Heat transfer by laminar Hartmann's flow in thermal entrance region with uniform wall heat flux: the Graetz problem extended

2003 ◽  
Vol 44 (1) ◽  
pp. 11-34 ◽  
Author(s):  
J. Lahjomri ◽  
K. Zniber ◽  
A. Oubarra ◽  
A. Alemany
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Heat Flux ◽  
Entrance Region ◽  
Graetz Problem ◽  
Thermal Entrance Region ◽  
Uniform Wall ◽  
Thermal Entrance ◽  
Uniform Wall Heat Flux

Laminar Convective Heat Transfer of a Bingham Plastic in a Circular Pipe With Uniform Wall Heat Flux: The Graetz Problem Extended

1999 ◽  
Vol 121 (3) ◽  
pp. 556-563 ◽  
Author(s):  
T. Min ◽  
J. Y. Yoo
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Yield Stress ◽  
Wall Heat Flux ◽  
Circular Pipe ◽  
Bingham Plastic ◽  
Graetz Problem ◽  
Uniform Wall ◽  
Uniform Wall Heat Flux

Thermally developing laminar flow of a Bingham plastic in a circular pipe with uniform wall heat flux has been studied analytically. Expressions for the fully developed temperature and Nusselt number are presented in terms of the yield stress, Peclet number, and Brinkman number. The solution to the Graetz problem has been obtained by using the method of separation of variables, where the resulting eigenvalue problem is solved approximately by using the method of weighted residuals. The effects of the yield stress, Peclet, and Brinkman numbers on the Nusselt number are discussed. In particular, it is shown that the heat transfer characteristics in the entrance region are significantly affected by the yield stress with the inclusion of viscous dissipation.

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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