Inversion of a heat transform by use of series

1967 ◽  
Vol 18 (1) ◽  
pp. 389-413 ◽  
Author(s):  
D. V. Widder
Keyword(s):  
Heat Transform

ESTIMATION OF THERMAL CONDUCTIVITY OF POROUS MATERIAL WITH FEM AND FRACTAL GEOMETRY

2009 ◽  
Vol 20 (04) ◽  
pp. 513-526 ◽  
Author(s):  
SHOUJU LI ◽  
YUEFANG WANG ◽  
YINGXI LIU ◽  
WEI SUN
Keyword(s):  
Thermal Conductivity ◽  
Fractal Dimension ◽  
Porous Material ◽  
Effective Thermal Conductivity ◽  
Pore Space ◽  
Thermal Flux ◽  
Solid Matrix ◽  
The Finite Element Method ◽  
Heat Transform ◽  
The Relationship

The relationship between thermal conductivity of porous material and fractal dimension is numerically simulated by using the finite element method. The solid matrix and pore space are generated randomly according to material porosity. Material parameters and element properties are changed by using ANSYS parameter design language. The effective thermal conductivity is derived according to thermal flux through some sections computed by FEM and Fourier heat transform law. The investigation shows that the effective thermal conductivity decreases with increasing porosity. The effective thermal conductivity will decrease exponentially with increasing fractal dimension of porosity space and increase exponentially with increasing fractal dimension of solid matrix.

scholarly journals On generalized heat polynomials

1988 ◽  
Vol 11 (2) ◽  
pp. 393-400 ◽  
Author(s):  
C. Nasim
Keyword(s):  
Heat Equation ◽  
Power Function ◽  
Initial Temperature ◽  
Series Representation ◽  
Generalized Heat Equation ◽  
Heat Transform

We consider the generalized heat equation ofnthorder∂2u∂r2+n−1r∂u∂r−α2r2u=∂u∂t. If the initial temperature is an even power function, then the heat transform with the source solution as the kernel gives the heat polynomial. We discuss various properties of the heat polynomial and its Appell transform. Also, we give series representation of the heat transform when the initial temperature is a power function.

Sign in / Sign up

Export Citation Format

Share Document