Analysis of Steady State Conjugate Heat Transfer in a Circular Microtube Inside a Substrate

The steady state heat transfer for laminar flow inside a circular microtube within a rectangular substrate has been investigated. Silicon, Silicon Carbide, and Stainless Steel were the substrates used and Water and FC-72 were the coolants employed. Equations governing the conservation of mass, momentum, and energy were solved in the fluid region. Within the solid wafer, the heat conduction was solved. A thorough investigation for velocity and temperature distributions for different substrates and coolants was performed by varying geometrical dimensions and Reynolds number. At a constant diameter and Reynolds number, for combinations comprising same coolant but different substrates, one with the lowest solid to fluid thermal conductivity ratio (k_s/k_f) attains the highest local peripheral average interface temperature. It was found that the Nusselt number is more for a system with Silicon as the substrate and FC-72 as the working fluid and the least for a system with Stainless Steel as the substrate and Water as the working fluid. The lower k_s/k_f ratio of Stainless Steel-Water combination is the main reason for the lower Nusselt number. With the increase in hydraulic diameter and Reynolds number, the average Nusselt number increased. It was also observed that the maximum temperature of the substrate and hence the outlet temperature of the fluid increased as the Reynolds number decreased.