Previous Article in Journal
Using Vegetation near CO2 Mediated Enhanced Oil Recovery (CO2-EOR) Activities for Monitoring Potential Emissions and Ecological Effects
Previous Article in Special Issue
Raman Spectra of Carbon-Based Materials (from Graphite to Carbon Black) and of Some Silicone Composites

Article

# On Description of Acceleration of Spinless Electrons in Law of Heat Conduction a capite ad calcem in Temperature

Electrical Program, San Jacinto College Central Campus, 8060 Spencer Highway, Pasadena, TX 77505, USA
Received: 17 August 2015 / Revised: 20 November 2015 / Accepted: 22 December 2015 / Published: 30 December 2015
Acceleration effects of heat flow are included in the law of heat conduction by eliminating the acceleration term between the equation of motion for a spinless electron and the Boltzmann equipartition energy theorem differentiated with respect to time. The resulting law of heat conduction is a capite ad calcem in temperature as given in Equations (17), (19) and (20). (qz/k)z = -(δT/δz) - 1/vh(δT/δt). Evaluation of use of this equation using the entropy production term reveals that as long as the flux, q, and the temperature accumulation both have the same signs, the law does not violate the second law of thermodynamics. For systems that obey the first law of thermodynamics, this is the case. σ == q/T2(q/k + 1/vh • q(δT/δt)). In the chemical potential Stokes-Einstein formulation, when acceleration of the molecule is accounted for, a law of diffusion a capite ad calcem concentration results. In cartesian one-dimensional heat conduction in semi-infinite coordinates, the governing equation for temperature or concentration was solved for by the method of Laplace transforms. The results are in terms of the modified Bessel composite function in space and time of the first order and first kind. This is when τ > X. X > τ the solution is in terms of the Bessel composite function in space and time of the first order and first kind. The wave temperature is a decaying exponential in time when X = τ. An approximate expression for dimensionless temperature was obtained by expanding the binomial series in the exponent in the Laplace domain and after neglecting fourth- and higher-order terms before inversion from the Laplace domain. The Fourier model, the damped wave model and the a capite ad calcem in temperature/concentration model solutions are compared side by side in the form of a graph. The a capite ad calcem model solution is seen to undergo the convex to concave transition sooner than the damped wave model. The results of the a capite ad calcem temperature model for distances further from the surface are closer to the Fourier model solution. View Full-Text
Show Figures

Graphical abstract

MDPI and ACS Style

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://0-doi-org.brum.beds.ac.uk/10.3390/c2010001

AMA Style

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://0-doi-org.brum.beds.ac.uk/10.3390/c2010001

Chicago/Turabian Style

Sharma, Kal R. 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://0-doi-org.brum.beds.ac.uk/10.3390/c2010001

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

1