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The heat equation is also widely used in image analysis (Perona & Malik 1990) and in machine learning as the driving theory behind scale-space or graph Laplacian methods. The heat equation can be efficiently solved numerically using the implicit Crank–Nicolson method of (Crank & Nicolson 1947).
Thermal conduction is the diffusion of thermal energy (heat) within one material or between materials in contact. The higher temperature object has molecules with more kinetic energy; collisions between molecules distributes this kinetic energy until an object has the same kinetic energy throughout.
The SI unit for heat capacity of an object is joule per kelvin (J/K or J⋅K −1). Since an increment of temperature of one degree Celsius is the same as an increment of one kelvin, that is the same unit as J/°C. The heat capacity of an object is an amount of energy divided by a temperature change, which has the dimension L 2 ⋅M⋅T −2 ...
The third chart in each set was supplemented by Gröber in 1961, and this particular one shows the dimensionless heat transferred from the wall as a function of a dimensionless time variable. The vertical axis is a plot of Q/Q o, the ratio of actual heat transfer to the amount of total possible heat transfer before T = T ∞.
As an extensive property, heat capacity is characteristic of an object; its corresponding intensive property is specific heat capacity, expressed in terms of a measure of the amount of material such as mass or number of moles, which must be multiplied by similar units to give the heat capacity of the entire body of material.
Simple solutions for transient cooling of an object may be obtained when the internal thermal resistance within the object is small in comparison to the resistance to heat transfer away from the object's surface (by external conduction or convection), which is the condition for which the Biot number is less than about 0.1.
The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watts (joules per second). Heat is the flow of thermal energy driven by thermal non-equilibrium, so the term 'heat flow' is a redundancy (i.e. a pleonasm). Heat must not be confused with stored thermal energy, and moving a hot ...
An equivalent statement of the Dulong–Petit law in modern terms is that, regardless of the nature of the substance, the specific heat capacity c of a solid element (measured in joule per kelvin per kilogram) is equal to 3R/M, where R is the gas constant (measured in joule per kelvin per mole) and M is the molar mass (measured in kilogram per mole).