‎A natural algorithm with an optimal order of convergence is proposed for numerical solution of a class of cordial weakly singular Volterra integral equations‎. ‎The equations of this class appear in heat conduction problems with mixed boundary conditions‎. ‎The algorithm is based on a representation of the solution and compound Gaussian quadrature rules with graded meshes‎. ‎A comparative stud...

We study the statistical mechanics of thermal conduction in a classical many-body system that is in contact with two thermal reservoirs maintained at different temperatures. The ratio of the probabilities, that when observed for a finite time, the time averaged heat flux flows in and against the direction required by Fourier's Law for heat flow, is derived from first principles. This result is ...

[1] We calculate viscoelastic dissipation in the Moon using a rheological (extended Burgers) model based on laboratory deformation of melt-free polycrystalline olivine. Lunar temperature structures are calculated assuming steady state conduction with variable internal heat production and core heat flux. Successful models can reproduce the dissipation factor (Q) measured at both tidal and seismi...

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the ...

– We study heat conduction in one dimensional (1D) anharmonic lattices analytically and numerically by using an effective phonon theory. It is found that every effective phonon mode oscillates quasi-periodically. By weighting the power spectrum of the total heat flux in the Debye formula, we obtain a unified formalism that can explain anomalous heat conduction in momentum conserved lattices wit...

abstract:a mathematical model for the performance prediction of an industrial glass furnace with six ports on each side was developed. this model comprises of two main sub-models for the combustion chamber and glass-melting tank. the first sub-model consists of the models for the combustion and the heat transfer model including, radiation, convection and conduction. the fuel combustion in atmos...

Integral transforms provide us great convenience in finding exact and approximate solutions of many mathematical physics engineering problems such as signals, wave equation, heat conduction, transfer. In this study, we consider the Kashuri Fundo transform, which is one these integral transforms, our aim to show that transform an effective method solving steady transfer obtained results are comp...

– A consistent description of a shear flow, the accompanied viscous heating, and the associated entropy balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the temperature distributions. In an appropriate macroscopic limit their transport equations go over into the Navier-Stokes and the heat conduction equation o...