Analytical and numerical study of natural convection induced by a volumetric heat generation in inclined cavities asymmetrically cooled by heat fluxes

This paper reports an analytical solution, based on the parallel flow approximation, of the steady laminar natural convection in an inclined cavity filled with a volumetric heat generating fluid and cooled asymmetrically by imposed heat fluxes on the sidewalls. Numerical solutions of the full governing equations are used to determine the limits of validity of the analytical solution as a function of the controlling parameters (aspect ratio A, heat flux ratio r, inclination angle ϕ, Prandtl number Pr and Rayleigh number Ra). It is shown that the agreement between the analytical and numerical results is excellent for 15° ≤ ϕ ≤ 165° if A ≥ 5 and Pr ≥ 0.7, regardless of the values of r and Ra (laminar regime). Analytical and/or Numerical predictions are also exploited to present the effects of the controlling parameters on the characteristics of the heat transfer and fluid flow within the cavity. Thus, in the middle of the cavity, it is found that the maximum temperature and its position depend strongly on the values of the controlling parameters.