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...

Solving an inverse Sturm-Liouville problem requires a mathematical process to determine unknown function in the Sturm-Liouville operator from given data in addition to the boundary values. In this paper, we identify a Sturm-Liouville potential function by using the data of one eigenfunction and its corresponding eigenvalue, and identify a spatial-dependent unknown function of a SturmLiouville d...

We propose a prescription based on the Fokker-Planck equation in the Stratonovich approach, with the diffusion coefficient dependent on temporal and spatial coordinates, for describing heat conduction by phonons in small structures. This equation can be analytically solved for a broad class of diffusion coefficients. It can also describe non-Gaussian processes. Further, it generalizes the model...

Some noteworthy and historical perspectives and overview of macroscale and microscale heat transport behavior in materials and structures are presented. The topic of heat waves is also discussed. The signiicance of constitutive models for both macroscale and microscale heat conduction are described in conjunction with generalizations drawn concerning the physical relevance and the role of relax...

We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the tempe...

We derive the macroscopic Fourier's Law of heat conduction from the exact gain-loss time convolutionless quantum master equation under three assumptions for the interaction kernel. To second order in the interaction, we show that the first two assumptions are natural results of the long time limit. The third assumption can be satisfied by a family of interactions consisting of an exchange effec...

Explicit schemes are attractive for obtaining finite difference solutions to partial differential equations because of their simplicity. However this feature is undermined by the severe restriction on stability that the schemes suffer. One method that appears to have better stability properties is Charlie’s method. The stability region of this method applied to a one-dimensional heat conduction...

We use equations similar to the heat conduction equation to calulate heat transfer, radiation transfer and hydrostatical equilibrium in our stellar evolution programs. We tried various numerical schemes and found that the most convenient scheme for complicated calculations (nonlinear, multidimensional calculations) is a symmetrical semi-implicit (SSI) scheme. The (SSI) scheme is easy to code, v...

Edge-emitting lasers started the era of semiconductor lasers and have existed up to nowadays, appearing as devices fabricated out of various materials, formed sometimes in very tricky ways to enhance light generation. However, in all cases radiative processes are accompanied by undesired heat-generating processes, like non-radiative recombination, Auger recombination, Joule effect or surface re...