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Encyclopedia > Fourier's Law
Heat flow along perfectly insulated wire
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Heat flow along perfectly insulated wire

Heat conduction is the transmission of heat across matter. Modified heat flow File links The following pages link to this file: Heat conduction Categories: GFDL images ... Modified heat flow File links The following pages link to this file: Heat conduction Categories: GFDL images ... A red-hot iron rod cooling after being worked by a blacksmith. ...


Heat transfer is always directed from a higher to a lower temperature. Denser substances are usually better conductors; metals are excellent conductors. Temperature is the physical property of a system which underlies the common notions of hot and cold; the material with the higher temperature is said to be hotter. ... Density (symbol: ρ - Greek: rho) is a measure of mass per unit of volume. ... For alternative meanings see metal (disambiguation). ...


The law of heat conduction also know as Fourier's law states that the time rate of heat flow Q through a slab (or a portion of a perfectly insulated wire, as shown in the figure) is proportional to the gradient of temperature difference: This article is in the process of being merged into Heat, and may be outdated. ... The word proportionality may have one of a number of meanings: In mathematics, proportionality is a mathematical relation between two quantities. ... In the above two images, the scalar field is in black and white, black representing higher values, and its corresponding gradient is represented by blue arrows. ...

A is the transversal surface area, Δ x is the thickness of the body of matter through which the heat is passing, K is a conductivity constant dependent on the nature of the material and its temperature, and ΔT is the temperature difference through which the heat is being transferred. This law forms the basis for the derivation of the heat equation. The heat equation or diffusion equation is an important partial differential equation which describes the variation of temperature in a given region over time. ...


Conductance

Writing

Fourier's law can also be stated as:

where U is the conductance. The reciprocal of conductance is resistance, equal to ' Conductance can refer to: Electrical conductance, the reciprocal of electrical resistance. ...

and it is resistance which is additive when several conducting layers lie between the hot and cool regions, because A and Q are the same for all layers. In a multilayer partition, the total conductance is related to the conductance of its layers by:

So, when dealing with a multilayer partition, the following formula is usually used:

When heat is being conducted from one fluid to another through a barrier, it is sometimes important to consider the conductance of the thin film of fluid which remains stationary next to the barrier. This thin film of fluid is difficult to quantify, its characteristics depending upon complex conditions of turbulence and viscosity, but when dealing with thin high-conductance barriers it can sometimes be quite significant. Film refers to the celluloid media on which movies are printed Film is a term that encompasses motion pictures as individual projects, as well as the field in general. ... Turbulent flow around an obstacle; the flow further away is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence in the tip vortex from an airplane wing In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by low momentum diffusion, high momentum convection... The Pitch Drop Experiment at the University of Queensland. ...


Newton's law of cooling

A related principle, Newton's law of cooling, states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. This form of heat loss principle, however, is not very precise; a more accurate formulation requires an analysis of heat flow based on the heat equation in an inhomogeneous medium. The general applicability of this simplification is characterized by the Biot number. The Biot number (Bi) is a dimensionless number used in unsteady-state (or transient) heat transfer calculations. ...


Nevertheless, it is easy to derive from this principle the exponential decay of temperature of a body. If T is the temperature of the body, then A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

where r is some positive constant. From which, it follows that

For example, simplified climate models may use Newtonian cooling instead of a full (and computationally expensive) radiation code to maintain atmospheric temperatures. Climate models use quantitative methods to simulate the interactions of the atmosphere, oceans, land surface, and ice. ...


See also



 
 

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