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.

scholarly journals ANALYTICAL SOLUTION OF A 2D TRANSIENT HEAT CONDUCTION PROBLEM USING GREEN´S FUNCTIONS

2020 ◽  
Vol 19 (1) ◽  
pp. 66
Author(s):  
J. R. F. Oliveira ◽  
J. A. dos Santos Jr. ◽  
J. G. do Nascimento ◽  
S. S. Ribeiro ◽  
G. C. Oliveira ◽  
...  
Keyword(s):  
Temperature Field ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Conduction Problem ◽  
Transient Heat Conduction ◽  
Heat Fluxes ◽  
Two Dimensional ◽  
One Dimensional ◽  
Transient Heat Conduction Problem

Through the present work the authors determined the analytical solution of a transient two-dimensional heat conduction problem using Green’s Functions (GF). This method is very useful for solving cases where heat conduction is transient and whose boundary conditions vary with time. Boundary conditions of the problem in question, with rectangular geometry, are of the prescribed temperature type - prescribed flow in the direction x and prescribed flow - prescribed flow in the direction y, implying in the corresponding GF given by GX21Y22. The initial temperature of the space domain is assumed to be different from the prescribed temperature occurring at one of the boundaries along x. The temperature field solution of the two-dimensional problem was determined. The intrinsic verification of this solution was made by comparing the solution of a 1D problem. This was to consider the incident heat fluxes at y = 0 and y = 2b tending to zero, thus making the problem one-dimensional, with corresponding GF given by GX21. When comparing the results obtained in both cases, for a time of t = 1 s, it was seen that the temperature field of both was very similar, which validates the solution obtained for the 2D problem.

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.

An Experimental Investigation of the Temperature Field Produced by a Cryosurgical Cannula

1974 ◽  
Vol 96 (3) ◽  
pp. 415-420 ◽  
Author(s):  
T. E. Cooper ◽  
W. K. Petrovic
Keyword(s):  
Experimental Investigation ◽  
Temperature Field ◽  
Liquid Crystals ◽  
Analytical Solution ◽  
Growth Rates ◽  
Experimental Results ◽  
Experimental Uncertainty ◽  
One Dimensional ◽  
Ice Growth

Liquid crystals, a material that exhibits brilliant changes in color over narrow temperature bands, have been successfully used to study the temperature field that is produced by a cryosurgical cannula (cryoprobe). Cryoprobe tip temperatures ranging from −36 to −117 C were used to produce frozen regions in a clear gel. Experimental results compare within experimental uncertainty with results of a one-dimensional analytical solution for predicting ice growth rates.

scholarly journals Numerical study of one-dimensional Stefan problem with periodic boundary conditions

2013 ◽  
Vol 17 (5) ◽  
pp. 1453-1458
Author(s):  
Liang-Hui Qu ◽  
Feng Ling ◽  
Lin Xing
Keyword(s):  
Boundary Condition ◽  
Temperature Field ◽  
Boundary Conditions ◽  
Stefan Problem ◽  
Periodic Boundary ◽  
Moving Boundary ◽  
Numerical Study ◽  
Periodic Boundary Conditions ◽  
One Dimensional ◽  
Stefan Number

A finite difference approach to a one-dimensional Stefan problem with periodic boundary conditions is studied. The evolution of the moving boundary and the temperature field are simulated numerically, and the effects of the Stefan number and the periodical boundary condition on the temperature distribution and the evolution of the moving boundary are analyzed.

Self-similar elastic regime of filtration through moving boundary

2018 ◽  
Vol 13 (3) ◽  
pp. 64-72 ◽  
Author(s):  
S.V. Khabirov ◽  
S.S. Khabirov
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Boundary Problem ◽  
Moving Boundary ◽  
Dimensional Problem ◽  
One Dimensional ◽  
Elastic Regime ◽  
Self Similar ◽  
The One ◽  
The Relationship

The one-dimensional problem of elastic filtration of fluid through moving boundary is considered. The boundary conditions for invariant problem is introduced. The problem is reduced to overdetermine boundary problem for Veber equation. The exact solutions are obtained. For arbitrary invariant filtration law the relationship between overdetermine invariant boundary conditions is obtained.

The transport equation with plane symmetry and isotropic scattering

1964 ◽  
Vol 60 (4) ◽  
pp. 909-921 ◽  
Author(s):  
M. G. Smith
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Point Sources ◽  
The Other ◽  
Isotropic Scattering ◽  
Dimensional Problem ◽  
Plane Symmetry ◽  
Double Integral ◽  
One Dimensional ◽  
The One

AbstractThe double integral equation, which takes the place of the Milne equation in the one-dimensional problem, is derived from the governing partial differentio-integral equations. An analytical solution of the problem of a distribution of point sources on a plane, when the other boundaries are at infinity, is then found. The possibility of more complicated boundary conditions is discussed.

scholarly journals Analytical Solution of Homogeneous One-Dimensional Heat Equation with Neumann Boundary Conditions

2020 ◽  
Vol 1551 ◽  
pp. 012002
Author(s):  
Norazlina Subani ◽  
Faizzuddin Jamaluddin ◽  
Muhammad Arif Hannan Mohamed ◽  
Ahmad Danial Hidayatullah Badrolhisam
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
One Dimensional
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