On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature
Abstract
:1. Introduction
- (i)
- the microscopic theory of reversibility of Onsager [2] is violated;
- (ii)
- it neglects the time needed for the acceleration of heat flow by free electrons (Sharma, [9]);
- (iii)
- (iv)
- the development of Fourier’s law was from observations at steady state;
- (v)
- (vi)
- Landau and Lifshitz observed the contradiction of the infinite speed of propagation of heat with Einstein’s light speed barrier [23];
- (vii)
- Fourier’s law breaks down at the Casimir limit [24].
2. Materials and Methods
2.1. Free Electron Theory
2.2. Derivation of Alternate Non-Fourier Conduction Equation
2.3. Entropy Production Term
2.4. Transport Parameters
3. Results and Discussion
4. Conclusions
Acknowledgments
Conflicts of Interest
Abbreviations
AN | Avagadro Number (6.023 × 1023 molecules/mole) |
A | cross-sectional area across which transport occurs (m2) |
CA | concentration of species A (mol/m3) |
CB | concentration of species B (mol/m3) |
Cp | heat capacity of material at constant pressure (J/mole/K) |
Cv | heat capacity of material at constant volume (J/mole/K) |
DAB | binary diffusion coefficient of species A in B (m2/s) |
erf(z) | error function of z. |
f | molecular drag coefficient (kg/s/molecule) |
k | thermal conductivity of the material (W/m/K) |
kB | Boltzmann Constant (J/molecule/K) |
H | enthalpy (J/mole) |
J″ | area averaged molar flux (mole/m2/s) |
Jp(x) | Bessel function of the pth order and first kind |
Ip(x) | modified Bessel function of the pth order and first kind |
t | time (s) |
T | Temperature ( °K) |
m | mass of the molecule (kg) |
N | molecular weight of oligonucleotide (kg/mole) |
qz | heat flux (area averaged) (W/m2) |
n | electron density (# of electrons/m3) |
R | universal molar gas constant (J/mole/K) |
R0 | radius of solute molecule (m) |
S | entropy (J/mole/K) |
u | dimensionless concentration, |
u(s) | temperature in Laplace domain |
ve | velocity of electron (m/s) |
vA | velocity of solute molecule (m/s) |
vy | velocity of fluid in y cartesian direction (m/s) |
vm | velocity of mass (m/s) |
z | z Cartesian distance (m) |
Z | dimensionless distance |
vh | velocity of heat (m/s) |
Zpen | dimensionless penetration distance |
Greek
σ | Entropy production term (W/m3/K) |
α | thermal diffusivity of material (m2/s) |
t | collision time of the electron and obstacle (seconds) |
τ | Dimensionless time in governing equation |
τr | relaxation time (heat) of material (s) |
τmr | relaxtion time (mass) of material (s) |
ρ | density of material (kg/m3) |
τxy | tangential shear stress (N/m2) |
τmom | relaxtion time (momentum) (s) |
µA | chemical potential (J/molecule) |
µ | viscosity (kg/m/s) |
λ2 | retardation time (s) |
xA | mole fraction of species A |
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Sharma, K.R. On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature. C 2016, 2, 1. https://doi.org/10.3390/c2010001
Sharma KR. On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature. C. 2016; 2(1):1. https://doi.org/10.3390/c2010001
Chicago/Turabian StyleSharma, Kal Renganathan. 2016. "On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature" C 2, no. 1: 1. https://doi.org/10.3390/c2010001
APA StyleSharma, K. R. (2016). On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature. C, 2(1), 1. https://doi.org/10.3390/c2010001