Joule-heating effects in mixed electro-osmotic and pressure-driven microflows under constant wall heat flux

Heat-transfer characteristics of mixed electro-osmotic and pressure-driven flows are obtained in a two-dimensional straight microchannel by a solving steady-state energy equation. Both thermally developing and fully developed regions are considered for hydraulically fully developed mixed flows under isoflux channel wall conditions. The steady temperature distribution is obtained from the superposition of homogeneous solution and particular function. The particular solution is derived based on the constant heat-flux condition in the fully developed region, while the homogeneous solution is presented in terms of infinite series containing Kummer confluent hypergeometric functions due to the existence of non-self-adjoint eigenvalues. The coefficients of the homogeneous solution are found by utilizing the Gram-Schmidt orthogonalization procedure, and the Secant method is utilized to obtain the corresponding eigenvalues. Our analytical techniques are verified by obtaining an excellent agreement with existing literature for slug, pressure-driven, and pure electroosmotic flow cases. In the fully developed region, the Nusselt number of mixed flow is independent of the thermal Peclet number for a particular Joule heating and imposed surface heat flux. The entry length of mixed flow significantly depends on the applied/induced pressure gradient to the electro-osmotic flow