THERMAL ENTRANCE REGION HEAT TRANSFER FOR RECTANGULAR DUCTS OF VARIOUS ASPECT RATIOS AND PECLET NUMBERS

1969 ◽  
Author(s):  
J. R. Dewitt ◽  
W. T. Snyder
Keyword(s):  
Heat Transfer ◽  
Entrance Region ◽  
Aspect Ratios ◽  
Thermal Entrance Region ◽  
Thermal Entrance

scholarly journals Heat transfer in the thermal entrance region of a flat duct

1975 ◽  
Vol 19 (2) ◽  
pp. 146-160 ◽  
Author(s):  
A. S. Jones
Keyword(s):  
Heat Transfer ◽  
Circular Tube ◽  
Fluid Velocity ◽  
Axial Direction ◽  
Entrance Region ◽  
Heat Transfer Mechanism ◽  
Axial Diffusion ◽  
Axial Temperature ◽  
Thermal Entrance Region ◽  
Thermal Entrance

AbstractThe problem of heat transfer in a duct or tube for large values of the Péclet number has traditionally been solved by assuming that diffusion in the axial direction is negligible. This approach was used by Graetz [2] for the circular tube and by Prins et al [5] for the flat duct to obtain a series solution for downstream temperature field.Since these series converge very slowly in the neighbourhood of the origin, some other approach is necessary in the thermal entrance region. This was supplied by Lévêque [3] and extended by Mercer [4] who matched the Lévêque solution to the eigenfunction expansion.In all these solutions it was assumed that the axial diffusion of heat was negligible, but this assumption is invalid close to the discontinuity, since in this region the axial temperature gradient is large and the fluid velocity is small, so that axial diffusion plays an important role.In this paper, the assumptions implicit in Lévêque's solution are re-examined, and the correct approximation in the neighbourhood of the discontinuity as well as the solution which matches this into Lévêque's solution are presented. In the first of these solutions, diffusion is the only heat-transfer mechanism, while in the matching solution diffusion and convection are in balance.The corresponding solutions for the case of prescribed flux on the boundary are also considered.

Transient Heat Transfer for Laminar Forced Convection in the Thermal Entrance Region of Flat Ducts

1959 ◽  
Vol 81 (1) ◽  
pp. 29-36 ◽  
Author(s):  
R. Siegel ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Steady State ◽  
Thermal Response ◽  
Step Function ◽  
Entrance Region ◽  
Arbitrary Time ◽  
Unit Step ◽  
Thermal Entrance Region ◽  
Thermal Entrance

An analysis is made for transient laminar heat transfer in the thermal entrance region of a flat duct (parallel plate channel) whose bounding surfaces are subjected to an arbitrary time variation of temperature or of heat flux. Initially, the system may be either in an already established steady-state heat-transfer situation, or else, the fluid and duct walls may be at the same uniform temperature. The velocity distribution in the flow is taken to be fully developed and unchanging with time. The solution for arbitrary time-dependent conditions is obtained by generalizing the thermal response to a unit step change in wall temperature or in wall heat flux. This step-function response is found by using the method of characteristics. Heat-transfer results are presented as simple analytical expressions. The time required to achieve steady state after a unit step is also given. Working formulas are summarized at the end of the paper.

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