The interval coupled lattice Boltzmann equations for electrons and phonons are used to analyse the heating process of thin metal films. The interval lattice Boltzmann method (ILBM) with the uncertainly defined external source function associated with the laser irradiation is used to simulate the heat transfer. The solution of the interval Boltzmann transport equations has been obtained taking into account the rules of directed interval arithmetic. A similar analysis has been done using the sensitivity model where the Boltzmann transport equations and boundary-initial conditions have been differentiated with respect to the no-interval laser parameter. The knowledge of the sensitivity function distribution and the application of the Taylor formula allow one to find the border solutions of the problem analysed which correspond to the solution obtained assuming the uncertainly defined source function. In the final part of the paper the results of numerical computations obtained using both methods are presented.
REFERENCES
1.
Chonga
, W.T.
, Al-Mamoona
, A.
, Poha
, S.Ch.
, Sawb
, L.H.
, Shamshirbandc
, S.
, Mojumder
, J.Ch
., “Sensitivity analysis of heat transfer rate for smart roof design by adaptive neuro-fuzzy technique
”, Energy and Buildings
124
, 112
–119
(2016
).2.
Dems
, K.
, Rousselet
, B.
, “Sensitivity analysis for transient heat conduction in a solid body – Part I
”, Structural Optimization
17
, 36
–45
(1999
).3.
Escobar
, R.A.
, Ghai
, S.S.
, Jhon
, M.S.
, Amon
, C.H.
, “Multi-length and time scale thermal transport using the lattice Boltzmann method with application to electronics cooling
”, Journal of Heat and Mass Transfer
49
, 97
–107
(2006
).4.
Eshraghi
, M.
, Felicelli
, S.D.
, “An implicit lattice Boltzmann model for heat conduction with phase change
”, International Journal of Heat and Mass Transfer
55
, 2420
–2428
(2012
).5.
Goethals
, K.
, Breeschb
, H.
, Janssens
, A.
, “Sensitivity analysis of predicted night cooling performance to internal convective heat transfer modeling
”, Energy and Building
, 43,
2429
–2441
(2011
).6.
Huanga
S. M.
et al., “Nanobump arrays fabricated by laser irradiation of polystyrene particle layers on silicon
”, Applied Physics Letters
86
, 161911
(2005
).7.
Hwang
, S.
, Son
, Ch.
, Seo
, D.
, Rhee
, D.H.
, Cha
, B.
, “Comparative study on steady and unsteady conjugate heat transfer analysis of a high pressure turbine blade
”, Applied Thermal Engineering
99
, 765
–775
(2016
).8.
Jasiński
, M.
, “Modeling of tissue thermal injury formation process with application of direct sensitivity method
”, Journal of Theoretical and Applied Mechanics
52
, 4
, 947
–957
(2014
).9.
Joshi
, A.A.
, Majumdar
, A.
, “Transient ballistic and diffusive phonon heat transport in thin films
”, Journal of Applied Physics
74
, 1
, 31
–39
(1993
).10.
Kałuża
, G.
, Majchrzak
, E.
, Turchan
, Ł.
, “1D generalized dual-phase lag equation. Sensitivity analysis with respect to the porosity
”, Journal of Applied Mathematics and Computational Mechanics
15
, 1
, 49
–58
(2016
).11.
Kleiber
, M.
, Parameter Sensitivity in Non-linear Mechanics
(J. Willey & Sons
, London
, 1997
).12.
Majchrzak
, E.
, Mochnacki
, B.
, “Sensitivity analysis of transient temperature field in microdomains with respect to the dual phase lag model parameters
”, International Journal for Multiscale Computational Engineering
12
, 1
, 65
–77
(2014
).13.
Mansoor
, S. B.
, Yilbas
, B. S.
, “Laser short-pulse heating of silicon-aluminum thin films
”, Optical and Quantum Electronics
42
, 601
–618
(2011
).14.
Mansoor
S. B.
, Yilbas
B. S.
, “Phonon transport in aluminum and silicon film pair: laser short-pulse irradiation at aluminum film surface
”, Canadian Journal of Physics
92
, 12
, 1614
–1622
(2014
).15.
Markov
, S.M.
, “On directed interval arithmetic and its applications
”, Journal of Universal Computer Science
1
, 514
–526
(1995
).16.
Mochnacki
, B.
, Majchrzak
, E.
, “Identification of macro and micro parameters in solidification model
”, Bulletin of the Polish Academy of Sciences, Technical Sciences
55
, 1
, 107
–113
(2007
).17.
Mohebbi
, F.
, Sellier
, M.
, “Estimation of thermal conductivity, heat transfer coefficient, and heat flux using a three dimensional inverse analysis
”, International Journal of Thermal Sciences
99
, 258
–270
(2016
).18.
Narumanchi
, S.
, Murthy
, J.Y.
, Amon
, C.H.
, “Simulation of unsteady small heat source effects in sub-micron heat conduction
”, Journal of Heat Transfer
123
, 896
–903
(2003
).19.
Neumaier
, A.
, Interval methods for system of equations
(Cambridge University Press
, Cambridge, New York
, Port Chester, Melbourne, Sydney, 1990
).20.
Piasecka Belkhayat
, A.
, Korczak
, A.
, “Modelling of transient heat transport in one-dimensional crystalline solids using the interval lattice Boltzmann method”, Recent Advances in Computational Mechanics
(Eds. T.
Łodygowski
, J.
Rakowski
and P.
Litewka
), Taylor & Francis Group, A Balkema Book
, London
, 363
–368
(2014
).21.
Piasecka Belkhayat
A.
, Korczak
A.
, “Numerical modelling of the transient heat transport in a thin gold film using the fuzzy lattice Boltzmann method with α-cuts
”, Journal of Applied Mathematics and Computational Mechanics
15
, 1
, 123
–135
(2016
).22.
Yilbas
, B.S.
, “A closed form solution for temperature rise inside solid substrate due to time exponentially varying pulse
”, International Journal of Heat and Mass Transfer
45
, 1993
–2000
(2002
).23.
Zhang
, X.
, Chu
, S.S.
, Ho
, J.R.
, Grigoropoulos
, C.P.
, “Excimer laser ablation of thin gold films on a quartz crystal microbalance at various argon background pressures
”, Applied Physics A
64
, 545
–55
(1997
).
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