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A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature spatial gradient is a vector quantity with dimension of temperature difference per unit length. The SI unit is kelvin per meter (K/m).
Geothermal gradient is the rate of change in temperature with respect to increasing depth in Earth's interior. As a general rule, the crust temperature rises with depth due to the heat flow from the much hotter mantle ; away from tectonic plate boundaries , temperature rises in about 25–30 °C/km (72–87 °F/mi) of depth near the surface in ...
The gradient of F is then normal to the hypersurface. Similarly, an affine algebraic hypersurface may be defined by an equation F(x 1, ..., x n) = 0, where F is a polynomial. The gradient of F is zero at a singular point of the hypersurface (this is the definition of a singular point). At a non-singular point, it is a nonzero normal vector.
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 P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2
The defining equation for thermal conductivity is =, where is the heat flux, is the thermal conductivity, and is the temperature gradient. This is known as Fourier's law for heat conduction. Although commonly expressed as a scalar , the most general form of thermal conductivity is a second-rank tensor .
The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well. The heat equation implies that peaks ( local maxima ) of u {\displaystyle u} will be gradually eroded down, while depressions ( local minima ...
The formula for the rate of heat flow is: ... is the temperature gradient across the material, and , the proportionality constant, is the thermal ...
At the atomic scale, a temperature gradient causes charge carriers in the material to diffuse from the hot side to the cold side. This is due to charge carrier particles having higher mean velocities (and thus kinetic energy) at higher temperatures, leading them to migrate on average towards the colder side, in the process carrying heat across the material.