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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. Since then, the ...
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 governing equation of the physics of the problem to be analyzed is the heat diffusion equation. It relates the flux of heat in space, its variation in time and the generation of power. ∇ ( κ ∇ T ) + g = ρ C ∂ T ∂ t {\displaystyle \nabla \left(\kappa \nabla T\right)+g=\rho C{\frac {\partial T}{\partial t}}}
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 ...
Joule heating (also known as resistive, resistance, or Ohmic heating) is the process by which the passage of an electric current through a conductor produces heat.. Joule's first law (also just Joule's law), also known in countries of the former USSR as the Joule–Lenz law, [1] states that the power of heating generated by an electrical conductor equals the product of its resistance and the ...
The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watts (joules per second). Heat is the flow of thermal energy driven by thermal non-equilibrium, so the term 'heat flow' is a redundancy (i.e. a pleonasm). Heat must not be confused with stored thermal energy, and moving a hot ...
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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 ...