Numerical Technique for Resolving the Dual Phase Lag Heat Conduction in Thin Film Metal

Abstract

In this article, a three-time level finite difference scheme is used to resolve the dual phase lag’s (DPL) heat conduction in a micro scale gold film subjected to spontaneous temperature boundary conditions without knowing the heat flux. Finite difference analog of DPL equation on applying to the intermediate grid points of the computational domain results into a system of linear, algebraic equations which can be solved using Thomas’ algorithm to finally obtain the transient temperature solution distributions in the film. The solution predicted by the DPL model is compared with that obtained by the single-phase Cattaneo–Vernotte’s model. Further, the way in which non-Fourier’s temperature distributions affected by the diffusion due to the increase in Heat Conduction Model numbers agree with the predecessor’s published results. The results by both the models revealed a finite thermal wave speed in the film contrasting the infinite speed of heat propagation as stated by the classical Fourier’s thermal model. Low spatial step and higher order finite difference schemes are recommended for better accurate numerical results of the non-Fourier’s temperature distributions occurring in the very short transient period between the instants of the suddenly applied spatial temperature gradient and the reaching of the steady state conditions.

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Notes on contributors

Dhanaraj Savary Nasan

Dhanaraj Savary Nasan is a faculty in the Department of Mechanical Engineering at the National Institute of Technology, Tadepalligudem, Andhra Pradesh, India. He received his M.Tech. degree in Thermal Engineering in 2008 from the Jawaharlal Nehru Technological University, Hyderabad, India and has recently submitted his Ph.D. thesis at the same university. His main research interests are computational fluid dynamics, heat transfer, and Tesla turbines.

Thopudurthi Karthikeya Sharma

Thopudurthi Karthikeya Sharma is a faculty in the Department of Mechanical Engineering at the National Institute of Technology Andhra Pradesh, Tadepalligudem, Andhra Pradesh, India. He received his Ph.D. degree from National Institute of Technology Warangal in 2016, and M.Tech. degree in Refrigeration and Air- Conditioning in 2011 from the Jawaharlal Nehru Technological University, Anantapur, India. His main research interests are computational fluid dynamics, internal combustion engines, homogeneous charge compression ignition combustion, heat transfer, refrigeration and air conditioning.

Gadale Amba Prasad Rao

Gadale Amba Prasad Rao is working as a Professor in the Department of Mechanical Engineering, NIT Warangal, India. He has been teaching for 25 years. His areas of interest are internal combustion engines, alternate fuels, emissions and its control, and engine simulation.

Kotha Madhu Murthy

Kotha Madhu Murthy is working as a Professor in Department of Mechanical Engineering, NIT Warangal, India. He has been teaching for 30 years. His areas of interest are internal combustion engines, emissions control, industrial management, and entrepreneurship.