The temperature gradient is a measure of how temperature changes with distance in a specific direction. It is essentially the rate at which temperature increases or decreases over a certain distance. The concept is important in various fields, including meteorology, geology, and engineering, as it can affect processes such as heat transfer, weather patterns, and geological phenomena.
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The temperature gradient is the vector describing the first-order spatial variation of a temperature field. It points toward fastest increase, and its magnitude is the increase per unit distance in that direction, measured in . Along a small displacement , .
For a uniform plate with , the temperature gradient is . In isotropic Fourier's law, heat flux is , so a larger gradient produces larger conductive transport at fixed thermal conductivity. In an anisotropic material, the thermal conductivity tensor can turn the flux away from the negative-gradient direction. A finite thermometer spacing estimates an average gradient over that spacing; resolving a thin thermal boundary layer requires a correspondingly fine spatial measurement.