(1)

(Welty, Rorrer, Foster, 6th Edition International Student Version 16.2)

It is desired to transport liquid metal through a pipe embedded in a wall at a point where the temperature is 650K. A 1.2-m thick wall constructed of a material having thermal conductivity varying with temperature according to , where T is in K and k is in W/m.K, has its inside surface maintained at 925 K. The outside surface is exposed to air at 300 K with a convective heat transfer coefficient of 23 W/m2.K. How far from the hot surface should the pipe be located. What is the heat flux for the wall? (2) WWWR 17.13 A 2.5-cm-thick sheet of plastic (k = 2.42 W/m.K) is to be bonded to a 5-cm-thick aluminium plate. The glue that will accomplish the bonding is to be held at a temperature of 325K to achieve the best adherence, and the heat to accomplish this temperature is to be provided by a radiant source. The convective heat transfer coefficient on the surfaces of both the plastic and aluminium is 12 W/m2.K, and the surrounding air is at 295 K. What is the required heat flux if it is applied to the surface of (a) plastic? (b) aluminium? (3) (Modified from Welty, Rorrer, Foster, 6th Edition International Student Version 16.1) The steady state expression for heat conduction through a plane wall is . For steady state heat conduction through a hollow cylinder, an expression similar to the equation is

Where

is the log-mean are defined as

a. Show that as defined above satisfies the equations for steady state radial heat transfer in a hollow cylindrical element. b. If arithmetic mean area, is used rather than the logarithm mean, calculate the resulting percent error for values of of 1.5, 3 and 5. (4) (Welty, Rorrer, Foster, 6th Edition International Student Version 16.12) A thin slab of material is subjected to microwave radiation that causes volumetric heating to vary according to where