ABSTRACT
Consider an electrical resistor shown in Figure 5.1. If there is a potential difference between the two ends of this resistor, a current will flow through it. The direction of this current is from the high potential to the low potential ends of this resistor, and its magnitude is given by the Ohm’s law;
I V V
R = −1 2 . (5.1)
Now, consider a layer with thickness L and surface area A as shown in Figure 5.2. If there is a temperature difference across this layer (i.e., T T1 2 0− ≠ ), there will be conduction heat transfer from its high temperature side to its low temperature side. Fourier’s law that was introduced in Chapter 4, Section 4.1, gives the magnitude of this conduction heat transfer rate as
Q kA T T
L cond =
−1 2 , (5.2)
or
Q T T L kA
cond = −1 2 /
. (5.3)
It will be shown in Chapter 8 that Equations 5.2 and 5.3 are strictly valid for one-dimensional steady-state heat transfer in a medium with no heat generation and constant thermal conductivity. There are three similarities between Equation 5.3 for conduction heat transfer rate and Ohm’s law, Equation 5.1: (1) temperature difference across a layer generates conduction heat transfer just as potential difference across an electrical resistor generates current flow, (2) conduction heat transfer rate is from high temperature to low temperature side of a layer similar to current flow that is from high potential to low potential end of a resistor, and (3) the term L/kA in the denominator of Equation 5.3 plays the same role as R in Equation 5.1. Using these similarities, Equation 5.3 is written similar to Ohm’s law:
Q T T Rcond cond
= −1 2 , (5.4)
where Rcond = L/kA is called conduction thermal resistance and is measured with the unit °C/W. This equation indicates that temperature difference across a layer drives the conduction heat transfer. On the other hand, conduction thermal resistance, which is directly proportional to the thickness of the layer and inversely proportional to its conductivity and surface area, opposes the conduction heat transfer. The equivalent thermal resistance for the physical layer shown in Figure 5.2 is shown in Figure 5.3.
