Wavelets in the Solution of Nongray Radiative Heat Transfer Equation

1998 ◽  
Vol 120 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Y. Bayazitoglu ◽  
B. Y. Wang
Keyword(s):  
Transfer Equation ◽  
Solution Method ◽  
Radiative Heat ◽  
Radiative Transfer Equation ◽  
Basis Functions ◽  
Wavelet Basis ◽  
System Of Equations ◽  
Heat Transfer Equation ◽  
One Dimensional ◽  
The One

The wavelet basis functions are introduced into the radiative transfer equation in the frequency domain. The intensity of radiation is expanded in terms of Daubechies’ wrapped-around wavelet functions. It is shown that the wavelet basis approach to modeling nongrayness can be incorporated into any solution method for the equation of transfer. In this paper the resulting system of equations is solved for the one-dimensional radiative equilibrium problem using the P-N approximation.

scholarly journals New Application for the Generalized Incomplete Gamma Function in the Heat Transfer of Nanofluids via Two Transformations

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Hibah S. Alhawiti
Keyword(s):  
Heat Transfer ◽  
Exact Solution ◽  
Boundary Conditions ◽  
Gamma Function ◽  
Transfer Equation ◽  
Nonlinear Differential Equations ◽  
Incomplete Gamma Function ◽  
Heat Transfer Equation ◽  
Layer Flow ◽  
The One

The boundary layer flow of nanofluids is usually described by a system of nonlinear differential equations with infinity boundary conditions. These boundary conditions at infinity are transformed into classical boundary conditions via two different transformations. Accordingly, the original heat transfer equation is changed into a new one which is expressed in terms of the new variable. The exact solutions have been obtained in terms of the exponential function for the stream function and in terms of the incomplete Gamma function for the temperature distribution. Furthermore, it is found in this project that a certain transformation reduces the computational work required to obtain the exact solution of the heat transfer equation. Hence, such transformation is recommended for future analysis of similar physical problems. Besides, the other published exact solution was expressed in terms of the WhittakerM function which is more complicated than the generalized incomplete Gamma function of the current analysis. It is important to refer to the fact that the analytical procedure followed in our project is easier and more direct than the one considered in a previous published work.

FREE-BOUNDARY PROBLEM OF THE ONE-DIMENSIONAL EQUATIONS FOR A VISCOUS AND HEAT-CONDUCTIVE GASEOUS FLOW UNDER THE SELF-GRAVITATION

2013 ◽  
Vol 23 (08) ◽  
pp. 1377-1419 ◽  
Author(s):  
MORIMICHI UMEHARA ◽  
ATUSI TANI
Keyword(s):  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Global Solvability ◽  
The Self ◽  
Fundamental Result ◽  
System Of Equations ◽  
One Dimensional ◽  
Unique Existence ◽  
The One

In this paper we consider a system of equations describing the one-dimensional motion of a viscous and heat-conductive gas bounded by the free-surface. The motion is driven by the self-gravitation of the gas. This system of equations, originally formulated in the Eulerian coordinate, is reduced to the one in a fixed domain by the Lagrangian-mass transformation. For smooth initial data we first establish the temporally global solvability of the problem based on both the fundamental result for local in time and unique existence of the classical solution and a priori estimates of its solution. Second it is proved that some estimates of the global solution are independent of time under a certain restricted, but physically plausible situation. This gives the fact that the solution does not blow up even if time goes to infinity under such a situation. Simultaneously, a temporally asymptotic behavior of the solution is established.

scholarly journals A Numerical Variational Method for Calculating Accurate Vibrational Energy Separations of Small Molecules and Their Ions

1986 ◽  
Vol 39 (5) ◽  
pp. 749 ◽  
Author(s):  
G Doherty ◽  
MJ Hamilton ◽  
PG Burton ◽  
EI von Nagy-Felsobuki
Keyword(s):  
Finite Element ◽  
Variational Method ◽  
Small Molecules ◽  
Vibrational Energy ◽  
Basis Functions ◽  
Variational Procedure ◽  
One Dimensional ◽  
Trial Wavefunction ◽  
Vibrational Energies ◽  
The One

A combination of known methods have been spliced together in order to calculate accurate vibrational energies and wavefunctions. The algorithm is based on the Rayleigh-Ritz variational procedure in which the trial wavefunction is a linear combination of configuration products of one-dimensional basis functions. The Hamiltonian is that due to Carney and Porter (1976). The kernel of the algorithm consists o( the one-dimensional basis functions, which are the finite element solutions of the associated one-dimensional problems.

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