Theoretical analysis of heat transfer in laminar pulsating flow (Q1348577)

This paper presents a theoretical study of pulsation effect on heat transfer in laminar incompressible flow in a circular tube starting from basic principles in an attempt to eliminate existing confusion at various levels. Pulsatile flow is frequently encountered in natural systems as well as engineering systems, such as circulation system, respiratory system, reciprocating pumps, pulse combustors, etc. The authors consider here the developing region in order to investigate the effect of different parameters, under different types of boundary conditions. Namely, two different cases of non-ideal boundary conditions are considered. The first case is that of a finite thermal resistance between fluid and its environment (called Robin-type boundary condition), while in the second case the tube wall is considered to have a finite thermal capacity. In the both cases, the governing equations are solved analytically and numerically. Also, a new time-averaged heat transfer coefficient for pulsating flow is defined such as to produce results that are both useful from the engineering point of view, and consistent with the energy balance. Thus, the effects of Reynolds and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated in detail. There are many new and interesting results obtained in this paper: one of these conclusions is that, as long as the analysis is restricted to laminar incompressible flow, with linear boundary conditions, the effect of pulsation on the time-averaged heat transfer coefficient tends to be negative, but remains relatively small. Nonlinear boundary conditions combined with pulsation may result in a noticeable enhancement of the time-averaged Nusselt number.