Integral transform solution for heat transfer in parallel-plates micro-channels: Combined electroosmotic and pressure driven flows with isothermal walls

This paper presents an analytical solution for heat transfer problems that occur in micro-channel flows driven by the combined effect of electroosmosis and a pressure gradient. Fully developed velocity profiles are considered, leading to an extended version of the Graetz problem. The formulation includes axial diffusion, viscous dissipation and Joule heating effects, and cases with both thin and thick electric double layers are analyzed. The adopted solution methodology is based on the Generalized Integral Transform Technique, which leads to a coupled boundary-value ODE system that can be integrated analytically. Although the solution is analytical, a numerical step for calculating eigenvalues and eigenvectors is required in the solution of the resulting ODE system. With the solution of the temperature field, the convergence behavior of the Nusselt number is investigated for different test-cases. The effects of different parameters such as EDL thickness, flow driving mechanism, Péclet number, Brinkman number, and a Joule heating parameter are analyzed. The results demonstrate that the convergence is strongly dependent on axial position and the Péclet number.