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The net flux of heat through a system equals the conductivity times the rate of change of temperature with respect to position. For convective transport involving turbulent flow, complex geometries, or difficult boundary conditions, the heat transfer may be represented by a heat transfer coefficient.
Informally, Alfvén's theorem refers to the fundamental result in ideal magnetohydrodynamic theory that electrically conducting fluids and the magnetic fields within are constrained to move together in the limit of large magnetic Reynolds numbers (R m)—such as when the fluid is a perfect conductor or when velocity and length scales are infinitely large.
In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states.
Let K 0 is the normal conductivity at one bar (10 5 N/m 2) pressure, K e is its conductivity at special pressure and/or length scale. Let d is a plate distance in meters, P is an air pressure in Pascals (N/m 2 ), T is temperature Kelvin, C is this Lasance constant 7.6 ⋅ 10 −5 m ⋅ K/N and PP is the product P ⋅ d/T .
Hence, units of electric flux are, in the MKS system, newtons per coulomb times meters squared, or N m 2 /C. (Electric flux density is the electric flux per unit area, and is a measure of strength of the normal component of the electric field averaged over the area of integration. Its units are N/C, the same as the electric field in MKS units.)
In physics and engineering, heat flux or thermal flux, sometimes also referred to as heat flux density [1], heat-flow density or heat-flow rate intensity, is a flow of energy per unit area per unit time. Its SI units are watts per square metre (W/m 2). It has both a direction and a magnitude, and so it is a vector quantity.
Fick's first law relates the diffusive flux to the gradient of the concentration. It postulates that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative), or in simplistic terms the concept that a solute will move from a region of high concentration to a region of low ...
Certain solutions of the heat equation known as heat kernels provide subtle information about the region on which they are defined, as exemplified through their application to the Atiyah–Singer index theorem. [8] The heat equation, along with variants thereof, is also important in many fields of science and applied mathematics.