NUMERICAL MODELLING OF MICROSCALE EFFECTS IN CONDUCTION FOR DIFFERENT THERMAL BOUNDARY CONDITIONS

Non-Fourier microscale effects are significant during the rapid heating of metallic substrates. Recently, a two phase lag model for conduction has been proposed, which accounts for the finite propagation speed of a thermal wave and the equilibration time between the electrons and lattice. Available...

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Published inNumerical heat transfer. Part A, Applications Vol. 38; no. 5; pp. 513 - 532
Main Authors SIVA PRAKASH, G, SREEKANTH REDDY, S, DAS, Sarit K, SUNDARARAJAN, T, SEETHARAMU, K. N
Format Journal Article
LanguageEnglish
Published London Informa UK Ltd 01.10.2000
Taylor & Francis
Subjects
Condensed matter: structure, mechanical and thermal properties
Exact sciences and technology
Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves
Physics
Transport properties of condensed matter (nonelectronic)
Propagation velocity
Scale effect
Laser-radiation heating
Theoretical study
Rapid process
Boundary conditions
Numerical method
Thermal wave
Implementation
Galerkin-Petrov method
Heating
Weighted residual method
Thermal conductivity
Mathematical models
Modelling
Miniaturization
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Summary:Non-Fourier microscale effects are significant during the rapid heating of metallic substrates. Recently, a two phase lag model for conduction has been proposed, which accounts for the finite propagation speed of a thermal wave and the equilibration time between the electrons and lattice. Available closed-form solutions for the dual phase lag model are found to be very different for apparently similar boundary conditions. In this study, the origin of the discrepancy in the available analytical results has been identified as the sensitivity of the predicted solution to the way of implementing the surface boundary condition. A numerical solution procedure based on the finite element method and fourth-order Runge?Kutta time marching procedure has been employed for the spatial and temporal discretisations, respectively. The predicted results for different boundary conditions clearly capture thermal wavelike and pure diffusion-type phenomena in the appropriate range of time lag values. Application of the two phase lag model to laser pulse heating illustrates that the effects of microscale phenomena on the spatial and temporal variations of temperature could become important for high frequency pulsing.
ISSN:1040-7782
1521-0634
DOI:10.1080/104077800750020414