A nonlinear partial differential equation of the following form is considered: u − div ( a(u)∇u ) + b(u) |∇u| = 0, which arises from the heat conduction problems with strong temperature-dependent material parameters, such as mass density, specific heat and heat conductivity. Existence, uniqueness and asymptotic behavior of initial boundary value problems under appropriate assumptions on the mat...

The numerical methods of the structural design optimization with transient response constraints have been studied in the paper. The new methods of the response analysis and sensitivity analysis for the transient dynamics and the heat conduction constraints with the precise time integration have been proposed. Particularly, an efficient method of sensitivity analysis for nonlinear transient heat...

In this paper, a numerical solution of an inverse non-dimensional heat conduction problem by spline method will be considered. The given heat conduction equation, the boundary condition, and the initial condition are presented in a dimensionless form. A set of temperature measurements at a single sensor location inside the heat conduction body is required. The result show that the proposed meth...

The propagation of thermal shock waves under the Maxwell–Cattaneo hyperbolic heat conduction theory is considered. In particular, the thermal conductivity is allowed to dependent on the temperature, which makes the model nonlinear. A solution for the evolution of a discontinuity under the linearized version of the governing equations is found via singular surface theory. Then, the Rankine–Hugon...

small scale thermal devices, such as micro heater, have led researchers to consider more accurate models of heat in thermal systems. moreover, biological applications of heat transfer such as simulation of temperature field in laser surgery is another pathway which urges us to re-examine thermal systems with modern ones. non-fourier heat transfer overcomes some shortcomings of fourier heat tran...

We study the dynamical correlation functions and heat conduction for the simplest model of quasi one-dimensional (1d) dielectric crystal i.e. a chain of classical particles coupled by quadratic and cubic intersite potential. Even in the weakly nonlinear regime, numerical simulation on long enough chains reveal sizeable deviations from the perturbative results in the form of a slower decay of co...

in this paper, the conjugate gradient method coupled with adjoint problem is used in order to solve the inverse heat conduction problem and estimation of the time- dependent heat flux using the temperature distribution at a point in a three layer system with none homogeneous boundary conditions. also, the effect of noisy data on final solution is studied. for solving this problem the general co...

XVIII. XIX. Introduction ........................................ Restructured Thermodynamics of Open Systems and the Concept of Thermobaric Transfer. ................................. New Chemical Thermodynamics .......................... Homogeneous Mixtures and Reformulation of the Gibbs-Duhem Theorem .......................................... Nontensorial Virtual Work Approach to Finite Str...

A data reduction method based on numerical solutions of the heat conduction equation has been developed for obtaining thermal diffusivity values from thermal flash measurements. Using the new method, the computed evolution in temperature is fitted to the measured temperature evolution instead of using the t1/2 point alone, as is done in many other analyzes. The numerical solutions used are base...