The study of non-linear transport in gas flows associated with micro and nanodevices has emerged as an important topic in recent years. In the field of microscale heat transfer, convective heat transfer in slip-flow regimes in simple geometries like channels and tubes is a key problem. Constant-wall-temperature convective heat transfer in microscale tubes and channels has been studied recently using analytical solutions to an extended Graetz problem. In addition, much effort has been put into the development of computational models beyond the theory of linear constitutive relations for the analysis of microscale gas flow and heat transfer, since the Navier-Stokes-Fourier theory is not known to remain valid in the flow regimes of large Knudsen number. The objective of the present paper is to investigate microscale heat transfer where temperature jump is the dominant phenomena. The emphasis will be on the qualitative features of microscale heat transfer, for example, enhancement or reduction of heat transfer in microscale geometries. General features of computational models such as the full kinetic model and fluid dynamics model are also discussed.

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