Analysis of heat recovery and heat transfer within entrapped porous triangular cavities via heatline approach

Abstract

A finite element analysis is carried out to investigate the heat transfer details in entrapped porous triangular cavities which are formed between a pair of square tubes for a situation where hot fluid passes through the stack and cold fluid is entrapped within the triangular cavities. The present numerical procedure is performed over a wide range of parameters of Darcy number, Da (10 −5–10 −1), Prandtl number, Pr (0.015–1000) and Rayleigh number, Ra (10 3–5 × 10 5). At low Darcy number ( Da = 10 −5), heat transfer is primarily due to conduction for both the triangles since the heatlines are normal to the isotherms. But, as Darcy number increases conduction dominant mode changes to convection dominant. At lower Prandtl number ( Pr = 0.015) with Da = 10 −3, circulations are formed within the upper triangular cavity. Multiple cells of heatlines with high intensity are also observed due to the multiple circulation cells in fluid flow and isotherms show oscillatory pattern within the upper triangular cavity. Dense heatlines are also found near the bottom portion of the inclined walls at higher Da (10 −3–10 −1) for the upper triangle, indicating enhanced heat transport. It is interesting to observe that change of Prandtl number does not show much variation in heating patterns within the lower triangle. Heat transfer rates are obtained in terms of local ( Nu l , Nu h ) and average Nusselt numbers ( Nu l ¯ , Nu h ¯ ) . It is observed that, at low Prandtl number with high Darcy number, local Nusselt numbers of the upper triangle follow oscillatory pattern due to the multiple circulations whereas local Nusselt numbers follow monotonic trend for the lower triangle irrespective of Prandtl number and Darcy number. Average Nusselt number shows overall larger heat transfer rate for upper triangular cavity comparing to the lower triangular cavity at Da = 10 −3. The decreasing trend of average Nusselt number for lower and upper triangles at higher Ra is due to smaller local Nusselt number at specific spatial positions.