Asymptotic analysis for the conjugate heat transfer problem in an electro-osmotic flow with temperature-dependent properties in a capillary

In this work, the conjugate heat transfer process in an electro-osmotic flow of a Newtonian liquid is studied asymptotically. The analysis includes Joule heating effects by taking into account the temperature dependent viscosity and electrical conductivity of the electrolyte solution and assuming finite thermal conductivity of the capillary wall. Due to Joule heating effects, temperature gradients in the liquid make the fluid properties change within the capillary, altering the electric potential and flow fields. The dimensionless temperature profiles in the fluid and the capillary wall are obtained as function of the dimensionless parameters involved in the analysis, and the interactions between the coupled continuity, momentum, thermal energy, and potential electric equations are examined in detail. Results show that the Joule heating induces a pressure gradient along the capillary, which in turn modifies the normal plug-like electroosmotic velocity profiles. In addition, it is pointed out that, depending on the values of the dimensionless parameters, the modified velocity profiles can induce positive or negative pressure gradients at the inlet or outlet of the capillary.