A Discussion of Transpiration Cooling Problems through an Analytical Solution of Local Thermal Nonequilibrium Model

2006 ◽  
Vol 128 (10) ◽  
pp. 1093-1098 ◽  
Author(s):  
J. H. Wang ◽  
H. N. Wang
Keyword(s):  
Analytical Solution ◽  
Biot Number ◽  
Thermal Conduction ◽  
Porous Plate ◽  
Local Thermal Equilibrium ◽  
Transpiration Cooling ◽  
Thermal Nonequilibrium ◽  
Cooling Effects ◽  
Local Thermal Nonequilibrium ◽  
Hot Surface

To study transpiration cooling problems, an analytical solution of the local thermal nonequilibrium (LTNE) model with the second or third boundary conditions is presented. This solution is obtained through neglecting the thermal conduction of the fluid coolant in porous media. By the analytical solution, two problems are investigated. At first, the parameters which influence transpiration cooling effects are analyzed, and the analysis indicates that the cooling effects are dominated by coolant mass flow rate, the Biot number at the hot surface of porous plate, and the Biot number in the pores. Second, the error caused by the assumption of the local thermal equilibrium (LTE) model is quantitatively discussed, and the variation trend of the LTE error is analyzed. Based on the analytical solution and the error analysis, a quantitative criterion to choose the LTNE or LTE model is suggested, and the corresponding expression is also given in this paper.

scholarly journals A heat transfer analysis from a porous plate with transpiration cooling

2019 ◽  
Vol 23 (5 Part B) ◽  
pp. 3025-3034 ◽  
Author(s):  
Mustafa Kilic
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Porous Plate ◽  
Particle Diameter ◽  
Heat Transfer Analysis ◽  
Transpiration Cooling ◽  
Cooling Efficiency ◽  
Cooling Effectiveness ◽  
Cooling Effects ◽  
Air Channel

Present study is focused on improving heat transfer from a porous plate by cooling of air with transpiration cooling. Effects of Reynolds number of the air channel flow and particle diameter on cooling effectiveness of porous plate and efficiency of system were investigated experimentally. It was observed that increasing Reynolds number of 15.2% causes a decrease of 6.9% on cooling efficiency of the system and a decrease of 8.6% on cooling effectiveness of porous plate. Decreasing particle diameter causes a significant decrease on surface temperature and an increase on cooling effectiveness of porous plate. Difference of cooling effectiveness of porous plate from dp = 40-200 ?m is 12%. Verification of this study was also shown by comparing experimental results of this study with literature.

Convective Instability of the Darcy Flow in a Horizontal Layer With Symmetric Wall Heat Fluxes and Local Thermal Nonequilibrium

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
A. Barletta ◽  
M. Celli ◽  
A. V. Kuznetsov
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Solid Phase ◽  
Fluid Phase ◽  
Heat Fluxes ◽  
Local Thermal Equilibrium ◽  
Neutral Stability ◽  
Thermal Nonequilibrium ◽  
Local Thermal Nonequilibrium ◽  
Darcy Rayleigh Number

The linear stability of the parallel Darcy throughflow in a horizontal plane porous layer with impermeable boundaries subject to a symmetric net heating or cooling is investigated. The onset conditions for the secondary thermoconvective flow are expressed through a neutral stability bound for the Darcy–Rayleigh number associated with the uniform heat flux supplied or removed from the walls. The study is performed by taking into account a condition of local thermal nonequilibrium between the solid phase and the fluid phase. The linear stability analysis is carried out according to the normal modes' decomposition of the perturbations to the basic state. The governing equations for the disturbances are solved numerically as an eigenvalue problem leading to the neutral stability condition. If compared with the asymptotic condition of local thermal equilibrium, the regime of local nonequilibrium manifests an enhanced instability. This behavior is displayed by lower critical values of the Darcy–Rayleigh number, eventually tending to zero when the thermal conductivity of the solid phase is much larger than the conductivity of the fluid phase. In this special limit, which can be invoked as an approximate model of a gas-saturated metallic foam, the basic throughflow is always unstable to external disturbances of arbitrarily small amplitude.

TRANSPIRATION COOLING WITH LOCAL THERMAL NONEQUILIBRIUM: MODEL COMPARISON IN MULTIPHASE FLOW IN POROUS MEDIA

2016 ◽  
Vol 19 (2) ◽  
pp. 131-153 ◽  
Author(s):  
Franz Lindner ◽  
Philipp Nuske ◽  
Kilian Weishaupt ◽  
Rainer Helmig ◽  
Christian Mundt ◽  
...  
Keyword(s):  
Porous Media ◽  
Multiphase Flow ◽  
Model Comparison ◽  
Flow In Porous Media ◽  
Transpiration Cooling ◽  
Thermal Nonequilibrium ◽  
Nonequilibrium Model ◽  
Local Thermal Nonequilibrium

Discussion of Boundary Conditions of Transpiration Cooling Problems Using Analytical Solution of LTNE Model

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
Jianhua Wang ◽  
Junxiang Shi
Keyword(s):  
Temperature Field ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Coolant Temperature ◽  
Transpiration Cooling ◽  
Dimensional Problem ◽  
Gas Temperature ◽  
One Dimensional ◽  
Hot Gas ◽  
Hot Surface

To compare five kinds of different boundary conditions (BCs), an analytical solution of a steady and one-dimensional problem of transpiration cooling described by a local thermal nonequilibrium (LTNE) model is presented in this work. The influence of the five BCs on temperature field and thermal effectiveness is discussed using the analytical solution. Two physical criteria, if the analytical solution of coolant temperature may be higher than hot gas temperature at steady state and if the variation trend of thermal effectiveness with coolant mass flow rate at hot surface is reasonable, are used to estimate the five BCs. Through the discussions, it is confirmed which BCs at all conditions are usable, which BCs under certain conditions are usable, and which BCs are thoroughly unreasonable.

Free Convection and Mass Transfer Flow Near a Moving Vertical Porous Plate: An Analytical Solution

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
C. J. Toki
Keyword(s):  
Mass Transfer ◽  
Analytical Solution ◽  
Free Convection ◽  
Schmidt Number ◽  
Porous Plate ◽  
Grashof Number ◽  
Vertical Porous Plate ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Transfer Flow

An exact solution of the problem of the unsteady free convection and mass transfer flow near an infinite vertical porous plate, which moves with time-dependent velocity in a viscous and incompressible fluid, is presented here by the Laplace transform technique. All expressions of the new solutions of the present problem were obtained in closed forms with arbitrary Prandtl number (Pr), Schmidt number (Sc), thermal Grashof number (Gr), and mass Grashof number (Gm). Two applications of physical interest for porous or nonporous plate are discussed. Applying numerical values into the expressions of analytical solution, we was also discussed the vertical air flows—the usual phenomenon at plumes into the atmosphere.

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