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The steady-state heat equation for a volume that contains a heat source (the inhomogeneous case), is the Poisson's equation: − k ∇ 2 u = q {\displaystyle -k\nabla ^{2}u=q} where u is the temperature , k is the thermal conductivity and q is the rate of heat generation per unit volume.
Steady-state methods, in general, work by applying a known heat flux, ˙ (/), to a sample with a surface area, (), and thickness, (); once the sample's steady-state temperature is reached, the difference in temperature, , across the thickness of the sample is measured.
Steady state is also used as an approximation in systems with on-going transient signals, such as audio systems, to allow simplified analysis of first order performance. Sinusoidal Steady State Analysis is a method for analyzing alternating current circuits using the same techniques as for solving DC circuits. [1]
Over time, the field of temperatures inside the bar reaches a new steady-state, in which a constant temperature gradient along the bar is finally set up, and this gradient then stays constant in time. Typically, such a new steady-state gradient is approached exponentially with time after a new temperature-or-heat source or sink, has been ...
There are several ways to measure thermal conductivity; each is suitable for a limited range of materials. Broadly speaking, there are two categories of measurement techniques: steady-state and transient. Steady-state techniques infer the thermal conductivity from measurements on the state of a material once a steady-state temperature profile ...
Thermodynamic temperature is a specifically thermodynamic concept, while the original directly measureable state variables are defined by ordinary physical measurements, without reference to thermodynamic concepts; for this reason, it is helpful to regard thermodynamic temperature as a state function.
In electrical engineering, Neher–McGrath is a method of estimating the steady-state temperature of electrical power cables for some commonly encountered configurations. By estimating the temperature of the cables, the safe long-term current-carrying capacity of the cables can be calculated.
The steady state approximation, [1] occasionally called the stationary-state approximation or Bodenstein's quasi-steady state approximation, involves setting the rate of change of a reaction intermediate in a reaction mechanism equal to zero so that the kinetic equations can be simplified by setting the rate of formation of the intermediate equal to the rate of its destruction.