Effects of the Slip Flow and Viscous Dissipation on the Graetz Problem in Microchannels

In this chapter, the slip flow and viscous dissipation effects on the Graetz problem in microchannels are investigated. The developed velocity profile and the temperature distribution are analytically calculated using an original method. At the inlet, a non-uniform temperature profile satisfying the energy equation in the entrance section is imposed. The Nusselt number is determined in terms of the Knudsen and Brinkman numbers and some known values of the fully developed Nusselt number are validated using the literature. It is found that for a constant pressure drop, the Nusselt number increases as the Knudsen number increases. With viscous dissipation for the no-slip flow, the value of the Brinkman number has no influence on the fully developed Nusselt number. However, the fully developed Nusselt number value increases as the Knudsen number increases. The different values of the Brinkman number change the Nusselt number only in the thermal entrance region before reaching the constant independent value at different lengths.