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In mathematics and physics, the heat equation is a certain partial differential equation. Solutions of the heat equation are sometimes known as caloric functions . The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region.
Quantity (common name/s) (Common) symbol/s Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer
The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is [6] = +, ˙, where q is heat flux vector, −ρc p (∂T/∂t) is temporal change of internal energy (ρ is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and ˙ is the energy conversion to and from thermal ...
The heat equation is an important partial differential equation that describes the distribution of heat (or temperature variation) in a given region over time. In some cases, exact solutions of the equation are available; [ 26 ] in other cases the equation must be solved numerically using computational methods such as DEM-based models for ...
Thus, they are essentially equations of state, and using the fundamental equations, experimental data can be used to determine sought-after quantities like G (Gibbs free energy) or H . [1] The relation is generally expressed as a microscopic change in internal energy in terms of microscopic changes in entropy , and volume for a closed system in ...
The author then explains how heat is defined or measured by calorimetry, in terms of heat capacity, specific heat capacity, molar heat capacity, and temperature. [ 42 ] A respected text disregards the Carathéodory's exclusion of mention of heat from the statement of the first law for closed systems, and admits heat calorimetrically defined ...
Only one equation of state will not be sufficient to reconstitute the fundamental equation. All equations of state will be needed to fully characterize the thermodynamic system. Note that what is commonly called "the equation of state" is just the "mechanical" equation of state involving the Helmholtz potential and the volume:
This equation is derived in Section 49, at the opening of the chapter on "Thermal Conduction in Fluids" in the sixth volume of L.D. Landau and E.M. Lifshitz's Course of Theoretical Physics. [1] It might be used to measure the heat transfer and air flow in a domestic refrigerator, [ 4 ] to do a harmonic analysis of regenerators, [ 5 ] or to ...