Natural convective heat transfer from isothermal cuboids

The paper presents results of theoretical and experimental investigations of the convective heat transfer from isothermal cuboid. The analytical solution was performed taking into account complete boundary layer length and the manner of its propagation around isothermal cuboid. It arises at horizontal bottom surface and grows on vertical lateral surface of the block. After changing its direction, the boundary layer occurs above horizontal surface faced up and next it is transformed into buoyant convective plume. To verify obtained theoretical solution the experimental study has been performed. The experiment was carried out for three possible positions of the same tested cuboid. As the characteristic linear dimension in Nusselt–Rayleigh theoretical and experimental correlations we proposed the ratio of six volumes to the cuboids surface area, for the analogy to the same ratio using as the characteristic dimension for the sphere, which is equal to the sphere’s diameter. It allowed performing the experimental results independently from the orientation of the block. The Rayleigh numbers based on this characteristic length ranged from 105 to 107. The Nusselt number describing intensity of convective heat transfer from the cuboid can be expressed by: Nu=XRa1/5+YRa1/4, where X and Y are coefficients dependent on the cuboid’s dimensions. For the range of provided experiment the experimental Nusselt–Rayleigh relation can be presented in the form: Nu=1.61Ra1/5 or 0.807Ra1/4 with the good agreement with the theoretical one recalculated for the tested cuboid dimensions.