Abstract

An analytical solution to the problem of flow in a tube with a diameter of the same order as the mean free path of the fluid is presented. Under these conditions, the Knudsen number becomes an important parameter and the fluid may exhibit slip flow and thermal nonequilibrium at the tube walls. A power-law fluid is considered to be hydrodynamically fully developed at the tube entrance and an isoflux thermal condition is assumed. A direct solution technique is applied to the Energy Equation to determine the temperature field in the thermal entrance region of the tube as well as in the thermally fully-developed region. The direct solution technique is in contrast to an indirect method reported earlier for a Newtonian fluid only. For all values of the Knudsen number, the fully-developed Nusselt number is seen to increase with a decreasing flow index n. The increase in the fully-developed Nusselt number for a shear-thinning non-Newtonian fluid (n = 0.5) relative to that for the Newtonian fluid (n = 1) decreases from approximately 9 to 3.5 percent as the Knudsen number increases from 0 (non-slip flow) to 0.12. Thus, the slip flow and temperature jump effects tend to diminish the non-Newtonian effects as they apply to the temperature field.

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