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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 ...
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.
In engineering, physics, and chemistry, the study of transport phenomena concerns the exchange of mass, energy, charge, momentum and angular momentum between observed and studied systems. While it draws from fields as diverse as continuum mechanics and thermodynamics , it places a heavy emphasis on the commonalities between the topics covered.
Thermal physics, generally speaking, is the study of the statistical nature of physical systems from an energetic perspective. Starting with the basics of heat and temperature, thermal physics analyzes the first law of thermodynamics and second law of thermodynamics from the statistical perspective, in terms of the number of microstates corresponding to a given macrostate.
Transfers of energy as work, or as heat, or of matter, between the system and the surroundings, take place through the walls, according to their respective permeabilities. Matter or energy that pass across the boundary so as to effect a change in the internal energy of the system need to be accounted for in the energy balance equation.
Substituting from the ideal gas equation gives finally: = where n = number of moles of gas in the thermodynamic system under consideration and R = universal gas constant. On a per mole basis, the expression for difference in molar heat capacities becomes simply R for ideal gases as follows:
[13] [14] The governing equation when heat conduction is the primary heat transfer mechanism is the one-dimensional energy equation: = where is the material's density, is the material's specific heat capacity, is the material's thermal conductivity.
For a viscous, Newtonian fluid, the governing equations for mass conservation and momentum conservation are the continuity equation and the Navier-Stokes equations: = = + where is the pressure and is the viscous stress tensor, with the components of the viscous stress tensor given by: = (+) + The energy of a unit volume of the fluid is the sum of the kinetic energy / and the internal energy ...