Axial Heat Conduction in the Fluid

In the following sections, the main deviations from classical theory for the calculation of heat transfer in microchaimels are discussed. This discussion includes axial heat conduction in the fluid, conjugate heat transfer, surface roughness, viscous dissipation, thermophysical property variations, electric double layers, entrance region and measurement accuracy. Whenever possible, the reader is referred to design criteria and Nu correlations when the different aspects have to be taken into account. 

Axial conduction in the fluid leads to an increased temperature difference between the wall and the fluid. Therefore, Nu decreases in the entrance region. Axial 

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In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. 

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