Now that we have obtained the temperature distribution in the rod Equation
(3.16), the heat flux at any
location is determined using Fourier's law. The heat flux (W/m2)
is
The outward directed component of the vector
at
z = 0 and
z = L and respectively
where
is the outward drawn normal to the surface. the net outflow from the rod is
then
| (3.20) |
|
| where |
Q = net outflow of heat from the rod, watts |
| |
Ac = cross sectional area of rod, m2 |
Start with Equation (3.20).
To determine dT/dz we have to differentiate the temperature profile
with respect to z. The temperature distribution is given by equation
(3.16)
Differentiating equation (
3.16)
At
z = 0 and
z = L.
Inserting Equations (3.16b) and (3.16c) into equation (
3.20)
and simplifying we obtain
The coefficients are
The positive sign says that the net heat flow is out of the rod.
Copyright © 1998 Rensselaer Polytechnic Institute.
All Rights Reserved.