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

C—Journal of Carbon Research

Kal Renganathan Sharma¹ 

[1] Electrical Program, San Jacinto College Central Campus, 8060 Spencer Highway, Pasadena, TX 77505, USA

关键词: law of heat conduction;    acceleration of spinless electron;    free electron theory;    method of laplace transforms;    bessel composite function;    transient temperature;    second law of thermodynamics;   

DOI  :  10.3390/c2010001

来源: mdpi

【 摘 要 】

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).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. For 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.

【 授权许可】

CC BY   
© 2015 by the author; licensee MDPI, Basel, Switzerland.