Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-04T19:07:56.915Z Has data issue: false hasContentIssue false
  • English
  • Français

Exact Analytical Hyperbolic Temperature Profile in a Three-Dimensional Media Under Pulse Surface Heat Flux

Published online by Cambridge University Press:  29 December 2015

M. R. Talaee ,
V. Sarafrazi  and
S. Bakhshandeh
M. R. Talaee*
Affiliation:
School of Railway EngineeringIran University of Science and Technology (IUST)Tehran, Iran
V. Sarafrazi
Affiliation:
School of Railway EngineeringIran University of Science and Technology (IUST)Tehran, Iran
S. Bakhshandeh
Affiliation:
School of Railway EngineeringIran University of Science and Technology (IUST)Tehran, Iran
*
*Corresponding author ([email protected])
Get access

Abstract

In this paper three-dimensional hyperbolic heat conduction equation in a cubic media with rectangular cross-section under a pulsed heat flux on the upper side has been solved analytically using the method of separation of variables and the Duhamel integral. The closed form solution of both Fourier and non-Fourier profiles are introduced with both modes of steady and pulsed fluxes. The results show the considerable difference between the Fourier and Non-Fourier temperature profiles. Then the answer procedure is used for modeling of interaction of a cubical tissue under a short laser pulse heating. The effects of pulse duration and laser intensity are studied analytically. Furthermore the results can be applied as a verification branch for other numerical solutions or laser treatments of biological tissues.

Keywords

Hyperbolic heat conductionTime-dependent boundary conditionsThree-dimensional cartesian coordinatesTissue laser interaction
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. 339 - 347
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Cattaneo, C., “A Form of Heat Conduction Equation Which Eliminates the Paradox of Instantaneous Propagation,” Compute Rendus, 247, pp. 431–433 (1958).Google Scholar
2.Vernotte, P., “Les Paradoxes De La Théorie Continue De I'Equation De La Chaleur,” Compute Rendus, 246, pp. 3154–3155(1958).Google Scholar
3.Chandrasekharaiah, D. S., “Hyperbolic Thermoelasticity: A Review of Recent Literature,” Applied Me chanics Reviews, 51, pp. 705–729 (1998).CrossRefGoogle Scholar
4.Tang, D. W. and Araki, N., “Non-Fourier Heat Conduction in a Finite Medium Under Periodic Surface Thermal Disturbance,” International Journal of Heat and Mass Transfer, 39, pp. 1585–1590 (1996).Google Scholar
5.Tang, D. W. and Araki, N., “Non-Fourier Heat Conduction in a Finite Medium Under Periodic Surface Thermal Disturbance-II, Another Form of Solution,“ International Journal of Heat and Mass Transfer, 39, pp. 3305–3308 (1996).Google Scholar
6.Tang, D. W. and Araki, N., “Analytical Solution of Non-Fourier Temperature Response in a Finite Medium Under Laser-Pulse Heating,” International Journal of Heat and Mass Transfer, 31, pp. 359–363 (1996).CrossRefGoogle Scholar
7.Tang, D. W. and Araki, N., “Non-Fourier Heat Conduction Behavior in Finite Mediums Under Pulse Surface Heating,” Materials Science and Engineering, A, 292, pp. 173–178 (2000).Google Scholar
8.Lewandowska, M. and Malinowski, L., “Hyperbolic Heat Conduction in the Semi-Infinite Body with the Heat Source Which Capacity Linearly Depends on Temperature,” International Journal of Heat and Mass Transfer, 33, pp. 389–393 (1998).CrossRefGoogle Scholar
9.Lewandowska, M. and Malinowski, L., “Ananalytical Solution of the Hyperbolic Heat Conduction Equation for the Case of a Finite Medium Symmetrically Heated on Both Sides,” International Communication in Heat and Mass Transfer, 33, pp. 61–69 (2006).Google Scholar
10.Abdel-Hamid, B., “Modeling Non-Fourier Heat Conduction with Periodic Thermal Oscillation Using the Finite Integral Transform,” Applied Mathematical Modelling, 23, pp. 899–914 (1999).Google Scholar
11.Moosaie, A., “Non Fourier Heat Conduction in a Finite Medium Subjected to Arbitrary Periodic Surface Disturbance,” International Communication in Heat and Mass Transfer, 34, pp. 996–1002 (2007).CrossRefGoogle Scholar
12.Moosaie, A., “Non-Fourier Heat Conduction in a Finite Medium Subjected to Arbitrary Non-Periodic Surface Disturbance,” International Communication in Heat and Mass Transfer, 35, pp. 376–383 (2008).Google Scholar
13.Mikhailov, M. D. and Cotta, R. M., “Steady-Periodic Hyperbolic Heat Conduction in a Finite Slab,” In ternational Communication in Heat and Mass Transfer, 24, pp. 725–731 (1997).Google Scholar
14.Lam, T. T. and Fong, E., “Application of Solution Structure Theorem to Non-Fourier Heat Conduction Problems, Analytical Approach,” International Journal of Heat and Mass Transfer, 54, pp. 4796–4806 (2011).CrossRefGoogle Scholar
15.Barletta, A. and Zanchini, E., “Three Dimensional Propagation of Hyperbolic Thermal Waves in a Solid Bar with Rectangular Cross Section,” International Journal of Heat and Mass Transfer, 42, pp. 219–229 (1999).CrossRefGoogle Scholar
16.Atefi, G. and Talaee, M. R., “Non-Fourier Tempera ture Field in a Solid Homogeneous Finite Hollow Cylinder,” Archive of Applied Mechanics, 81, pp. 569–583 (2011).Google Scholar
17.Talaee, M. R. and Atefi, G., “Non-Fourier Heat Conduction in a Finite Hollow Cylinder with Periodic Surface Heat Flux,” Archive of Applied Mechanics, 81, pp. 1793–1806 (2011).Google Scholar
18.Ozisik, M. N., Heat Conduction, 2nd Ed, Wiley Inc., New York (1993).Google Scholar
19.Yilbas, B. S., “Laser Short-Pulse Heating of a Gold Surface: Comparison of Absorption and Surface Heat Flux Heating Situations,” Numerical Heat Transfer, Part A, 52, pp. 87–100 (2007).Google Scholar