ECH3624_sp09_HW_08 - find the solution for the transient...

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ECH 3264: Elementary Transport Phenomena (Spring 2009) Homework Set #08 Due: Will not be collected (1) BSL 12A.1 (2) BSL 12B.5 – the solution from Carslaw and Jaeger that is used in parts (b) and (c) is given below. (3) In class, we did a simple heat transient problem for a slab with fixed temperatures at the end of the slab. Consider a thin circular ring shown below. Let us assume that we can approximate the circular ring as a 1-dimensional slab with –L x L. (a) What are the boundary conditions for this problem? (hint: consider the heat flux and temperature at x = -L and L) (b) Given the above boundary conditions and letting f(x) = T(x,0) (the initial temperature distribution),
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Unformatted text preview: find the solution for the transient temperature profile (T(x,t)). Your solution should be general but given a f(x) would allow for the specific solution. Note: you do not need dimensionless variables in this problem. (c) Solve this problem for the steady state profile: (i) directly and (ii) using the solution from (b). (4) A roast is usually considered ready when the center has reached some minimum temperature TM. Assuming that it takes 1 hr to cook a 4-kg roast, use dimensional analysis to estimate the cooking time for a 7.5 kg roast. Assume that the roast is a sphere. List all other assumptions....
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This note was uploaded on 08/30/2009 for the course ECH 3264 taught by Professor Asthagiri during the Spring '09 term at University of Florida.

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