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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 other (trivial) solution is for all spatial temperature gradients to disappear as well, in which case the temperature become uniform in space, as well. The equation is much simpler and can help to understand better the physics of the materials without focusing on the dynamic of the heat transport process.
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
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.
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 formula for the rate of heat flow is: ... is the temperature gradient across the material, and , the proportionality constant, is the thermal ...
In this case, temperature gradients within the sphere become important, even though the sphere material is a good conductor. Equivalently, if the sphere is made of a thermally insulating (poorly conductive) material, such as wood or styrofoam, the interior resistance to heat flow will exceed that at the fluid/sphere boundary, even with a much ...