Unsteady Laminar Forced Convective Tube Flow Under Dynamic Time Dependent Heat Flux

Abstract

A new alltime model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary timedependent heat flux. Slug flow (SF) condition is assumed for the velocity profile inside the tube. The solution to the timedependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel's integral technique. A cyclic timedependent heat flux is considered and new compact closedform relationships are proposed to predict (i) fluid temperature distribution inside the tube, (ii) fluid bulk temperature and (iii) the Nusselt number. A new definition, cyclic fully developed Nusselt number, is introduced and it is shown that in the thermally fully developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forcedconvective tube flow. We also performed an independent numerical simulation using ansys fluent to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.