The paper reports the results of a parametric investigation on the effects of temperature dependent viscosity and thermal conductivity on forced convection in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Uniform temperature boundary conditions are specified at the microchannel walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries, namely circular and flat microchannels, are considered. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. The parabolic approximation of the Navier-Stokes and energy equations can be considered adequate for values of the Reynolds and Péclet numbers larger than 50. Computed axial distributions of the local Nusselt number are presented for different values of the Brinkman number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain an approximate value of the Nusselt number by separately considering the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity. Finally, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is almost independent of the value of the Brinkman number, i.e., it is approximately the same no matter whether viscous dissipation is negligible or not.

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