This paper describes a hybrid analytical-numerical solution of conjugate heat transfer of laminar flow in a circular duct with axial wall conduction. An improved lumped-differential formulation is used to treat heat conduction in the wall; the Generalised Integral Transform Technique (GITT) is used to solve the energy equation in laminar flow. The coupled partial differential equations in the solid and fluid regions are reduced to a set of coupled ordinary differential equations. Analytical solution is obtained for a truncated set of ordinary differential equations. Improvement is expected over classical lumped models which are only applicable to problems with Biot numbers less than 0.1.

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