This paper presents semi-analytical solutions to the Extended Graetz Problem in micro-channels. The flow driving mechanism is electroosmosis combined with a pressure gradient. The hypothesis of a thin electrical double layer (EDL) is not considered, leading to a more realistic model. The considered problem is that of laminar flow in a rectangular channel. The solution methodology is based on the Generalized Integral Transform Technique. The presented solution yields a closed-form expression for calculating the Nusselt number. The only numerical step required by the solution involves the numerical computation of eigenvalues and eigenvectors, necessary for a matrix exponential evaluation. With the results, the effects of the channel geometry and flow driving mechanisms on the Nusselt number are analyzed.

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