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  3. 22 a hot water pipe with outside radius r has...

Question: 22 a hot water pipe with outside radius r has...

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2.2 A hot water pipe with outside radius r has a temperature T1. A thick insulation, applied to reduce the heat loss, has an outer radius 12 and tempera- ture T2. On T r coordinates, sketch the temperature distribution in the insulation for one-dimensional, steady-state heat transfer with constant properties. Give a brief explanation, justifying the shape of your curve.
ol 2.21 Uniform internal heat generation at 5 x 10 W/m3 is occurring in a cylindrical nuclear reactor fuel rod of 50-mm diameter, and under steady-state conditions the temperature distribution is of the form Tr-abr2. where T is in degrees Celsius and r is in meters, while a 800°C and b-4.167 x 105 oC/m2. The fuel rod properties are k 30 W/m K, p 1100 kg/m3, and cp 800 J/kg K. (a) What is the rate of heat transfer per unit length of 1- the rod at r = 0 (the centerline) and at r = 25 mm (the surface)? (b) If the reactor power level is suddenly increased to 42 103 W/m3, what is the initial time rate of tem- perature change at r 0 and r 25 mm?
2.22 The temperature distribution across a wall 0.3 m thick at a certain instant of time is T(x) = a + bx + cr where T is in degrees Celsius and x is in meters, a 200°C, b-200°C/m, and c-30°C/m2. The wall has a thermal conductivity of 1 W/m K. (a) On a unit surface area basis, determine the rate of heat transfer into and out of the wall and the rate of change of energy stored by the wall. (b) If the cold surface is exposed to a fluid at 100°C, e, what is the convection coefficient? re
2.41 A spherical shell of inner and outer radii r and ro respectively, contains heat-dissipating components, and at a particular instant the temperature distribution in the shell is known to be of the formm T(r)C2 Are conditions steady-state or transient? How do the heat flux and heat rate vary with radius?
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