Computes the temperature inside a thin homogeneous spherical wall.

Contents

Interface Function Documentation Page Comments

Interface

#include <codecogs/engineering/heat_transfer/conduction/hm_sphere.h>

using namespace Engineering::Heat_Transfer::Conduction;

	double	hm_sphere (double r, double d1, double d2, double t1, double t2)[inline] Computes the temperature inside a thin homogeneous spherical wall.
	Real	cc_hm_sphere (Real r, Real d1, Real d2, Real t1, Real t2) This function is available as a Microsoft Excel add-in.

Function Documentation

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:

(4)

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 (degrees Celsius).

Authors:

Grigore Bentea, Lucian Bentea (October 2006)