Geothermal gradient is the rate of temperature change 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 most of the world. However, in some cases the temperature may drop with increasing depth, especially near the surface, a phenomenon known as inverse or negative geothermal gradient. The effects of weather, sun, and season only reach a depth of approximately 10-20 metres. Strictly speaking, geo-thermal necessarily refers to Earth but the concept may be applied to other planets. In SI units, the geothermal gradient is expressed as °C/km, K/km or mK/m. These are all equivalent. Earth's internal heat comes from a combination of residual heat from planetary accretion, heat produced through radioactive decay, latent heat from core crystallization, and possibly heat from other sources. The major heat-producing nuclides in Earth are potassium-40, uranium-238, uranium-235, and thorium-232. The inner core is thought to have temperatures in the range of 4000 to 7000 K, and the pressure at the centre of the planet is thought to be about 360 GPa (3.6 million atm). (The exact value depends on the density profile in Earth.) Because much of the heat is provided for by radioactive decay, scientists believe that early in Earth's history, before nuclides with short half-lives had been depleted, Earth's heat production would have been much higher. Heat production was twice that of present-day at approximately 3 billion years ago, resulting in larger temperature gradients within Earth, larger rates of mantle convection and plate tectonics, allowing the production of igneous rocks such as komatiites that are no longer formed. The top of the geothermal gradient is influenced by atmospheric temperature. The uppermost layers of the solid planet are at the temperature produced by the local weather, decaying to approximately the annual mean-average temperature (MATT) at a shallow depth of about 10-20 metres depending on the type of ground, rock etc; it is this depth which is used for many ground-source heat pumps. The top hundreds of meters reflect past climate change; descending further, warmth increases steadily as interior heat sources begin to dominate. (Wikipedia).
Gradient (1 of 3: Developing the formula)
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From playlist Further Linear Relationships
This video explains what information the gradient provides about a given function. http://mathispower4u.wordpress.com/
From playlist Functions of Several Variables - Calculus
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From playlist MATH2018 Engineering Mathematics 2D
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From playlist 3D Calc Plotter
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From playlist Engineering Mathematics
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From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
A Pathway for Widespread Geothermal Energy
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From playlist Lecture Collection | Energy Seminar
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From playlist Climate
The Equation of State for Water IAPWS-95 Programmed in Mathematica 11.1
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From playlist Wolfram Technology Conference 2017
Lagrange Multipliers Maximum of f(x, y, z) = xyz subject to x + y + z - 3 = 0
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From playlist Calculus 3
Earth System Science 21. On Thin Ice. Lecture 09. Permafrost
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From playlist Earth System Science 21: On Thin Ice: Climate Change and the Cryosphere
Horizontal convection: ocean energetics, heat flux,... - Young - Workshop 1 - CEB T3 2019
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From playlist 2019 - T3 - The Mathematics of Climate and the Environment
Harnessing the Power of Yellowstone’s Supervolcano | Podcast | Overheard at National Geographic
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From playlist Podcast | Overheard at National Geographic
Earth System Science 21. On Thin Ice. Lecture 10. Permafrost and the Carbon Cycle
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From playlist Earth System Science 21: On Thin Ice: Climate Change and the Cryosphere
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Year 11 Earth and Environmental Science Module 1 Earth's Resources Structure of the Earth The Asthenosphere The Mantle
From playlist Y11 EES Mod 1 Resources
The Gradient Operator in Vector Calculus: Directions of Fastest Change & the Directional Derivative
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From playlist Engineering Math: Vector Calculus and Partial Differential Equations
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Find the Gradient of z = ln(x^2 - y) at (3, 4)
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From playlist Calculus