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 and the holographic system. Then, read how temperature gradients as measured from interferometric holograms can be used to infer heat transfer--in particular, the Nusselt number.
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.