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hm sphere

Computes the temperature inside a thin homogeneous spherical wall.
Controller: CodeCogs

Interface

C++
Excel

Hm Sphere

 
doublehm_spheredoubler
doubled1
doubled2
doublet1
doublet2 )[inline]
Consider the case of a thin homogeneous spherical wall with internal radius \inline r_1, external radius \inline r_2, and temperatures \inline t_1, \inline t_2 corresponding to each surface. Also let the thermal conductivity \inline \lambda be constant at any point inside the wall.

The total conductive heat flow that passes through the surface \inline S = 4 \pi r^2 (\inline r_1 < r < r_2) is expressed by the following equation:

which in turn gives:

By integrating the previous equation and considering appropriate limit conditions, it follows that the temperature inside the spherical wall at a radius of r is:

In the diagram below the value of the function \inline t(r) is shown for a particular value of \inline r.

1/hm_sphere-378.jpg
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Example 1

#include <codecogs/engineering/heat_transfer/conduction/hm_sphere.h>
#include <stdio.h>
 
int main()
{
  // input data
  double r = 0.28, d1 = 0.5, d2 = 0.6, 
        t1 = 45.7, t2 = 20.8;
 
  // display the various input data
  printf("Input data:\n\n");
  printf(" r = %.2lf\n", r);
  printf("d1 = %.2lf\nd2 = %.2lf\n", d1, d2);
  printf("t1 = %.2lf\nt2 = %.2lf\n\n", t1, t2);
 
  // compute the temperature inside the spherical wall
  double t = Engineering::Heat_Transfer::Conduction::hm_sphere
  (r, d1, d2, t1, t2);
 
  // display the result
  printf("The temperature inside the spherical wall is:\n\n");
  printf("%.10lf\n\n", t);
 
  return 0;
}

Output

Input data:
 
 r = 0.28
d1 = 0.50
d2 = 0.60
t1 = 45.70
t2 = 20.80
 
The temperature inside the spherical wall is:
 
29.6928571429

Note

The following inequalities must always hold when passing values to the function:

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Parameters

rthe given radius (<i>meters</i>)
d1the internal diameter of the spherical wall (<i>meters</i>)
d2the external diameter of the spherical wall (<i>meters</i>)
t1the temperature of the heat flow at the entry surface (<i>degrees Celsius</i>)
t2the temperature of the heat flow at the exit surface (<i>degrees Celsius</i>)

Returns

The temperature at radius r within the spherical wall (<i>degrees Celsius</i>).

Authors

Grigore Bentea, Lucian Bentea (October 2006)
Source Code

Source code is available when you buy a Commercial licence.

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Last Modified: 18 Oct 07 @ 17:07     Page Rendered: 2022-03-15 06:35:23