AbstractAn analytical study has been made of the general problem of heat-transfer to liquid metals flowing between parallel plates. All the results are for the conditions of uniform heat fluxes and fully-established temperature and velocity profiles. Both unilateral and bilateral heat-transfer situations have been considered. In the former, three different methods of determining the velocity profiles were compared; and for each of these, three different types of profile curves for the eddy diffusivity of momentum,ϵM, were compared. The three different methods of determining the velocity profiles showed remarkably good agreement.In the case of bilateral heat transfer, the fraction of total heat transfer to the fluid from any one plate,ξ, was varied from zero to unity. It was found that the heat-transfer coefficient for any one plate is a sensitive function ofξfor that plate. Aboveξ= 0.31, the coefficients are positive; below it, they are negative. Atξ= 0.31, the coefficient is infinite, because at this condition the difference between wall and bulk temperatures is zero.Asξapproaches 0.50, from either above or below, the shape of theεMprofile in the vicinity of the center of the channel has less and less effect on the heat-transfer coefficient. Whenξ= 0.50, the effect is negligible for all practical purposes.There are no adequate experimental data available with which to test the calculated Nusselt numbers, but indications are that the recommended relationships are reasonably correct.