Analysis of mixed convection in a lid-driven porous square cavity with linearly heated side wall(s)

Abstract

Mixed convection flows in a lid-driven square cavity filled with porous medium are studied numerically using penalty finite element analysis for uniformly heated bottom wall, linearly heated side walls or cooled right wall. The top wall is well insulated and set with uniform velocity. The relevant parameters in the present study are Darcy number ( Da = 10 - 5 – 10 - 3 ) , Grashof number ( Gr = 10 3 – 10 5 ) , Prandtl number ( Pr = 0.015–10) and Reynolds number ( Re = 1–10 2). The isotherms are generally symmetric at smaller Pr irrespective of Da and Re at Gr = 10 5 for linearly heated side walls. The isotherms are also almost symmetric at small Re with higher Gr ( Gr = 10 5 ) and Da ( Da = 10 - 3 ) and natural convection is found to be dominant whereas the isotherms are compressed near the left and bottom walls at higher Re for linearly heated side walls. Compression of isotherms and dominance of forced convection is also observed at Re = 10 2 for linearly heated left wall and cooled right wall. The local Nusselt number of the bottom wall ( Nu b ) for low Da is almost constant whereas Nu b for higher Da and Pr shows non-monotonic variation at Re = 10 and an overall decreasing trend is observed at Re = 10 2 for linearly heated side walls. The local Nusselt numbers of left and right walls ( Nu l and Nu r ) increase for Da = 10 −3 and Pr = 0.7 whereas oscillatory trend is observed at Re = 10–10 2 and Pr = 10. For linearly heated left wall and cooled right wall, Nu b increases from the left edge towards the right edge of the bottom wall for both cases Re = 10 and 10 2 irrespective to Pr and Da. It is also observed that Nu r for higher Pr and Da is found to increase monotonically at both Re = 10 and 10 2 and Nu l show non-monotonic trend for higher Pr and Da at Re = 10 whereas for Re = 10 2 , Nu l increases monotonically. Average Nusselt numbers Nu b ¯ , Nu l ¯ , Nu r ¯ are found almost invariant with Gr for low Pr with all Da for linearly heated side walls or cooled right wall. On the other hand, Nu b ¯ is found to vary exponentially at higher Pr and Da and oscillations in Nu l ¯ and Nu r ¯ are observed for Re = 10 whereas increasing trend is observed for Nu l ¯ and Nu r ¯ for Re = 10 2 for both linearly heated side walls or cooled right wall.