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Heat equation. Animated plot of the evolution of the temperature in a square metal plate as predicted by the heat equation. The height and redness indicate the temperature at each point. The initial state has a uniformly hot hoof-shaped region (red) surrounded by uniformly cold region (yellow). As time passes the heat diffuses into the cold region.
The heat equation is an important partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. In some cases, exact solutions of the equation are available; [27] in other cases the equation must be solved numerically using computational methods such as DEM-based models for ...
Thermal conduction. Conduction is the process by which heat is transferred from the hotter end to the colder end of an object. The ability of the object to conduct heat is known as its thermal conductivity, and is denoted k . Heat spontaneously flows along a temperature gradient (i.e. from a hotter body to a colder body).
Quantity (common name/s) (Common) symbol/s Defining equation SI units Dimension Temperature gradient: No standard symbol K m −1 [Θ][L] −1 Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer
In fluid dynamics, the general equation of heat transfer is a nonlinear partial differential equation describing specific entropy production in a Newtonian fluid subject to thermal conduction and viscous forces: [1] [2] where is the specific entropy, is the fluid's density, is the fluid's temperature, is the material derivative, is the thermal ...
One of the fundamental thermodynamic equations is the description of thermodynamic work in analogy to mechanical work, or weight lifted through an elevation against gravity, as defined in 1824 by French physicist Sadi Carnot. Carnot used the phrase motive power for work. In the footnotes to his famous On the Motive Power of Fire, he states ...
In anisotropic media, the diffusion coefficient depends on the direction. It is a symmetric tensor Dji = Dij. Fick's first law changes to it is the product of a tensor and a vector: For the diffusion equation this formula gives The symmetric matrix of diffusion coefficients Dij should be positive definite.
In thermodynamics, heat is the thermal energy transferred between systems due to a temperature difference. [1] In colloquial use, heat sometimes refers to thermal energy itself. Thermal energy is the kinetic energy of vibrating and colliding atoms in a substance. An example of formal vs. informal usage may be obtained from the right-hand photo ...