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Some of the designations for the Greens function number system are given next. Coordinate system designations include: X, Y, and Z for Cartesian coordinates; R, Z, φ for cylindrical coordinates; and, RS, φ, θ for spherical coordinates. Designations for several boundary conditions are given in Table 1.
The physical processes and solutions of the governing equations are considered separately for each object in two subdomains. Matching conditions for these solutions at the interface provide the distributions of temperature and heat flux along the body–flow interface, eliminating the need for a heat transfer coefficient.
It is commonly denoted by , , or and is measured in W·m −1 ·K −1. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal conductivity. For instance, metals typically have high thermal conductivity and are very efficient at conducting heat, while the opposite is true for insulating ...
A 2008 review paper written by Philips researcher Clemens J. M. Lasance notes that: "Although there is an analogy between heat flow by conduction (Fourier's law) and the flow of an electric current (Ohm’s law), the corresponding physical properties of thermal conductivity and electrical conductivity conspire to make the behavior of heat flow ...
The Black–Scholes option pricing model's differential equation can be transformed into the heat equation allowing relatively easy solutions from a familiar body of mathematics. Many of the extensions to the simple option models do not have closed form solutions and thus must be solved numerically to obtain a modeled option price.
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.
Conduction heat flux q k for ideal gas is derived with the gas kinetic theory or the Boltzmann transport equations, and the thermal conductivity is =, -, where u f 2 1/2 is the RMS (root mean square) thermal velocity (3k B T/m from the MB distribution function, m: atomic mass) and τ f-f is the relaxation time (or intercollision time period ...
System analysis by the lumped capacitance model is a common approximation in transient conduction that may be used whenever heat conduction within an object is much faster than heat conduction across the boundary of the object. This is a method of approximation that reduces one aspect of the transient conduction system—that within the object ...