The heat flux vector for highly inhomogeneous nonequilibrium fluids in very narrow pores

1995 ◽  
Vol 103 (22) ◽  
pp. 9804-9809 ◽  
Author(s):  
B. D. Todd ◽  
Denis J. Evans
Keyword(s):  
Heat Flux ◽  
Flux Vector ◽  
Heat Flux Vector

PROPERTIES OF HEAT FLUX FUNCTIONS AND A LINEAR THEORY OF HEAT FLUX

1995 ◽  
Vol 09 (09) ◽  
pp. 1113-1122 ◽  
Author(s):  
LIQIU WANG
Keyword(s):  
Thermal Conductivity ◽  
Heat Flux ◽  
Temperature Gradient ◽  
Linear Function ◽  
Linear Theory ◽  
Strain Tensor ◽  
Positive Definiteness ◽  
Positive Definite ◽  
Flux Vector ◽  
Heat Flux Vector

The symmetry and positive definiteness of thermal conductivity tensor K are used to derive some properties of heat flux functions ɸi (i=0, 1, 2). All ɸi are shown to be real-valued. Both ɸ0 and ɸ2 are found to be positive definite, and ɸ1 is constrained between −(ɸ0 + ɸ2) and (ɸ0 + ɸ2). By assuming heat flux vector q to be a linear function of temperature gradient ∇θ and velocity strain tensor D, ɸi reduce to three coefficients which are independent of D and ∇θ.

Heat flux vector in highly inhomogeneous nonequilibrium fluids

1995 ◽  
Vol 51 (5) ◽  
pp. 4362-4368 ◽  
Author(s):  
B. D. Todd ◽  
Peter J. Daivis ◽  
Denis J. Evans
Keyword(s):  
Heat Flux ◽  
Flux Vector ◽  
Heat Flux Vector

Hydromagnetic waves for a collisionless plasma in strong magnetic fields

1985 ◽  
Vol 34 (1) ◽  
pp. 67-76 ◽  
Author(s):  
S. Duhau ◽  
A. De La Torre
Keyword(s):  
Heat Flux ◽  
Collisionless Plasma ◽  
Phase Speed ◽  
Larmor Radius ◽  
Heat Conducting ◽  
Flux Vector ◽  
Heat Flux Vector ◽  
Vector Direction ◽  
Hydromagnetic Waves ◽  
Dynamic Variables

A hydrodynamic system of equations, valid in the limit in which the Larmor radius and the electron to ion mass ratio are both zero, and including the thermo-dynamic variables and the energy equation of the electrons, is used to investigate the propagation of small-amplitude waves in a collisionless heat-conducting plasma. The result is compared with that derived from the Chew, Goldberger & Low equations. It is found that for zero heat flux, the inclusion of the electron pressure does not change the number and characteristic of the modes but modifies the mirror stability criterion. In the general case, the phase speed is symmetric with respect to two axes: one parallel to the heat flux vector and the other normal to it. The heat flux generates a new mode and couples strongly the slow and fast magnetosonic modes whose wavenumber vectors have projections in the positive flux vector direction, giving rise to a new overstability whose existence does not depend on the ion anisotropy.

scholarly journals Heat Flux Distribution Near a Crevasse

1963 ◽  
Vol 4 (34) ◽  
pp. 461-465
Author(s):  
C. J. Pings
Keyword(s):  
Heat Flux ◽  
Heat Flow ◽  
Flux Distribution ◽  
Temperature Data ◽  
Flux Vector ◽  
Heat Flux Distribution ◽  
Flow Lines ◽  
Heat Flux Vector ◽  
Graphical Differentiation ◽  
Improved Accuracy

AbstractPreviously reported experimental temperature data were used to compute the two components of the heat flux vector in the ice body adjacent to a crevasse in a glacier of the ice sheet of northern Greenland. Graphical differentiation techniques were employed. The computed components were used to synthesize values of the beat flux vector, including magnitude and direction. Improved accuracy was achieved over the previously reported technique of sketching heat flow lines orthogonal to the isotherms.

scholarly journals A Constitutive Formulation for the Linear Thermoelastic Behavior of Arbitrary Fiber-Reinforced Composites

2010 ◽  
Vol 2010 ◽  
pp. 1-19 ◽  
Author(s):  
Melek Usal
Keyword(s):  
Heat Flux ◽  
Free Energy ◽  
Composite Material ◽  
Series Expansion ◽  
Symmetric Tensor ◽  
Elastic Behavior ◽  
Free Energy Function ◽  
Flux Vector ◽  
Conservation Of Energy ◽  
Heat Flux Vector

The linear thermoelastic behavior of a composite material reinforced by two independent and inextensible fiber families has been analyzed theoretically. The composite material is assumed to be anisotropic, compressible, dependent on temperature gradient, and showing linear elastic behavior. Basic principles and axioms of modern continuum mechanics and equations belonging to kinematics and deformation geometries of fibers have provided guidance and have been determining in the process of this study. The matrix material is supposed to be made of elastic material involving an artificial anisotropy due to fibers reinforcing by arbitrary distributions. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and two vectors whereas the heat flux vector function is dependent on a symmetric tensor and three vectors. The free energy and heat flux vector functions have been represented by a power series expansion, and the type and the number of terms taken into consideration in this series expansion have determined the linearity of the medium. The linear constitutive equations of the stress and heat flux vector are substituted in the Cauchy equation of motion and in the equation of conservation of energy to obtain the field equations.

Heat Flux Vector Potential in Convective Heat Transfer

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Vector Potential ◽  
Heat Convection ◽  
Two Dimensional ◽  
Flux Vector ◽  
Heat Function ◽  
Heat Flux Vector

The heat function concept introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) for two-dimensional (2D) heat transfer is being extended in this note to three dimensions. It is shown that a heat flux vector potential exists and can be used in three-dimensional (3D) heat convection problems. It is further shown that this heat flux vector potential degenerates to the heat function introduced by Kimura and Bejan (1983, “The Heatline Visualization of Convective Heat Transfer,” ASME J. Heat Transfer, 105(4), pp. 916–919) when the heat convection is two-dimensional.

scholarly journals Entropy Analysis for a Nonlinear Fluid with a Nonlinear Heat Flux Vector

Entropy ◽  
2017 ◽  
Vol 19 (12) ◽  
pp. 689 ◽  
Author(s):  
Hyunjin Yang ◽  
Mehrdad Massoudi ◽  
A. Kirwan
Keyword(s):  
Heat Flux ◽  
Flux Vector ◽  
Entropy Analysis ◽  
Heat Flux Vector ◽  
Nonlinear Fluid

scholarly journals Effect of voids in a heat-flux dependent theory for thermoelastic bodies with dipolar structure

2020 ◽  
Vol 36 (3) ◽  
pp. 463-474
Keyword(s):  
Heat Flux ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Uniqueness Result ◽  
The Body ◽  
Flux Vector ◽  
Dependent Theory ◽  
Heat Flux Vector ◽  
Independent Variable ◽  
Initial Boundary Value

In our paper we formulate a theory for thermoelastic porous dipolar bodies in which we consider a new independent variable, namely the heat-flux vector. Furthermore, we add, to the differential equations that describe the behavior of the body, a new differential equation which is an equation of evolution which is satisfied by the components of the heat-flux vector. The basic system of the mixed initial-boundary value problem in this context consists of equations of the hyperbolic type. In order to ensure the consistency of the constructed theory, we formulate and prove an uniqueness result, with regards to the solution of the mixed problem.

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