Significance Of Deciphering Jeffrey's Heat Conduction Equation By Taylor's Series For Knowing The Instants Of Temperature Gradient And Heat Flux

Dhanaraj Savary Nasan*, T. Kishen Kumar Reddy**
*Research Scholar, R & D Cell, Jawaharlal Nehru Technological University, Hyderabad, India.
**Professor, Department of Mechanical Engineering, Jawaharlal Nehru Technological University, Hyderabad, India
Periodicity:November - January'2015
DOI : https://doi.org/10.26634/jme.5.1.3067

Abstract

It is well known that the heat flux constitutive model of Jeffrey's type heat transport equation yields various modes of thermal energy transport. The significance of varying a given parameter “K” in the equation starting from zero and the sequence of events describing the hyperbolic (propagative / non-Fourier) wave nature of the thermal energy transport through a mildly hyperbolic transition to a fully parabolic (diffusive / Fourier) is well described in the earlier works. Based on the Taylor's series expansion, this paper interprets the Jeffrey's type heat transport equation from strategic computational method point of view so as to incorporate the parameter “K” as the time difference in the series expansion of the temperature in time at a given spatial point. This paper not only leads to better understanding of the parameter “K” as the time lag between the temperature gradient as the driving potential and its response the heat flux, but also transforms the Jeffrey's thermal model into a computationally advantageous form similar to that of Fourier's thermal model. This paper is the introducer to the series of research works carried out in the computational methods for characterizing and resolving Jeffrey's thermal problems culminating to a most power full numerical scheme in CFD, the Flow field Dependent Variation (FDV) method

Keywords

Thermo Elasticity, Non-Fourier, Hyperbolic, Thermal / Heat waves, Second Sound, Relaxation Time, Phonons, Unified CFD (computational Fluid Dynamics) Method & Flow Field Dependent Variation (FDV) Theory

How to Cite this Article?

Nasan, D. S., and Reddy, T. K. K. (2015). Significance of Deciphering Jeffrey's Heat Conduction Equation by Taylor's Series For Knowing The Instants of Temperature Gradient and Heat Flux. i-manager’s Journal on Mechanical Engineering, 5(1), 12-17. https://doi.org/10.26634/jme.5.1.3067

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