Numerical analysis of laminar natural convection in isosceles triangular enclosures

In this work, a numerical analysis of laminar natural convection in an isosceles triangular enclosure has been performed for two different thermal boundary conditions. In case 1, the base is heated and the two inclined walls are symmetrically cooled, and in case 2, the base is cooled and the two top inclined walls are symmetrically heated. This configuration is encountered in solar engineering applications such as: solar stills that usually have triangular cavities and triangular built-in-storage-type solar water heaters; and heat transfer in attic spaces in both wintertime and summertime conditions. To perform the computational analysis, the finite-volume method is used for the discretization of the governing equations. Base angles varying from 15 to 75° have been used for different Rayleigh numbers ranging from 10³ to 10⁵. The effects of the Rayleigh number and aspect ratio on the flow field and heat transfer are analysed. The detailed streamline patterns and temperature distributions are presented. The variation of the mean Nusselt numbers versus Rayleigh numbers for different base angles is given. It is found that the base angle has a drastic influence on the flow field and isotherms for the two cases. For case 1, at small base angles, as the Rayleigh number increases, a multi-cellular flow structure developed inside the enclosure enhances the heat transfer. For case 2, the temperature profiles are always stable and stratified for all Rayleigh numbers and base angles.