The present analysis deals with the conjugate problem of combined free and forced convection through vertical non-circular ducts. The equations coupling heat conduction in the walls with the convection inside the fluid are solved to establish the influence of peripheral wall conduction, using variational technique. Fully developed laminar flow with uniform axial heat input and constant fluid properties, except for the small variation of density in the buoyancy term of the momentum equation, is assumed. The problem has been solved in a generalized way and the results have been presented for rectangular ducts. It is found that large values of the free convection effects and/or of the conduction parameter tend to minimize the asymmetries in circumferential wall temperature.

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