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COST (GBP)
this unit 1.25
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hm plane

Computes the temperature at a given distance within a thin planar homogeneous wall.
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Interface

C++
Excel

Hm Plane

 
doublehm_planedoublex
doubledelta
doublet1
doublet2 )[inline]
For a planar homogeneous thin wall, the conductive heat flow per unit area is unidirectional and based on Fourier's Law it is given by:

where \lambda is the thermal conductivity of the wall (constant at any point) and t_1>t_2.

Considering t_2 as a function t(x) of the distance within the wall, we obtain a new expression for the conductive heat flow:

Next we will make the heat flow constant at any distance within the wall:

thus obtaining the formula which gives the value of the temperature at distance x within the wall:

In the left figure of the following diagram you may notice that the distance x is considered starting from the hotter side of the wall, marked in red. Also in the right figure the value of t_x is shown for a particular value of x = x_0.

1/hm_plane_two_figures-746.jpg
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The example code below computes the value of t_x for some particular input data.

Example 1

#include <codecogs/engineering/heat_transfer/conduction/hm_plane.h>
#include <stdio.h>
 
int main()
{
  // the distance within the wall
  double x = 0.165;
 
  // the the thickness of the wall
  double delta = 0.213;
 
  // the temperature of the entry surface for the heat flux
  double t1 = 32.257;
 
  // the temperature of the exit surface for the heat flux
  double t2 = 22.421;
 
  // display the various input values
  printf("   t1 = %.3lf\n   t2 = %.3lf\ndelta = %.3lf\n", t1, t2, delta);
  printf("    x = %.3lf\n\n", x);
 
  printf("The temperature at distance %.3lf within the wall is %.5lf\n",
  x, Engineering::Heat_Transfer::Conduction::hm_plane(x, delta, t1, t2));
 
  return 0;
}
Output
t1 = 32.257
   t2 = 22.421
delta = 0.213
    x = 0.165
 
The temperature at distance 0.165 within the wall is 24.63756

Note

The distance within the wall x must be a real positive number less than or equal to the thickness of the wall \delta and it must be true that t_1 > t_2.

References

Dan Stefanescu, Mircea Marinescu - "Termotehnica"

Parameters

xthe distance within the planar wall (<i>meters</i>)
deltathe thickness of the planar wall (<i>meters</i>)
t1the temperature of the heat flow at the entry surface (degrees Celsius)
t2the temperature of the heat flow at the exit surface (degrees Celsius)

Returns

The temperature at distance x within the wall (<i>degrees Celsius</i>)

Authors

Grigore Bentea, Eduard Bentea (September 2006)
Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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