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...

Non-Fourier heat conduction model with dual phase lag wave-diffusion model was analyzed by using well-conditioned asymptotic wave evaluation (WCAWE) and finite element method (FEM). The non-Fourier heat conduction has been investigated where the maximum likelihood (ML) and Tikhonov regularization technique were used successfully to predict the accurate and stable temperature responses without t...

We calculate the Lagrangian for certain type of differential equations of nonlinear heat conduction, applying potential function method introduced previously. On the other hand, we point out that these kind of nonlinear parabolic differential equations describe Markovian processes in a new phase space.

In this study, thermal performance across straight convecting- radiating fin with temperature dependent thermal conductivity is considered. The variation of parameters (VPM) is adopted to analyze the nonlinear higher order differential equations arising due to thermal conductivity and heat transfer coefficient on temperature distribution. Pertinent parameters such as thermo geometric and radiat...

This paper deals with transient non-linear heat conduction through the insulation wall of the tank for transportation of liquid aluminum. Tanks designed for this purpose must satisfy certain requirements regarding temperature of loading and unloading, during transport. Basic theoretical equations are presented, which describe the problem of heat conduction finite element analysis, starting from...

In the context of the problem of heat conduction in one-dimensional systems, we present an analytical calculation of the instantaneous energy transfer across a tagged particle in a one-dimensional gas of equal-mass, hard-point particles. From this, we obtain a formula for the steady-state energy flux, and identify and separate the mechanical work and heat conduction contributions to it. The nat...

We address the problem of heat conduction in 1D nonlinear chains; we show that, acting on the parameter which controls the strength of the on-site potential inside a segment of the chain, we induce a transition from conducting to insulating behavior in the whole system. Quite remarkably, the same transition can be observed by increasing the temperatures of the thermal baths at both ends of the ...