engineeringheat_transferconduction

hm plane

Available under GPL (Free) and Commercial licence
get a GPL licence
COST (GBP)
this unit 0.80
sub units 0.00
add a commercial licence to your cart
0
viewed 810 times and licensed 1 times
www.codecogs.com/d-ox/engineering/heat_transfer/conduction/hm_plane.php
Controller: CodeCogs    Contact Controller

Interface

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

using namespace Engineering::Heat_Transfer::Conduction;

double hm_plane (double x, double delta, double t1, double t2)[inline]
Computes the temperature at a given distance within a thin planar homogeneous wall.
Click for details on using CodeCogs in ExcelReal cc_hm_plane (Real x, Real delta, Real t1, Real t2)
This function is available as a Microsoft Excel add-in.

Function Documentation

Add calculator to your site or email
 
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:

(1)
\displaystyle q = -\lambda\frac{\mathrm{d}t}{\mathrm{d}x} = \frac{\lambda}{\delta}(t_1 - t_2) \quad \left[\frac{W}{m^2}\right]
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:
(2)
\displaystyle q(x) = \frac{\lambda}{x}\left[t_1 - t(x)\right] 
\quad \left[\frac{W}{m^2}\right].

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

(3)
\displaystyle q(x) = q, \qquad \forall x \in [0, \delta]

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

(4)
\displaystyle t(x) = t_1 \left(1 - \frac{x}{\delta} \right) + t_2 \frac{x}{\delta} 
\quad \left[ {}^{\circ} \mathrm{C} \right].

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
The example code below computes the value of t_x for some particular input data.
Example:
#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
Parameters:
xthe distance within the planar wall (meters)
deltathe thickness of the planar wall (meters)
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 (degrees Celsius)
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"
Authors:
Grigore Bentea, Eduard Bentea (September 2006)
Source Code:
Register

- To get code register with CodeCogs. Already a Member, then Login.


Last Modified: 12 Nov 07 @ 13:48     Page Rendered: 2008-05-14 16:27:18

Page Comments

  You must login to leave a messge


Valid CSS!   Valid XHTML 1.0 Transitional