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In stars and planets natural processes heat convective flows in the bulk of a convective region rather than at hard boundaries. By characterizing how convective dynamics are determined by the strength of an internal heating source we can…
We propose a theory of low temperature thermal transport in nano-wires in the regime where a competition between phonon and flexural modes governs the relaxation processes. Starting with the standard kinetic equations for two different…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
We consider a scaled Navier--Stokes--Fourier system describing the motion of a compressible, heat-conducting, viscous fluid driven by inhomogeneous boundary temperature distribution together with the gravitational force of a massive object…
We numerically investigate turbulent Rayleigh-B\'enard convection within two immiscible fluid layers, aiming to understand how the layer thickness and fluid properties affect the heat transfer (characterized by the Nusselt number $Nu$) in…
The equation for temporary evolution of spectral energy of collisionless Alfven waves is derived in framework of weak turbulence theory. The main nonlinear processes for such conditions are induced scattering and two quantum absorption of…
The characteristics of the hydro-thermal flow which occurs when a cold fluid is injected into a hot fractured bedrock depend on the morphology of the fracture. We consider a sharp triangular asperity, invariant in one direction, perturbing…
This work proposes an extensive review of laminar and turbulent forced convective heat transfer correlations inside tubes by analyzing both experimental and computational research. Convective heat transfer is influenced by fluid turbulence…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
Advances in the fabrication and characterization of nanoscale systems now allow for a deeper understanding of one of the most basic issues in science and technology: the flow of energy at the microscopic level. In this Colloquium we survey…
We develop a two-fluid model (TFM) for heat transfer in dense non-Brownian suspensions. Specifically, we propose closure relations for the inter-phase heat transfer coefficient and the thermal diffusivity of the particle phase based on…
We study thermal fluctuation corrections to charge and heat conductivity in systems with locally conserved energy and charge, but without locally conserved momentum. Thermal fluctuations may naturally lead to a lower bound on diffusion…
This review summarizes recent studies of thermal transport in nanoscaled semiconductors. Different from bulk materials, new physics and novel thermal properties arise in low dimensional nanostructures, such as the abnormal heat conduction,…
Non-isothermal particles suspended in a fluid lead to complex interactions -- the particles respond to changes in the fluid flow, which in turn is modified by their temperature anomaly. Here, we perform a novel proof-of-concept numerical…
Thermal convection in fluid layers heated from below are usually realized experimentally as well as treated theoretically with fixed boundaries on which conditions for the temperature and the velocity field are prescribed. The thermal and…
The accuracy of the classical heat conduction model, known as Fourier's law, is highly questioned, dealing with the micro and nanosystems and biological tissues. In other words, the results obtained from the classical equations deviate from…
We present the Onsager--Stefan--Maxwell thermodiffusion equations, which account for the Soret and Dufour effects in multicomponent fluids. Unlike transport laws derived from kinetic theory, this framework preserves the structure of the…
In this paper we study Cauchy problem for thermoelastic plate equations with friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat conduction is modeled by Fourier's law. We explain some qualitative properties of…
Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally…
The clearing up of a wave nature of the energy and mass transfer phenomena in classical expressions of the molecular-kinetic theory has allowed to find a quantitative measure of intensity of processes of a thermal conductivity, viscosity…