The problem considered is that of determining the heat losses from a gas flowing turbulently in a poorly insulated pipe where the heat lost from the outer surface is by free convection and radiation. The approach employed in solving the heat equation is analogous to that first introduced by Latzko for the solution of the uniform wall temperature problem. Later, in 1957, Fettis obtained a solution to the same problem in terms of Jacobi polynomials. A method for coupling the inner convection with the environment is given in the later portion of the paper. The results obtained for a numerical case are also presented.

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