Solution for Transient Conjugated Forced Convection in the Thermal Entrance Region of a Duct With Periodically Varying Inlet Temperature

Abstract

This work presents an analytical solution of the transient conjugated laminar forced convection problem of a slug flow in the thermal entrance region inside a parallel plate duct. A solution in series form is already known for this kind of problem. This solution leads to a complex eigenvalue problem with transcendental equations. The present solution obtained by using the Laplace transform completely eliminates this problem. The amplitudes and phase lags with respect to the inlet conditions are determined for the complex wall temperature, fluid bulk temperature, and wall heat flux from this solution. The results are plotted for comparison with the results obtained with the series solution.

Application of integral transform technique to the transient laminar flow heat transfer in the ducts

“…The investigations on forced convection with periodic inlet temperature have been performed by numerous researchers [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The solution of heat transfer problems of this type usually leads to a non classical Sturm-Liouville complex system which no known solutions are available.…”

“…In references [7][8][9][10][11][12][13][14][15][16], the methodologies used in the previous works are advanced further by considering the effects of heat capacity of a duct wall. Sparrow and Farias [7] seem to be the first investigators who included the effect of wall conjugation.…”

A simplified approach to solving conjugate heat transfer problems in annular and dissimilar parallel plate ducts

“…Sucec and Sawant (1984) used a quasi-steady approach with the actual parabolic fully developed velocity profile to study the unsteady conjugate heat transfer problems in a parallel plate channel with periodic variations in the inlet fluid temperature with time. Travelho and Santos (1991) presented an analytical solution for transient conjugate forced convection in the entrance region of a duct with periodically varying inlet temperature. Olek et al (1991) pressented an analytical solution for a similar problem in laminar pipe flow, where the flow is both hydrodynamically and thermally fully developed.…”

Adaptive neuro-fuzzy modeling of transient heat transfer in circular duct air flow

“…Transient convective heat transfer in tubes and ducts is very important in connection with the control of modern high performance heat transfer devices, and has been widely studied [1][2][3][4][5][6][7][8][9][10][11][12][13]. Problems arising from start-ups, shut-downs, power surges and pump failures etc., during normal operating conditions or time-varying inlet temperature and flow rates can induce the transient behavior in thermal equipment.…”