A Comparative Study of Diffusion, Thermal Wave and Dual-Phase-Lag Heat Conduction in Thin Layer

Abstract

In the present work, three different modes of heat conduction, diffusion, thermal wave, and dual-phase lag, across a thin layer subjected to a constant temperature and insulated boundary conditions are compared by using a finite element solution. The finite element model is developed by considering relaxation time to heat flux and relaxation time to temperature gradient for a single element. After assembling all the elements, the number of algebraic equations obtained is solved to predict the temperature distribution across the thin layer using Python. The solution predicted by the dual-phase lag is compared with that obtained by the single-phase Cattaneo-Vernotte's model and diffusion Fourier model. The developed model is validated with analytical, numerical, and experimental solutions with good agreement. The temperature contours are plotted for all three conditions and the way it propagates differently through the thin layer is clearly shown. Further, the temperature variation at the center of the layer, at which collision occurred, is predicted and the speed of the thermal wave, infinite in the Fourier diffusion model and finite in both single and dual-phase lag, is examined under transient to steady-state condition.

Hydration of Nitriles to Amides under In situ Nano‐Pd Catalysis in PEG‐400

“…Predominantly, hydration of nitriles to primary amides has become one of the most widely used methods in both academia and industry [3,4] . Metal catalytic systems which includes Ru, [5] Rh, [6] Au, [7] Ag, [8] Cu, [9] Zn, [10] Os, [11] Ni [12] and Co [13] were reported to promote hydration of nitriles to primary amides.…”