The onset of longitudinal vortex rolls in the thermal entrance region of plane Poiseuille flow heated with a constant heat flux

2006 ◽  
Vol 49 (19-20) ◽  
pp. 3708-3716 ◽  
Author(s):  
Joung Hwan Park ◽  
Tae Joon Chung ◽  
Eun Suk Yun ◽  
Min Chan Kim ◽  
Chang Kyun Choi
Keyword(s):  
Heat Flux ◽  
Poiseuille Flow ◽  
Constant Heat Flux ◽  
Entrance Region ◽  
Longitudinal Vortex ◽  
Plane Poiseuille Flow ◽  
Constant Heat ◽  
Thermal Entrance Region ◽  
Thermal Entrance

Testing of Rectangular Channels With Perturbed Entrances for Temperature Difference Under Constant Heat Flux

2011 ◽  
Author(s):  
Jacek Marek Matyja ◽  
Tunde Bello-Ochende
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Heat Transfer Performance ◽  
Cold Water ◽  
Constant Heat Flux ◽  
Entrance Region ◽  
Average Error ◽  
Transfer Performance ◽  
Rectangular Duct ◽  
Constant Heat

In this paper convective heat transfer performance of various duct geometries are compared using theoretical and experimental analyses. The experiments stretch further by perturbing the entrance region of the 2:1 rectangular duct (both inwards and outwards) and to obtain the effect on heat transfer performance. The cross-sectional area and length of the ducts are fixed and constant heat flux is applied to the ducts while cold water is used as the flow stream. The laminar flow regime is analysed. The theoretical and experimental cases are in agreement, with slight deviances attributed to certain assumptions made during the theoretical analysis and non-ideal testing conditions. The analyses concludes that perturbing the entrance region of a standard rectangular duct, both inwards and outwards, has a visible increase in heat transfer performance. The inward perturbed duct shows the highest increase in performance. The average variation between the theoretical and experimental case is about 18% for constant heat flux. The average error imposed on the results due experimental equipment is about 3% for constant heat flux experiments.

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.

Convective Instability in the Thermal Entrance Region of a Horizontal Parallel-Plate Channel Heated from Below

1973 ◽  
Vol 95 (1) ◽  
pp. 72-77 ◽  
Author(s):  
G. J. Hwang ◽  
K. C. Cheng
Keyword(s):  
Prandtl Number ◽  
Parallel Plate ◽  
Entrance Region ◽  
Longitudinal Vortex ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Thermal Entrance Region ◽  
Plate Channel ◽  
Thermal Entrance ◽  
Perturbation Equations

An investigation is carried out to determine the conditions marking the onset of longitudinal vortex rolls due to buoyant forces in the thermal entrance region of a horizontal parallel-plate channel where the lower plate is heated isothermally and the upper plate is cooled isothermally. Axial heat conduction is included in an analytical solution for the Graetz problem with fully developed laminar velocity profile. Linear-stability theory based on Boussinesq approximation is employed in the derivation of perturbation equations. An iterative procedure using high-order finite-difference approximation is applied to solve the perturbation equations and a comparison is made against the conventional second-order approximation. It is found that for Pr ≥ 0.7 the flow is more stable in the thermal entrance region than in the fully developed region, but the situation is just opposite for small Prandtl number, say Pr ≤ 0.2. Graphical results for the critical Rayleigh numbers and the corresponding disturbance wavenumbers are presented for the case of Pe → ∞ with Prandtl number as a parameter and the case of air (Pr = 0.7) with Peclet number as a parameter in the range of dimensionless axial distance from the entrance between x = 0.001 and 4 × 10−1.

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