In thermal engineering, Heisler charts are a graphical analysis tool for the evaluation of heat transfer in transient, one-dimensional conduction.
Heisler charts allow the evaluation of the central temperature for transient heat conduction through an infinitely long plane wall of thickness 2L, an infinitely long cylinder of radius ro, and a sphere of radius ro.
[1] Although Heisler–Gröber charts are a faster and simpler alternative to the exact solutions of these problems, there are some limitations.
Additionally, the temperature of the surroundings and the convective heat transfer coefficient must remain constant and uniform.
[1][3][4] These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: where Ti 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.
Plotted along the vertical axis of the chart is dimensionless temperature at the midplane,
The curves within the graph are a selection of values for the inverse of the Biot number, where Bi = hL/k.
[1] [5] The second chart is used to determine the variation of temperature within the plane wall at other location in the x-direction at the same time of
On the horizontal axis is the plot of (Bi2)(Fo), a dimensionless time variable.
[5] For the infinitely long cylinder, the Heisler chart is based on the first term in an exact solution to a Bessel function.