Unsteady thermal entrance heat transfer of power-law fluids in pipes and plate slits

Abstract

An instant-local similarity method is proposed to analyze the unsteady state Graetz problems. Unsteady heat transfer for fully-developed laminar flow of power-law non-Newtonian fluids in the thermal entrance region of pipes and plate slits, with viscous dissipation considered, is studied. For the unsteady thermal entrance heat transfer problems, only large Graetz numbers (small normalized axial distance) are concerned and the normalized time from transient up to steady state is of order 10 −1; therefore, the instant-local similarity approach gives results of high accuracy. The effects of the flow index, viscous dissipation and Graetz number on the heat transfer rate are demonstrated with numerical solutions. The corresponding steady-state Graetz problems are studied by the local similarity method whose solutions agree very well with the extended Leveque solutions particularly for large Graetz number and Brinkman number.