Experimental and Numerical Studies of Natural Convection in Trapezoidal Cavities

Abstract

Natural convection heat transfer has been studied experimentally and numerically for horizontal prismatic cavities of trapezoidal section having a hot horizontal base, a cool inclined top, and insulated vertical walls. Experimental results are presented for a cavity with width-to-mean height ratio of 4, Rayleigh numbers (based on the mean cavity height) from 103 to 107, and top surface inclinations from 0 to 25 deg to the horizontal. For a given top surface inclination, the Nusselt–Rayleigh relationship follows the usual trend, but with an interesting anomaly, in which higher Nusselt numbers than expected are obtained in the range 8 × 103 < Ra < 2 × 105 for inclinations of 0 and 5 deg. Overall, as the inclination of the top surface is increased, the Nusselt number decreases, an effect that becomes greater at higher angles. The proportions of convective heat flow rate into the high side and low side of the cavity were measured and show distinct maxima at particular Rayleigh numbers (which are independent of the top surface inclination angle). The equation Nu = 0.168 [Ra (1 + cos θ)/2]0.278 [(1 − cos θmax)/(cos θ − cos θmax)]−0.199 correlates the experimental results to within 6.9 percent for the ranges 4 × 103 < Ra < 107 and 0 deg ≤ θ ≤ 25 deg, apart from the anomalous region previously indicated. It is suggested that this correlation applies for A ≥ 4. The numerical model uses a false transient ADI finite difference scheme to solve the governing two-dimensional vorticity and energy transport equations. Nusselt numbers computed by the model are in good agreement with the experimental values. The convective flow patterns generated by the model exhibit changes in number and in size of cells for different Rayleigh numbers and different top surface inclinations.