Hydrodynamic and heat transfer aspects of low Peclet gaseous flows through an isothermally heated pipe

Abstract

For the gaseous flow applications involving axial diffusion of heat, the hydrodynamic and thermal aspects get erroneously predicted if the conventional extended Graetz problem is attended. The present work highlights such deviations of the flow field and the respective derived parameters under the influence of axial conduction and radial advection with the variation of thermophysical properties retained. The complete transport equations are numerically solved for the low Peclet (Pe) gaseous flows through a circular pipe for the Pe and wall temperature in the ranges [1–100] and [350–1200 K], respectively. The results are validated for the conventional case of the extended Graetz problem with its conditional assumptions. For the general case, it is observed that the required pipe length is overpredicted when the property variation is not accounted for. The rising wall temperature tends to shift the whole non-isothermal region upstream that we tabulate for its extreme ends for the limiting cases. The spatially varying strength of diffusion and advection bring in the non-parabolic and non-self-similar velocity profile that reports sheer dependence on the supplied heat. The Nusselt number is seen to drop to a minimum before increasing to the asymptotic value, and the respective axial locations are found to be varying with Pe and the supplied heat.