Study of Heat and Mass transports due to modulated rotational flow in a triply diffusive Newtonian liquid saturated porous medium/fluid layer: A comparative study

Abstract

Rotational modulation and the third diffusive component are investigated in relation to transports in the Rayleigh Bènard convection in the x− direction of an infinitely extended fluid layer or fluid-saturated porous layer using a weakly non-linear theory. The direction of travel for the z-axis is upward. The z-axis is interpreted as pointing upward. Temperature and concentration of both the solutes at lower plate are higher than the upper plate. The time dependent rotational speed of fluid is assumed to be modulated by small parameter ϵ2 with amplitude (δ). A linear differential matrix approach is used to examine the system’s behaviour. Ginzburg–Landau’s equation, a non-autonomous differential equation, has been derived using the Fredholm-solvability condition. The impact of dimensionless parameters on stationary convection is also discussed. The expression of the critical Rayleigh number is obtained for three different cases: clear fluid layer, Darcy porous layer, and sparsely packed porous layer (Darcy–Brinkman model). The Nusselt number (Nu) and Sherwood numbers (Sh1, Sh2) for each solute are used to quantify the convective transports. The impact of modulation and other dimensionless parameters on these convective transports has been discussed using graphical representation Furthermore, among the three models under consideration, it is discovered that the heat and mass transports are highest in the fluid layer and minimum in the densely packed porous layer.