Berkovsky-Polevikov Correlations for Natural Convection in a Nonhomogeneous Enclosure Filled With a Fluid and Disconnected-Conducting Solid Particles

This study investigates the suitability of the known Berkovsky-Polevikov correlations, used for predicting the wall-averaged Nusselt number, Nu_av, of “wide” enclosures heated from the side and filled with a fluid undergoing natural convection, to predict the heat transfer coefficient inside a nonhomogeneous enclosure heated from the side, filled with uniformly distributed, disconnected and conducting solid objects also saturated with a fluid undergoing natural convection. Hence, defining γ = Ra_HPr/(0.2+Pr), a correlation in the form of Nu_av = Aγ^B is investigated for curve fitting numerical simulation results. The numerical results are obtained by simulating the heat transfer process of the two distinct constituents, namely the fluid and the solid, within the enclosure using the finite-volume method with appropriate conservation equations and compatibility conditions at their interfaces. The right wall of the enclosure is maintained at temperature lower than that of the left wall, with the horizontal top and bottom surfaces of the enclosure assumed to be adiabatic. Results for 1, 4, 9, 16, and 36, evenly distributed square solid blocks are presented. Appropriate numerical values for coefficients A and B are determined and presented for the utilization of the corresponding Berkovsky-Polevikov correlations. Good correlation is obtained when the Rayleigh number is high (≥10⁷), as to yield distinct boundary layers inside the enclosure.