Algebraically Explicit Analytical Solution of Three- Dimensional Hyperbolic Heat Conduction Equation

In this paper, the three-dimensional hyperbolic effect subjected to a cosine heat flux boundary condition is carried out. Equations in rectangular coordinates are solved. Analytical solution with method of separation of variables is derived. The main aim of this paper is to obtain some possibly explicit analytical solution of the (1+3)-dimensional hyperbolic heat conduction equation for given initial and boundary condition with method of separation of variables. The temperature layers and profiles for various relaxation times in three different examples are calculated. Also, the reflection of the heat wave in the solid in some examples is shown.

[1]  B. Pulvirenti,et al.  Hyperbolic thermal waves in a solid cylinder with a non-stationary boundary heat flux , 1998 .

[2]  H. Q. Yang.  Solution of two-dimensional hyperbolic heat conduction by high-resolution numerical methods , 1992 .

[3]  Amin Moosaie,et al.  Non-Fourier heat conduction in a finite medium with insulated boundaries and arbitrary initial conditions , 2008 .

[4]  M. Al-Nimr,et al.  Variational formulation of hyperbolic heat conduction problems applying Laplace transform technique , 2008 .

[5]  D. Tang,et al.  Non-Fourier heat conduction in a finite medium under periodic surface thermal disturbance , 1996 .

[6]  A. Mullis.  Rapid solidification within the framework of a hyperbolic conduction model , 1997 .

[7]  J. K. Chen,et al.  Non-Fourier Heat Conduction Effect on Laser-Induced Thermal Damage in Biological Tissues , 2008 .

[8]  Tzer-Ming Chen.  Numerical solution of hyperbolic heat conduction in thin surface layers , 2007 .

[9]  J. C. Jaeger,et al.  Conduction of Heat in Solids , 1952 .

[10]  E. Zanchini,et al.  Three-dimensional propagation of hyperbolic thermal waves in a solid bar with rectangular cross-section , 1999 .

[11]  M. Maeda,et al.  [Heat conduction]. , 1972, Kango kyoshitsu. [Nursing classroom].

[12]  A. Moosaie.  Non-Fourier heat conduction in a finite medium subjected to arbitrary periodic surface disturbance , 2007 .

[13]  Robert A. Guyer,et al.  SECOND SOUND IN SOLID HELIUM , 1966 .

[14]  Chen Han-Taw,et al.  Analysis of two-dimensional hyperbolic heat conduction problems , 1994 .

[15]  Y. Shanjani,et al.  Numerical Heat Transfer Modeling in Coated Powder as Raw Material of Powder-Based Rapid Prototyping Subjected to Plasma Arc , 2007 .

[16]  X. Tan,et al.  Non-Fourier conduction model with thermal source term of ultra short high power pulsed laser ablation and temperature evolvement before melting , 2005 .

[17]  Wilfried Roetzel,et al.  Hyperbolic axial dispersion model : concept and its application to a plate heat exchanger , 1995 .

[18]  S. Torii,et al.  Heat transfer mechanisms in thin film with laser heat source , 2005 .

[19]  Hsin-Sen Chu,et al.  Effect of interface thermal resistance on heat transfer in a composite medium using the thermal wave model , 2000 .

[20]  Z. Tan,et al.  Heat transfer during asymmetrical collision of thermal waves in a thin film , 1997 .

[21]  L. Malinowski,et al.  An analytical solution of the hyperbolic heat conduction equation for the case of a finite medium symmetrically heated on both sides , 2006 .

[22]  Hyperbolic axial dispersion model for heat exchangers , 2002 .