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Heisler Chart: Heisler Charts Are A Graphical Analysis Tool For The Evaluation of

Heisler charts are a graphical analysis tool used to evaluate heat transfer through infinitely long plane walls, cylinders, and spheres. The charts allow users to determine the central temperature over time for transient heat conduction problems. While simpler than exact solutions, Heisler charts have limitations such as assuming uniform initial temperature and constant external conditions. The charts plot dimensionless variables related to temperature, time, position, and heat transfer to provide temperature profiles and heat transfer rates for the different geometries.

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Krishna Kalikiri
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860 views4 pages

Heisler Chart: Heisler Charts Are A Graphical Analysis Tool For The Evaluation of

Heisler charts are a graphical analysis tool used to evaluate heat transfer through infinitely long plane walls, cylinders, and spheres. The charts allow users to determine the central temperature over time for transient heat conduction problems. While simpler than exact solutions, Heisler charts have limitations such as assuming uniform initial temperature and constant external conditions. The charts plot dimensionless variables related to temperature, time, position, and heat transfer to provide temperature profiles and heat transfer rates for the different geometries.

Uploaded by

Krishna Kalikiri
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Heisler chart

From Wikipedia, the free encyclopedia


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Heisler charts are a graphical analysis tool for the evaluation of heat transfer in thermal
engineering. They are a set of two charts per included geometry introduced in 1947 by M. P.
Heisler[1] which were supplemented by a third chart per geometry in 1961 by H. Gröber.
Heisler charts permit evaluation of the central temperature for transient heat conduction
through an infinitely long plane wall of thickness 2L, an infinitely long cylinder of radius r o,
and a sphere of radius ro.

Although Heisler-Gröber charts are a faster and simpler alternative to the exact solutions of
these problems, there are some limitations. First, the body must be at uniform temperature
initially. Additionally, the temperature of the surroundings and the convective heat transfer
coefficient must remain constant and uniform. Also, there must be no heat generation from
the body itself.[2][3][4]

Contents
 1 Infinitely long plane wall
 2 Infinitely long cylinder
 3 Sphere (of radius ro)
 4 Modern alternatives
 5 See also
 6 References

Infinitely long plane wall


These first Heisler-Gröber charts were based upon the first term of the exact Fourier Series
solution for an infinite plane wall:

,[2]

where Ti is the initial temperature of the slab, T∞ is the constant temperature imposed at the
boundary, x is the location in the plane wall, λn is π(n+1/2), and α is thermal diffusivity. The
position x=0 represents the center of the slab.

The first chart for the plane wall is plotted using 3 different variables. Plotted along the

vertical axis of the chart is dimensionless temperature at the midplane, θo* . Plotted
along the horizontal axis is the Fourier Number, Fo=αt/L2 . The curves within the graph are a
selection of values for the inverse of the Biot Number, where "Bi = hL/k. k is the thermal
conductivity of the material and h is the heat transfer coefficient."[2]
[5]

The second chart is used to determine the variation of temperature within the plane wall for
different Biot Numbers. The vertical axis is the ratio of a given temperature to that at the

centerline θ/θo where the x/L curve is the position at which T is taken. The horizontal axis
−1
is the value of Bi .
[5]

The third chart in each set was supplemented by Gröber in 1961 and this particular one shows
the dimensionless heat transferred from the wall as a function of a dimensionless time
variable. The vertical axis is a plot of Q/Qo, the ratio of actual heat transfer to the amount of
total possible heat transfer before T=T∞ . On the horizontal axis is the plot of (Bi2)(Fo), a
dimensionless time variable.

[5]

Infinitely long cylinder


For the infinitely long cylinder, the Heisler chart is based on the first term in an exact solution
to a Bessel function.[2]

Each chart plots similar curves to the previous examples, and on each axis is plotted a similar
variable.
[5]
[5]

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