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# hm sphere

Computes the temperature inside a thin homogeneous spherical wall.
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## Hm Sphere

 doublehm_sphere( double r double d1 double d2 double t1 double t2 )[inline]
Consider the case of a thin homogeneous spherical wall with internal radius , external radius , and temperatures , corresponding to each surface. Also let the thermal conductivity be constant at any point inside the wall.

The total conductive heat flow that passes through the surface () 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 is shown for a particular value of .

### 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

 r the given radius (meters) d1 the internal diameter of the spherical wall (meters) d2 the external diameter of the spherical wall (meters) t1 the temperature of the heat flow at the entry surface (degrees Celsius) t2 the temperature of the heat flow at the exit surface (degrees Celsius)

### 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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