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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 ...
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 ...
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 object from one place to another must not be called heat transfer. However, it is common to say ‘heat flow’ to mean ‘heat content’. [1]
The porous medium equation name originates from its use in describing the flow of an ideal gas in a homogeneous porous medium. [6] We require three equations to completely specify the medium's density , flow velocity field , and pressure : the continuity equation for conservation of mass; Darcy's law for flow in a porous medium; and the ideal gas equation of state.
In physics and engineering, heat flux or thermal flux, sometimes also referred to as heat flux density [1], heat-flow density or heat-flow rate intensity, is a flow of energy per unit area per unit time. Its SI units are watts per square metre (W/m 2). It has both a direction and a magnitude, and so it is a vector quantity.
The number of transfer units (NTU) method is used to calculate the rate of heat transfer in heat exchangers (especially parallel flow, counter current, and cross-flow exchangers) when there is insufficient information to calculate the log mean temperature difference (LMTD). Alternatively, this method is useful for determining the expected heat ...
Each pair in the equation are known as a conjugate pair with respect to the internal energy. The intensive variables may be viewed as a generalized "force". An imbalance in the intensive variable will cause a "flow" of the extensive variable in a direction to counter the imbalance. The equation may be seen as a particular case of the chain rule.
R = Resistance(s) to heat flow in pipe wall (K/W) Other parameters are as above. [16] The heat transfer coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place. The areas for each flow will be different as they represent the contact ...