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These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
An example of a new source of heat "turning on" within an object, causing transient conduction, is an engine starting in an automobile. In this case, the transient thermal conduction phase for the entire machine is over, and the steady-state phase appears, as soon as the engine reaches steady-state operating temperature. In this state of steady ...
In the study of heat conduction, the Fourier number, is the ratio of time, , to a characteristic time scale for heat diffusion, .This dimensionless group is named in honor of J.B.J. Fourier, who formulated the modern understanding of heat conduction. [1]
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 ...
The transient hot wire method has advantage over the other thermal conductivity method since there is a fully developed theory and there is no calibration or single-point calibration. Furthermore, because of the very small measuring time (1 s) there is no convection present in the measurements and only the thermal conductivity of the fluid is ...
The lumped-capacitance model is a common approximation in transient conduction, which may be used whenever heat conduction within an object is much faster than heat transfer across the boundary of the object. The method of approximation then suitably reduces one aspect of the transient conduction system (spatial temperature variation within the ...
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As noted, a Biot number smaller than about 0.1 shows that the conduction resistance inside a body is much smaller than heat convection at the surface, so that temperature gradients are negligible inside of the body. In this case, the lumped-capacitance model of transient heat transfer can be used. (A Biot number less than 0.1 generally ...