Non-Darcian Benard Marangoni Convection in a superposed fluid-porous layer with temperature dependent heat source

Abstract

The investigation of Non-Darcian Benard Marangoni Convection (NDBMC) is carried out in a Superposed Fluid-Porous (SFP) layer, which consists of an incompressible, sparsely packed single component fluid saturated porous layer above which lies a layer of the same fluid, with temperature dependent heat sources in both the layers. The upper surface of the SFP layer is free with Marangoni effects depending on Temperature, where the lower surface of the SFP layer is rigid. The thermal Marangoni numbers are obtained in closed form for two sets of thermal boundaries set (i) Adiabatic-Adiabatic and set (ii) Adiabatic-Isothermal. Influence of temperature dependent heat source in terms of internal Rayleigh numbers, viscosity ratio, Darcy Number, thermal diffusivity ratio on NDBMC, is investigated in detail.

Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources

“…... (9) ... (10) is the interface temperature, f(z) and f m (z m ) are the dimensionless temperature profiles in the fluid and the porous medium respectively. Following Sumithra et al [14], the basic solution is perturbed, linearized, non-dimensionalized by taking suitable scale lengths in both the layers. After subject to normal mode analysis, differential equations so obtained are (refer [14]):…”

“…Following Sumithra et al [14], the basic solution is perturbed, linearized, non-dimensionalized by taking suitable scale lengths in both the layers. After subject to normal mode analysis, differential equations so obtained are (refer [14]):…”

“…Recently, Vanishree et al [16] have studied the effects of linear and non linear temperature gradients on Benard-Marangoni convection with constant heat source in a composite layer. Sumithra et al [12,13,14,15] have studied the linear stability analysis of Marangoni convection in a composite layer with constant/ temperature dependent heat sink or source for the Darcy and Darcy-Brinkman cases.…”

“…Boundary conditionsThe associated boundary conditions are non-dimensionalized and subjected to normal mode analysis. (Refer Sumithra et al[14]Marangoni number,  represents surface tension and T u is the temperature at the upper layer of the fluid, is the depth ratio and represents the ratio of thermal diffusivities.…”

Two Component Benard-Marangoni Convection in a Composite System Subjected to Variable Heat Source

“…The time derivative can be removed from the perturbed dimensionless equations since the concept of exchange of stability holds for the provided composite system. Then we perform normal mode expansion to obtain solutions for w, w m , ,  m , s, and s m in the form ... (13) ... (14) The differential equations so obtained by applying equations ( 13) and ( 14 Here is the depth ratio, is the thermal diffusivity ratio, is the solute diffusivity ratio, is the Darcy number, is the thermal Marangoni number and is the solute Marangoni number, where  is the surface tension.…”