In this paper, we consider a heat transfer problem of forced convection of liquids in an arbitrary straight channel with arbitrarily prescribed wall heat flux when the flow is steady, laminar, and of constant-property type and when the effect of viscous dissipation is taken into account. The assumption of fully developed flow has been made. An arbitrary heat source is assumed to be present in the channel. The general solution of the problem, in terms of integral formulas, is directly presented by using the methods of conformal transformation. In a separate section, some aspects of the problem are discussed briefly, especially with respect to wall heat-flux function, heat-source function, and mapping function, and a general series solution is then given. In the end, the problem of a cardioid duct is investigated numerically, and the results of nondissipative and dissipative cases are compared.

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