ME 320L – Heat Transfer Laboratory
 1 
University of New Mexico
Demonstration of Fourier’s Law
Heat transfer is one of the basis on which the engineering is built. Among the topic that define
the heat transfer there is the Fourier’ Law. The purpose of this report is to confirm
experimentally this law.
Introduction
Three experiments were established in order to get the
relationship between the heat flux, the temperature and the
position. The experiment consisted in connect an insulated
brass rod to a heater in one end and to water cooled sink in
the other (see Fig 1). Then, different thermocouples
measured the temperatures along the rod. With this, an
expression for the gradient of the temperature can be
obtained. Change in the area and the material were also
investigated. Steady state condition is assumed.
Figure 1
Theoretical Background
The relation between the heat flux and the temperature
gradient is given by the Fourier’s Law, which states that the
heat flux is proportional to the temperature gradient.
Mathematically,
(1)
x
dT
q
dx
∝
(2)
x
dT
qk
dx
=−
The proportionality constant is
k
and it is called thermal
conductivity. The minus sign implies that the heat must
occur from a higher to a lower temperature. Finally, the heat
flux across a certain area gives the total heat:
(3)
x
dT
QA
k
dx
In this case, the rod is insulated on the sides and one
dimension analysis is assumed.
The experiments were divided in three parts. The first part
consisted in get a relation between the temperature gradient
and the heat. In the second part, the area variation was
studied. And in the third part, the variation of thermal
conductivity was considered.
Equipment and procedure
The experiments were performed in the heat transfer
facilities, at the Mechanical Engineering Building.
The insulated brass rod has two sections; each one contains
three thermocouples connected to an oscilloscope. One end
of the rod was connected to a water cooled heater sink, at 4º
C. The other end was connected to an electrical heater. The
electrical heater was operated also by the oscilloscope (see
Fig 2). The thermocouples were spaced 15 mm apart and
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 Spring '08
 mamoli
 Thermodynamics, Heat, Steady State, Heat Transfer, Thermal conductivity, Heat Transfer Laboratory

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