hm_sphere

Consider the case of a thin homogeneous spherical wall with internal radius $r_1$, external radius $r_2$, and temperatures $t_1$, $t_2$ corresponding to each surface. Also let the thermal conductivity $\lambda$ be constant at any point inside the wall.

The total conductive heat flow that passes through the surface $S = 4 \pi r^2$ ($r_1 < r < r_2$) 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 $t(r)$ is shown for a particular value of $r$.

#include <codecogs/engineering/thermodynamics/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::Thermodynamics::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;
}

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

Parameters

Returns

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

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"