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The heat transfer coefficient has SI units in watts per square meter per kelvin (W/(m 2 K)). The overall heat transfer rate for combined modes is usually expressed in terms of an overall conductance or heat transfer coefficient, U. Upon reaching steady state, the heat transfer rate is: ˙ = ()
The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy , Prandtl–Taylor analogy) developed to directly relate heat transfer coefficients, mass transfer coefficients and friction factors, Chilton and Colburn J-factor analogy proved to be the most accurate.
The Biot number (Bi) is a dimensionless quantity used in heat transfer calculations, named for the eighteenth-century French physicist Jean-Baptiste Biot (1774–1862). The Biot number is the ratio of the thermal resistance for conduction inside a body to the resistance for convection at the surface of the body.
This article describes how to use a computer to calculate an approximate numerical solution of the discretized equation, in a time-dependent situation. In order to be concrete, this article focuses on heat flow, an important example where the convection–diffusion equation applies. However, the same mathematical analysis works equally well to ...
In mathematics and physics, the heat equation is a parabolic partial differential equation. The theory of the heat equation was first developed by Joseph Fourier in 1822 for the purpose of modeling how a quantity such as heat diffuses through a given region. Since then, the heat equation and its variants have been found to be fundamental in ...
The statement of Newton's law used in the heat transfer literature puts into mathematics the idea that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. For a temperature-independent heat transfer coefficient, the statement is:
describes heat transfer across a surface = Here, is the overall heat transfer coefficient, is the total heat transfer area, and is the minimum heat capacity rate. To better understand where this definition of NTU comes from, consider the following heat transfer energy balance, which is an extension of the energy balance above:
This equation shows that the temperature decreases exponentially over time, with the rate governed by the properties of the material and the heat transfer coefficient. [7] The heat transfer coefficient, h, is measured in , and represents the transfer of heat at an interface between two materials. This value is different at every interface and ...