Analysis of efficiency of convection in porous geometries (square vs triangular) with multiple discrete heaters on walls

Abstract

PurposeThe purpose of the paper is to study natural convection within porous square and triangular geometries (design 1: regular isosceles triangle, design 2: inverted isosceles triangle) subjected to discrete heating with various locations of double heaters along the vertical (square) or inclined (triangular) arms.Design/methodology/approachGalerkin finite element method is used to solve the governing equations for a wide range of modified Darcy number,Dam= 10−5–10−2with various fluid saturated porous media,Prm= 0.015 and 7.2 at a modified Rayleigh number,Ram= 106involving the strategic placement of double heaters along the vertical or inclined arms (types 1-3). Adaptive mesh refinement is implemented based on the lengths of discrete heaters. Finite element based heat flow visualization via heatlines has been adopted to study heat distribution at various portions.FindingsThe strategic positioning of the double heaters (types 1-3) and the convective heatline vortices depict significant overall temperature elevation at bothDam= 10−4and 10−2compared to type 0 (single heater at each vertical or inclined arm). Types 2 and 3 are found to promote higher temperature uniformity and greater overall temperature elevation atDam= 10−2. Overall, the triangular design 2 geometry is also found to be optimal in achieving greater temperature elevation for the porous media saturated with various fluids (Prm).Practical implicationsMultiple heaters (at each side [left or right] wall) result in enhanced temperature elevation compared to the single heater (at each side [left or right] wall). The results of the current work may be useful for the material processing, thermal storage and solar heating applications.Originality/valueThe heatline approach is used to visualize the heat flow involving double heaters along the side (left or right) arms (square and triangular geometries) during natural convection involving porous media. The heatlines depict the trajectories of heat flow that are essential for thermal management involving larger thermal elevation. The mixing cup or bulk average temperature values are obtained for all types of heating (types 0-3) involving all geometries, and overall temperature elevation is examined based on higher mixing cup temperature values.