The Third Problem for the Laplace Equation with a Boundary Condition from Lp

2005 ◽  
Vol 54 (2) ◽  
pp. 235-258 ◽  
Author(s):  
Dagmar Medková
Keyword(s):  
Boundary Condition ◽  
Laplace Equation ◽  
The Third

Forced convection in ducts with a boundary condition of the third kind

10.2514/3.744 ◽  
1995 ◽  
Vol 9 (4) ◽  
pp. 800-802 ◽  
Author(s):  
R. C. Xin ◽  
Z. F. Dong ◽  
M. A. Ebadian ◽  
W. Q. Tao
Keyword(s):  
Boundary Condition ◽  
Forced Convection ◽  
The Third

Heat Transfer in Composite Spheroids

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rajai Alassar
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Prolate Spheroid ◽  
Published Data ◽  
Composite Sphere ◽  
Legendre Series ◽  
The Third ◽  
Type Boundary ◽  
Type Boundary Condition ◽  
The Impact

Abstract Heat transfer from a composite prolate spheroid under the third-type boundary condition is investigated using a Legendre series expansion. The model is verified against published data on cooling boiled eggs and also against the asymptotic solution of a composite sphere. The impact of Biot number on the heat transfer in spheroids with realistic dimensions and properties, such as eggs and olives, is investigated. The results are also presented for varying conductivity ratios and fractional volume of the inner part of the spheroid.

scholarly journals Volume derivatives of the Grüneisen parameter in the limit of infinite pressure

2019 ◽  
Vol 97 (1) ◽  
pp. 114-116 ◽  
Author(s):  
A. Dwivedi
Keyword(s):  
Boundary Condition ◽  
Fourth Order ◽  
Fundamental Theorem ◽  
High Pressures ◽  
Grüneisen Parameter ◽  
Third Order ◽  
Gruneisen Parameter ◽  
The Third ◽  
Properties Of Materials ◽  
Derivatives Of

Expressions have been obtained for the volume derivatives of the Grüneisen parameter, which is directly related to the thermal and elastic properties of materials at high temperatures and high pressures. The higher order Grüneisen parameters are expressed in terms of the volume derivatives, and evaluated in the limit of infinite pressure. The results, that at extreme compression the third-order Grüneisen parameter remains finite and the fourth-order Grüneisen parameter tends to zero, have been used to derive a fundamental theorem according to which the volume derivatives of the Grüneisen parameter of different orders, all become zero in the limit of infinite pressure. However, the ratios of these derivatives remain finite at extreme compression. The formula due to Al’tshuler and used by Dorogokupets and Oganov for interpolating the Grüneisen parameter at intermediate compressions has been found to satisfy the boundary condition at infinite pressure obtained in the present study.

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