Akademik Veri Yönetim Sistemi
JOURNAL OF POROUS MEDIA, cilt.25, sa.6, ss.53-63, 2022 (SCI-Expanded)
The goal of the current paper is to analyze the free convection flow of fluids due to a vertical permeable flat surface/cone immersed in saturated porous media subjected to a nonconstant heat flux at the wall together with an internal heat generation/absorption. Dissimilar to the available numerical studies on the topic, the essential idea here is to look for analytical solutions corresponding to the temperature field of the porous medium when a specific heat flux at the boundary is applied. Closed form solutions of the exponentially decaying kind are detected, which point to unique or multiple (dual/triple) solutions, whose diversity highly depend on whether the porous medium is subject to cooling or heating. The thresholds guaranteing the existence of such multiple solutions are explicitly determined. In addition to this, further algebraically decaying solutions are shown to exist to prevail the natural convection. Exact solutions are also validated through some simplified real models available in the open literature. The effects of wall transpiration and heat generation absorption on the shape of the temperature profiles as well as on the form of the heat transfer rate of engineering interest are easy to follow from the presented formulae in this paper. These results will certainly shed light upon further research in the ongoing subject on freely convecting flows within porous environments where justification of the employed numerical methods is essential.