Joule heating induced heat transfer for electroosmotic flow of power-law fluids in a microcapillary

Capillary electrophoresis systems mainly used for chemical analyses and biomedical diagnoses usually involve biofluids in electrolyte buffers which cannot be treated as Newtonian fluids. In addition, the presence of Joule heating can limit the performance of capillary electrophoresis systems. This study presents a detailed analysis of Joule heating induced heat transfer for electroosmotic flow (EOF) of power-law fluids in a microcapillary. The steady, fully developed EOF field of power-law fluids governed by the Cauchy momentum equation is solved analytically by using two approximate schemes for modified Bessel functions, I ₀(x) and I ₁(x). Subsequently, under the widely accepted assumption of thin electric double layer (EDL) in microfluidics, an exact solution for temperature field induced by Joule heating is analytically solved from the energy equation subject to a mixed thermal boundary condition outside the capillary. Closed form expressions are obtained for the two-dimensional temperature field, the average fluid temperature and the local Nusselt number in both thermally developing and thermally developed regions. It is found that the rheological properties of power-law fluids affect the heat transfer characteristics mainly through the thermal Peclet number.