Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

Analytical Solution of the Hyperbolic Heat Conduction Equation for Moving Semi-Infinite Medium under the Effect of Time-Dependent Laser Heat Source

This paper presents an analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time dependent laser heat source. Laser heating is modeled as an internal heat source, whose capacity is given by g x, t I t 1 − R μe−μx while the semi-infinite body has insulated boundary. The solution is obtained by Laplace transforms method, and the discus...

Approximate Solution of the Nonlinear Heat Conduction Equation in a Semi-Infinite Domain

We use an approximation method to study the solution to a nonlinear heat conduction equation in a semi-infinite domain. By expanding an energy density function defined as the internal energy per unit volume as a Taylor polynomial in a spatial domain, we reduce the partial differential equation to a set of first-order ordinary differential equations in time. We describe a systematic approach to ...

Splitting schemes for hyperbolic heat conduction equation

Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of heat fluxes. In this case, the mathematical model is based on a hyperbolic equation of second order or a system of equations for the temperature and heat flu...

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 i...

Semi-analytical solution to the frequency-dependent Boltzmann transport equation for cross-plane heat conduction in thin films