This paper considers the conjugate problem of convective heat transfer in microchannel coupled to the conduction problem within the channel wall thickness. A Graetz-type simplification is assumed, for which the flow is dynamically developed, while being thermally developing. The boundary conditions for the problem are applied within the outer thickness of the channel wall, and both a constant heat flux condition and a constant are analyzed. The solution procedure is based on the Generalized Integral Transform Technique, by means of which, the temperature field within the fluid and solid wall are expressed in terms of orthogonal eigenseries expansions. The solution is implemented within a computational framework and verified against previously published results and analyses of simple limiting cases. After verification, the effects of the velocity profile and wall thickness on the Nusslet numb are investigated.

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