perturbations, and the regular perturbation technique is applied to obtain the Rayleigh number. The results of detailed stability characteristics are presented for crucial physical factors, such as thermal Rayleigh number, the inverse Lewis number, depth ratio, the solute Rayleigh number, and heat source strength.
This study examined the flow and thermal transfer feature of MHD (magnetohydrodynamic) Casson, Carreau, and Williamson fluid movements over a parabolic extending region with exponential heat generation effect. The mathematical model is transformed into Ordinary Differential Equations (ODEs) by utilizing appropriate similarity variables and resolved using bvp5c Matlab package. The influence of applicable limits on transfer facts is illustrated via plots and tabular values. The current study outcomes reveal the comparisons of flow, thermal profiles, wall friction, and local Nusselt number of these (Casson, Carreau, and Williamson) different non-Newtonian liquids. Casson fluid shows more excellent thermal conductivity when compared to Carreau and Williamson fluids and observed that the drive and thermal gradient of three non-Newtonian fluids are not uniform. Also, the magnetic force tends to condense the stream and thermal transport rate of these three fluids. The rate of thermal transport is amplified by growing the magnitude of Prandtl and exponential parameters.
The effects of thermal anisotropy and mechanical anisotropy on the onset of Bernard-Marangoni convection in composite layers with anisotropic porous material is studied. The upper fluid surface, free to atmosphere is considered to be deformable. The eigen value problem is solved using a regular perturbation technique with wave number a as perturbation parameter. It is observed that both stabilizing and destabilizing factors can be enhanced thermal anisotropic parameter and mechanical anisotropic parameter so that a more precise control (suppress or augment) of thermal convective instability in a layer of fluid or porous medium is possible.
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