Overview
NOTE: In all the following problems, the solids are initially at a uniform temperature.
1) Metallic spheres of 4 cm diameter initially at 200 0C are subjected air flowing at 20 0C providing a convection coefficient of 200 W/m2/K. Find how long these will take to reach a center temperature of 100 0C if the material is (1) copper and (2) stainless steel, AISI 304.
2) Concrete slabs 10 cm thick initially at 25 0C are subjected to air flowing at 55 0C providing a convection coefficient of 100 W/m2/K on both sides. How long will it take for the center-plane temperature to reach 40 0C? What will be the surface temperature at that time?
2.a) Consider clay slabs to be used as thermal storage devices. These slabs are 20 cm thick and initially at a uniform temperature of 50 0C. Air at 55 0C flows over providing a convection coefficient of 100 W·m−2·K−1 on both sides of the slabs. What will be the surface temperature after one hour? What will be the center-line temperature after 1 hour?
3) Concrete pavement initially at -10 0C is suddenly subjected to a heavy precipitation bringing its surface temperature up to 2 0C. How long will it take for a plane at a depth of 0.5 cm to reach 0 0C?
4) A one-inch thick steak initially at room temperature is placed inside an oven maintained at 250 0C. Estimate how long it will take for its internal temperature to reach 70 0C. What will be the surface temperature at that time if we assume no steam generation? Include radiation (see slide #12; Lecture 8) as well as convection (h ~ 3 W/m2/K) in your analysis.
Please follow the homework format below for every question 1) Draw a schematic and show your control volume (CV); include directions (if known) of energy input/output between your CV and it's Surroundings.
2) Show on your Schematic what info is provided (Given/Known); what is to be calculuated/determined (Find/Unknown).
3) Assumptions; any material properties including their source (Table No., eg).
4) Relevant Equations: write out the basic laws and formulae you think will be useful.
5) Analysis: Show all your calculations step by step, beginning with the appropriate equations; simplify and find the final algebraic expression(s) for your answer(s) before plugging any numerical input.
6) Answer(s): Box or highlight your answers; must include appropriate units.
7) Comments/Observations: Note anything that is worthy of our attention; an unexpectedly high or low figure, eg. Correct/Modify your Assumptions and review/correct your Analysis if necessary.