Steady two-dimensional free convective flow in a finite non-rectangular vertical porous cavity subject to modulating temperature on a bounding surface

Abstract

In theoretical studies of free convective flows taking place in finite porous/non-porous geometries, boundary thermal conditions, especially time-dependent temperature conditions, significantly alter the convection currents and, hence, the resulting real-life applications. This paper has thus considered a fully developed steady buoyancy dominated flow of incompressible viscous fluid in a finite trapezoidal vertical porous cavity. It is assumed that the left vertical wall of this enclosure has been subjected to an oscillatory modulation in the temperature, while the remaining vertical/horizontal/inclined walls have been kept at either constant temperature or subjected to adiabatic thermal conditions. The set of governing PDEs, representing the momentum and thermal transport, together with the Darcy law for porous medium used, have been first transformed to another setup in terms of a stream function, velocity component and temperature in a non-dimensional form. These equations, subject to appropriate boundary conditions at 4 bounding surfaces, have then been solved numerically using an algebraic grid generation technique together with finite difference method. There arises a number of key physical or geometrical nondimensional parameters in our analysis whose effects, across various parameter ranges, have been exhibited on the physical variables of great interest, namely, contours of streamlines and isotherms. Some more aspects related to heat transfer taking place on the bounding walls, have been dealt with to highlight engineering features of this convective flow. It is worth emphasizing that assessing the effect of oscillatory time-dependent wall thermal modulation on natural convection occurring in a non-rectangular finite permeable cavity is the main objective here and first attempt in the literature. © Indian Academy of Sciences 2025.