# hm plane

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

Controller: **CodeCogs**

**Contents**

doublehm_plane( | double | x | |

double | delta | ||

double | t1 | ||

double | t2 | )[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 is the thermal conductivity of the wall (constant at any point) and .
Considering as a function 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 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 is shown for a particular value of . The example code below computes the value of 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 and it must be true that .

### References

- Dan Stefanescu, Mircea Marinescu - "Termotehnica"

### Parameters

x the distance within the planar wall (<i>meters</i>) delta the thickness of the planar wall (<i>meters</i>) 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 distance
*x*within the wall (<i>degrees Celsius</i>)

### Authors

*Grigore Bentea, Eduard Bentea (September 2006)*

##### Source Code

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