The divergence of the heat conductivity in the thermodynamic limit is investigated in 2d-lattice models of anharmonic solids with nearest-neighbour interaction from single-well potentials. Two different numerical approaches based on nonequilibrium and equilibrium simulations provide consistent indications in favour of a logarithmic divergence in ”ergodic”, i.e. highly chaotic, dynamical regimes...

In this paper we study the existence and geometric properties of an optimal configuration to a nonlinear optimization problem in heat conduction. The quantity to be minimized is R ∂D Γ(x, uμ)dσ, where D is a fixed domain. A nonconstant temperature distribution is prescribed on ∂D and a volume constraint on the set where the temperature is positive is imposed. Among other regularity properties o...

The present essay scrutinizes the application of discrete mollification as a filtering procedure to solve a nonlinear backward inverse heat conduction problem in one dimensional space. These problems are seriously ill-posed. So, we combine discrete mollification and space marching method to address the ill-posedness of the proposed problem. Moreover, a proof of stability and<b...

We study the heat conduction of two nonlinear lattices joined by a weak harmonic link. When the system reaches a steady state, the heat conduction of the system is decided by the tunneling heat flow through the weak link. We present an analytical analysis by the combination of the self-consistent phonon theory and the heat tunneling transport formalism, and then the tunneling heat flow can be o...

Present study explores the effect of Hall current, non-linear radiation, irregular heat source/sink on magnetohydrodynamic flow of Casson nanofluid past a nonlinear stretching sheet. Viscous and Joule dissipation are incorporated in the energy equation. An accurate numerical solution of highly nonlinear partial differential equations, describing the flow, heat and mass transfer...

longitudinal heat conduction is an important parameter in the cryogenic field, especially in cryogenic heat exchangers. in the present work, the parasitic effect of tube wall longitudinal heat conduction on temperature measurement has been studied in cryogenic laminar hydrogen flow. the effects of various parameters such as wall cold end temperature, wall thermal conductivity, gas volumetric fl...

The non-Fourier effect in heat conduction is important in strong thermal environments and thermal shock problems. Generally, commercial FE codes are not available for analysis of non-Fourier heat conduction. In this study, a meshless formulation is presented for the analysis of the non-Fourier heat conduction in the materials. The formulation is based on the symmetric local weak form of the sec...

We present a first-principle based approach that leads from many-particle description to nonlinear, stochastic constitutive relation for the modeling of transient heat conduction processes at nano-mechanical scale. By enforcing statistical consistency, in statistics local energy is consistent with an all-atom description, we identify driving force as well model parameters these generalized mode...