Slip flow heat transfer in rectangular microchannels

Understanding slip flow internal convection characteristics has been of great importance in the emerging development of micro thermal fluid systems. Since rectangular or trapezoidal microchannels are the most probable mode of fluid conduits, this research is directed toward analytically investigating slip flow laminar thermal entry problems for rectangular microchannels. The subjects investigated include: (1) the two most common boundary conditions—isothermal and isoflux, (2) axial conduction effects, (3) behavior of entrance Nusselt numbers, and (4) analytical solution techniques. The isoflux circular tube case is also analytically studied for completeness. Slip flow heat transfer problems are modeled using continuum momentum and energy equations with slip flow boundary conditions. Analytical solutions for rectangular ducts are obtained using a modified integral transform technique, whereas for the circular tube the separation of variable method is employed. The solutions are transformed into compact forms by introducing two dimensionless variables that reflect microscale effects and the fluid/wall interaction. It is found that heat transfer may increase, decrease, or remain unchanged for both isothermal and isoflux boundary conditions and for both rectangular ducts and circular tubes, compared to nonslip flow conditions, strongly depending on the two dimensionless variables. The dependence of heat transfer on aspect ratios and axial conduction is also investigated. The transition points that separate heat transfer enhancement from reduction are identified for the various cases. The universal nature of the entrance Nusselt number for slip flow is described. This entrance Nusselt number is always finite and can be evaluated by a simple equation that includes slip flow parameters. It is further verified that the entrance Nusselt number characteristics are valid for both isothermal or isoflux boundary conditions and for any conduit geometry.