A semiquantitative theory of convective heat transfer in a heat-generating fluid

A semiquantitative theory of heat transfer in a heat-generating fluid within a closed volume is developed. The analysis is based on relationships derived from the condition of energy balance and on modern physical concepts of heat transfer processes in an energy-neutral fluid. Four main regimes and one asymptotic regime of heat transfer are singled out, which differ in the exponents of power in the expression relating the Nusselt number, Nu, and the modified Rayleigh number, Ra-I. In the asymptotic limit, with Ra-I(-1/32) much greater than 1, heat transfer to the upper horizontal part of the boundary and the curved part of the boundary facing downward obeys dependences Nu(up) similar to Ra-I(7/32) and Nu(dn) similar to Ra-I(1/4), respectively. In the range of values of Ra-I which is of interest with regard to the safety problem of the nuclear power engineering the established theoretical correlations are in good agreement with the experimental data. (C) 1998 Elsevier Science Ltd.