Problem: Deduce the cross-sectional profile of a heated conductive
bar based on its temperature.
Heat flows through thermally conductive materials by a process generally known
as 'gradient transport'. Gradient heat transport depends on three quantities:
the conductivity of the material, the cross-sectional area of the material,
and the spatial gradient of temperature. The larger the conductivity, gradient,and/or
cross-section, the faster the heat flows.
In this experiment, the flow of heat through a collection of conductive bars
which vary in cross-section is simulated. The simulation is performed as a one-dimensional,
time-dependent process--along the x-axis. Heat flow in the y-direction is assumed
to be negligible, and variations in the cross-sections of the bars are taken
into account by characterizing the conductivity C(x)of each bar a function of
position. As the simulation begins, heat flows into the bar and changes the
bar's temperature distribution. From that distribution, the task is to deduce
the bar's cross-section.
Heat is applied to the bar at x=0 in one of three ways: as constant temperature,
as constant heat flux, or as sinusoidal temperature. Heat is managed at the
far end of the bar x=L in one of two ways: no heat loss, as constant temperature.
Expressed as boundary conditions for temperature as a function of position and
time: T(0,t)=100, dT(0,t)/dx=D, T(0,t)=A+Bcos(t), dT(L,t)/dx=0, T(L,t)=0.
There are two modes for running the experiment: 1) one in which temperature
is recorded from movable temperature probes, and 2) one in which the temperature
profile along the length of the bar is displayed. In both of these modes, boundary
conditions and bar cross-sections are chosen randomly.
There is a third mode for the simulation: a practice mode in which the user
can choose his own bar cross-sections and boundary conditions. In this case
the simulation generates temperature profiles.
Try your luck at deducing the randomly-chosen bar in each of the first two
modes. Click on 'done' when you're finished, and record the values of 'parameter'--the
answer key. (Of course, try the practice mode first to get a sense for the experiment.)
Start the conduction