A Method to Obtain the Analytical Solution of the Thermal Conduction Equation with Moving Boundaries

1983 ◽  
pp. 349-356 ◽  
Author(s):  
Lianke Dong ◽  
Liangyu Bai ◽  
Benlian Zhou
Keyword(s):  
Analytical Solution ◽  
Thermal Conduction ◽  
Moving Boundaries ◽  
Conduction Equation ◽  
Thermal Conduction Equation

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.

Analytical Solution of Thermal Stresses in a Functionally Graded Solid Cylinder within Parabolic Continuous Grading

2013 ◽  
Vol 307 ◽  
pp. 364-367 ◽  
Author(s):  
Ali Ozturk ◽  
Müfit Gülgeç
Keyword(s):  
Thermal Expansion ◽  
Analytical Solution ◽  
Material Properties ◽  
Thermal Conduction ◽  
Thermal Stresses ◽  
Elasticity Modulus ◽  
Functionally Graded ◽  
Solid Cylinder ◽  
Graded Materials ◽  
Parabolic Form

This paper presents analytical solutions of the thermal stresses in a functionally graded solid cylinder with fixed ends in elastic region. These thermal stresses are due to the uniform heat generation inside the cylinder. Material properties of the functionally graded (FG) cylinder vary radially according to a parabolic form. The material properties are assumed to be independent of the temperature which are yield strength, elasticity modulus, thermal conduction coefficient, thermal expansion coefficient and Poisson’s ratio. The solutions for the thermal stresses are valid for both homogeneous and functionally graded materials.

Analytical Solution for Three-Dimensional Hyperbolic Heat Conduction Equation with Time-Dependent and Distributed Heat Source

2016 ◽  
Vol 33 (1) ◽  
pp. 65-75 ◽  
Author(s):  
M. R. Talaee ◽  
V. Sarafrazi
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Heat Source ◽  
Heat Conduction Equation ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Closed Form Solution ◽  
Time Dependent ◽  
Conduction Equation ◽  
Hyperbolic Heat Conduction

AbstractThis paper is devoted to the analytical solution of three-dimensional hyperbolic heat conduction equation in a finite solid medium with rectangular cross-section under time dependent and non-uniform internal heat source. The closed form solution of both Fourier and non-Fourier profiles are introduced with Eigen function expansion method. The solution is applied for simple simulation of absorption of a continues laser in biological tissue. The results show the depth of laser absorption in tissue and considerable difference between the Fourier and Non-Fourier temperature profiles. In addition the solution can be applied as a verification branch for other numerical solutions.

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