Heat transfer by simultaneous conduction and radiation in a thermal radiation absorbing and emitting medium is considered. Consideration is given to a one-dimensional system consisting of two, diffuse, nonblack, infinite, isothermal, parallel plates separated by a finite distance. The space between the plates is filled with a thermal radiation absorbing and emitting medium. The problem is formulated in terms of a nonlinear integro-differential equation and the solution is obtained by reducing it to a nonlinear integral equation. The numerical results are obtained by an iterative method. The temperature distributions and heat transfer are calculated. Two approximate methods for formulating radiant heat-transfer problems are presented and comparisons of the results are made with the most exact solution.

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The effect of free convection on heat transfer and on the flow field about a rotating cone is studied. A similar solution for the laminar boundary-layer equations is found to exist when the cone surface temperature varies linearly with distance from the cone apex. The transformed boundary-layer equations contain the important parameter Gr/Re2. This parameter determines the relative importance of the free convection motions on forced convection. Numerical solutions of the transformed equations for aiding flows have been carried out for Prandtl number 0.7 and different values of Gr/Re2. Results are reported for the heat transfer, shear stress, shaft moment, and velocity and temperature fields. Criteria are given for subdividing the regimes of flow as purely free, purely forced, and combined flow. Preliminary experimental heat-transfer results are reported which indicate the trends predicted by theory.