ASSIGNMENT FOR FORCED CONVECTION

**Problem 1:** Estimate the total heat released into the atmosphere from the Mt.
St. Helens 1980 eruption. Some of the eruption data are found in the **Mt.
St. Helens** figure caption. You will also need an approximation
for the heat capacity of magma from an outside source to complete your
estimate. Give the answer in calories.

*In the following problems you will be required to estimate from experimental
data the rate at which heat is transported by forced convection away from
a heated, ribbed surface attached to the bottom surface of a horizontal
duct. The experimental data consist of interferograms from which the necessary
measurements are to be made. First familiarize yourself with the experimental
setup*

**Problem 2:** For this problem, heat is being fed into the ribbed lower surface
of the duct, but no air is blowing. The system has reached steady state,
i.e., there is no additional buildup of heat in the duct. Where is the
heat going? **View the interferogram**.
Since you know that heat flows down temperature gradients, and each fringe
is essentially an isotherm, you should be able to qualitatively sketch
the paths by which heat is leaving the system. Produce this sketch and
comment.

Here the system has reached steady state, i.e., heat entering the system
through the heated blocks is exactly compensated for by heat leaving the
system through the ends of the duct. The same is true in any control
volume.
Consider a rectangle whose bottom is one of the heated ribs, whose
top is the insulated top of the duct, and whose sides are lines extending
across the duct from bottom to top. In steady state, heat entering this
control volume must be matched by heat leaving the control volume. Since
we can deduce the flow of heat across any duct cross-section from the
angle of the fringes on the
interferogram, we can estimate the heat flux emanating from the heated
block. These are the **calculations**
you'll need to make. To take measurements
from the interferogram, click **here**.
Based on these measurements, what is the heat flux * q''*
across one heated block?

**Problem 3:** In this problem, there is air blowing through the duct with Reynolds
number 800. Estimate the heat transfer coefficient--the Nusselt number--in
the experiment in two places: near the trailing edge of the heated block,
and near the leading edge of the heated block. Click **here**
to make these measurements. As you make your measurements and calculations,
deduce the distance (in meters) between the two positions. Report the two
transfer coefficients. Explain why they're different (or the same). What
would you have predicted? Did your measurements confirm this prediction?

**Problem 4:** As part of estimating the Nusselt number in task 3, you had to calculate
the mean temperature at each of the two streamwise positions. These mean
temperatures were different. Why? The answer is that heat is added to the
flow along the length of block between the two cross-sections. Since you
can deduce the convective
velocity from the Reynolds number (Re=800), and if you assume steady-state heat
transport,
you can deduce the heat flux * q''* generated by the block.
Is this heat flux any different than that deduced in Problem 2? (In
principle, they should be the same since the blocks are driven with
constant power). Discuss why your answers may be different.