Heat current

About: Heat current is a research topic. Over the lifetime, 956 publications have been published within this topic receiving 25687 citations.

The Statistical Mechanical Theory of Transport Processes. IV. The Equations of Hydrodynamics

Abstract: The equations of hydrodynamics—continuity equation, equation of motion, and equation of energy transport—are derived by means of the classical statistical mechanics. Thereby, expressions are obtained for the stress tensor and heat current density in terms of molecular variables. In addition to the familiar terms occurring in the kinetic theory of gases, there are terms depending upon intermolecular force. The contributions of intermolecular force to the stress tensor and heat current density are expressed, respectively, as quadratures of the density and current density in the configuration space of a pair of molecules.

Solution of the Linearized Phonon Boltzmann Equation.

Abstract: The linearized Boltzmann equation for the pure phonon field may be solved formally in terms of the eigenvectors of the normal-process collision operator. This representation is particularly convenient as a basis for solutions, since in the isotropic dispersionless case the temperature deviation $\ensuremath{\delta}T$ and the heat current Q are related to zero-eigenvalue eigenfunctions of this operator. The formal solution is summarized by two macroscopic equations relating $\ensuremath{\delta}T$ and Q. The first of these is the usual thermal-energy conservation condition; the second is a generalized phonon-thermal-conductivity relation involving a k- and $\ensuremath{\Omega}$-dependent thermal conductivity $\ensuremath{\kappa}(\mathbf{k},\ensuremath{\Omega})$. Examination of $\ensuremath{\kappa}(0,0)$ clarifies the role of normal processes and momentum-relaxing $R$ processes in determining the steady-state heat current. An alternative to the Callaway equation for the thermal conductivity is obtained. Examination of $\ensuremath{\kappa}(\mathbf{k},\ensuremath{\Omega})$ leads to a discussion of space-time-dependent phenomena in a phonon gas. A set of macroscopic equations which describe second sound with damping and Poiseuille flow are obtained. Second sound from the linear-response point of view discussed by Griffin is considered briefly. In the companion paper the problem of Poiseuille flow in a phonon gas is dealt with in considerable detail using these equations. The pure phonon field in a harmonic crystal is characterized by zero expectation value of the density variation of the crystal. However, in addition to the pure phonon field one may also have an elastic dilatation field in the harmonic approximation, which does lead to periodic density variation. Anharmonic effects will couple the phonon field and the dilatation field, leading to a coupling between elastic (sound waves) and thermal waves. The coupled-field dispersion relations are discussed.

Phonon heat conduction in a semiconductor nanowire

Abstract: A model for phonon heat conduction in a semiconductor nanowire with dimensions comparable to the phonon mean free path is developed. It is based on the solution of Boltzmann’s equation, which takes into account (i) modification of the acoustic phonon dispersion due to spatial confinement, and (ii) change in the nonequilibrium phonon distribution due to partially diffuse boundary scattering. Numerical simulation is performed for a silicon nanowire with boundaries characterized by different interface roughness. Phonon confinement and boundary scattering lead to a significant decrease of the lattice thermal conductivity. The value of this decrease and its interface roughness and temperature dependence are different from the predictions of the early models. The observed change in thermal resistance has to be taken into account in simulation of deep-submicron and nanometer-scale devices.

Heat flux manipulation with engineered thermal materials.

Abstract: Utilizing a multilayered composite approach, we have designed and constructed a new class of artificial materials for thermal conduction. We show that an engineered material can be utilized to control the diffusive heat flow in ways inconceivable with naturally occurring materials. By shielding, concentrating, and inverting heat current, we experimentally demonstrate the unique potential and the utility of guiding heat flux.

Coherent phonon heat conduction in superlattices.

Abstract: The control of heat conduction through the manipulation of phonons as coherent waves in solids is of fundamental interest and could also be exploited in applications, but coherent heat conduction has not been experimentally confirmed. We report the experimental observation of coherent heat conduction through the use of finite-thickness superlattices with varying numbers of periods. The measured thermal conductivity increased linearly with increasing total superlattice thickness over a temperature range from 30 to 150 kelvin, which is consistent with a coherent phonon heat conduction process. First-principles and Green’s function–based simulations further support this coherent transport model. Accessing the coherent heat conduction regime opens a new venue for phonon engineering for an array of applications.