# Interdisciplinary Applied Mathematics

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Variation of temperature profiles across the channel is given in Figure 5.13 as a function of Mach number. Both the continuum and the rarefied flow cases are presented. Here, the nondimensional heat flux of q = ±1 is specified at the bottom surface of the channel. The temperature jump

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—0.15

Y (Slip Flow)

FIGURE 5.14. Variation of temperature profiles in a shear-driven channel flow for continuum and rarefied flows. The top row shows insulated channels, and the bottom row shows cooled channels with equation (5.18) such that there are no thermal creep effects (i.e.,    = 0). Re = 1.0 and Pr = 0.7.

effects are clearly seen in the rarefied flow case. In a microchannel the temperature of the insulated surface is less than that of the continuum predictions for heated channels, while the opposite is true for cooled channels. The effects of thermal creep on volumetric flowrate of the channel depends on the direction that the flow is sheared by the top surface, and whether the channel is cooled or heated. As long as the driving velocity Uis in the same direction with increasing , the volumetric flowrate of the channel will increase due to the thermal creep effects.

The temperature jump diminishes if both surfaces of the channel are insulated (see Figure 5.14, top). For this case, the viscous heating effect in a microchannel is less than the continuum prediction. Therefore, the temperature differences of top and bottom surfaces are relatively small in microchannels compared to the continuum case. It is also possible to specify heat flux on the boundaries that will cancel the viscous heating effects. This case gives zero tangential temperature gradient on the microchannel walls.

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