Heat transfer physics

Heat transfer physics describes the kinetics of energy storage, transport, and energy transformation by principal energy carriers: phonons (lattice vibration waves), electrons, fluid particles, and photons. Heat is energy stored in temperature-dependent motion of particles including electrons, atomic nuclei, individual atoms, and molecules. Heat is transferred to and from matter by the principal energy carriers. The state of energy stored within matter, or transported by the carriers, is described by a combination of classical and quantum statistical mechanics. The energy is also transformed (converted) among various carriers.The heat transfer processes (or kinetics) are governed by the rates at which various related physical phenomena occur, such as (for example) the rate of particle collisions in classical mechanics. These various states and kinetics determine the heat transfer, i.e., the net rate of energy storage or transport. Governing these process from the atomic level (atom or molecule length scale) to macroscale are the laws of thermodynamics, including conservation of energy. Heat transfer physics describes the kinetics of energy storage, transport, and energy transformation by principal energy carriers: phonons (lattice vibration waves), electrons, fluid particles, and photons. Heat is energy stored in temperature-dependent motion of particles including electrons, atomic nuclei, individual atoms, and molecules. Heat is transferred to and from matter by the principal energy carriers. The state of energy stored within matter, or transported by the carriers, is described by a combination of classical and quantum statistical mechanics. The energy is also transformed (converted) among various carriers.The heat transfer processes (or kinetics) are governed by the rates at which various related physical phenomena occur, such as (for example) the rate of particle collisions in classical mechanics. These various states and kinetics determine the heat transfer, i.e., the net rate of energy storage or transport. Governing these process from the atomic level (atom or molecule length scale) to macroscale are the laws of thermodynamics, including conservation of energy. Heat is thermal energy associated with temperature-dependent motion of particles. The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is where q is heat flux vector, -ρcp(∂T/∂t) is temporal change of internal energy (ρ is density, cp is specific heat capacity at constant pressure, T is temperature and t is time), and s ˙ {displaystyle extstyle {dot {s}}} is the energy conversion to and from thermal energy (i and j are for principal energy carriers). So, the terms represent energy transport, storage and transformation. Heat flux vector q is composed of three macroscopic fundamental modes, which are conduction (qk = -k∇T, k: thermal conductivity), convection (qu = ρcpuT, u: velocity), and radiation (qr = 2 π ∫ 0 ∞ ∫ 0 π {displaystyle 2pi extstyle int _{0}^{infty }int _{0}^{pi }} s Iph,ω sinθdθdω, ω: angular frequency, θ: polar angle, Iph,ω: spectral, directional radiation intensity, s: unit vector), i.e., q = qk + qu + qr. Once states and kinetics of the energy conversion and thermophysical properties are known, the fate of heat transfer is described by the above equation. These atomic-level mechanisms and kinetics are addressed in heat transfer physics. The microscopic thermal energy is stored, transported, and transformed by the principal energy carriers: phonons (p), electrons (e), fluid particles (f), and photons (ph). Thermophysical properties of matter and the kinetics of interaction and energy exchange among the principal carriers are based on the atomic-level configuration and interaction. Transport properties such as thermal conductivity are calculated from these atomic-level properties using classical and quantum physics. Quantum states of principal carriers (e.g.. momentum, energy) are derived from the Schrödinger equation (called first principle or ab initio) and the interaction rates (for kinetics) are calculated using the quantum states and the quantum perturbation theory (formulated as the Fermi golden rule). Variety of ab initio (Latin for from the beginning) solvers (software) exist (e.g., ABINIT, CASTEP, Gaussian, Q-Chem, Quantum ESPRESSO, SIESTA, VASP, WIEN2k). Electrons in the inner shells (core) are not involved in heat transfer, and calculations are greatly reduced by proper approximations about the inner-shells electrons. The quantum treatments, including equilibrium and nonequilibrium ab initio molecular dynamics (MD), involving larger lengths and times are limited by the computation resources, so various alternate treatments with simplifying assumptions have been used and kinetics. In classical (Newtonian) MD, the motion of atom or molecule (particles) is based on the empirical or effective interaction potentials, which in turn can be based on curve-fit of ab initio calculations or curve-fit to thermophysical properties. From the ensembles of simulated particles, static or dynamics thermal properties or scattering rates are derived. At yet larger length scales (mesoscale, involving many mean free paths), the Boltzmann transport equation (BTE) which is based on the classical Hamiltonian-statistical mechanics is applied. BTE considers particle states in terms of position and momentum vectors (x, p) and this is represented as the state occupation probability. The occupation has equilibrium distributions (the known boson, fermion, and Maxwell–Boltzmann particles) and transport of energy (heat) is due to nonequilibrium (cause by a driving force or potential). Central to the transport is the role of scattering which turn the distribution toward equilibrium). The scattering is presented by the relations time or the mean free path. The relaxation time (or its inverse which is the interaction rate) is found from other calculations (ab initio or MD) or empirically. BTE can be numerically solved with Monte Carlo method, etc. Depending on the length and time scale the proper level of treatment (ab initio, MD, or BTE). Heat transfer physics analyses may involve multiple scales (e.g., BTE using interaction rate from ab initio or classical MD) with states and kinetic related to thermal energy storage, transport and transformation. So, heat transfer physics covers the four principal energy carries and their kinetics from classical and quantum mechanical perspectives. This enables multiscale (ab initio, MD, BTE and macroscale) analyses, including low-dimensionality and size effects.