ChE 319 Homework #2 __________________________________________________Due: Thursday, 08 February 2018 1. An asbestos pad
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ChE 319 Homework #2 __________________________________________________Due: Thursday, 08 February 2018 1. An asbestos pad is square in cross section, measuring 5cm on a side at its small end increasing linearly to 10 cm on a side at the large end. The pad is 15 cm high. If the small end is held at 600 K and the large end at 300K, what heat-flow rate will be obtained if the four sides are insulated? Assume one-dimensional heat conduction. The thermal conductivity varies according to k = k0(1 + T), where k0 = 0.1 W/mK and = 210-4 K-1. 2. In a graphite-moderated nuclear reactor, heat is generated uniformly in a set of uranium rods of 0.05m o.d. at the rate (per axial rod length) of 8107 W/m. These rods are jacketed by an annulus through which water at an average temperature of 120oC is circulated. The water cools the rods, and the average heat transfer coefficient is estimated to be 30,000 W/m2K. The thermal conductivity of uranium is 30 W/m/K. Determine the center temperature, and the surface temperature, of the uranium fuel rods. 3. Radioactive waste (k = 20 W/mK) is stored in a cylindrical stainless steel (k = 15 W/m/K) container with inner and outer diameters of 1.0 and 1.2 m, respectively. Thermal energy is generated uniformly within the waste material at a volumetric rate of 2 105 W/m3. The outer container surface is exposed to water at 25°C, with a surface coefficient of 1000 W/m2K. The ends of the cylindrical assembly are insulated so that all heat transfer occurs in the radial direction. For this situation determine (a) the steady-state temperatures at the inner and outer surfaces of the stainless steel (b) the steady-state temperature at the center of the waste material 4. Liquid nitrogen is stored in a thin-walled metallic sphere of radius r1 = 0.25 m. The sphere is covered with an insulating material (k = 0.0015 W/mK) of thickness 30 mm. The exposed surface of the insulation is surrounded by air at 300K. The convective heat transfer coefficient to the air is 25 W/m2 K. The latent heat of evaporation and density of liquid nitrogen are 2105 J/kg and 804 kg/m3, respectively. Liquid nitrogen boils at 77K at one atmosphere. What is the rate of liquid boil off, in kilograms per day? 5. A spherical copper shell, of inside radius 5 cm and wall thickness 1 cm, loses heat to the surrounding air, which is maintained at 25 oC. The inside surface of the shell is maintained at Ti = 120 oC. The external heat transfer coefficient is h = 10 W/m2 K. What is the rate of heat loss to the ambient? Suppose that an additional layer of material is coated onto the exterior of the shell. Is the rate of heat loss increased or decreased by this additional layer? Specifically, answer the following questions. i) If the thermal conductivity of the additional material is one-tenth that of copper, plot the heat loss against the thickness of the additional material for thicknesses in the 0.01 – 0.1 cm range. ii) If the additional material has a thickness of 1 mm, plot the heat loss against the thermal conductivity of the material, for thermal conductivities in the range from one-tenth that of copper to 10 times that of copper. 6. Derive a differential equation (do not attempt to solve it) for the steady temperature distribution in a circumferential rectangular fin as shown right. Assume that the temperature (T = T1) at r = r1 is known and that convective losses occur to the ambient medium at temperature Ta. Give a sufficient set of physically meaningful boundary conditions for solution of the equation.
7. A cylindrical rod 3cm in diameter is partially inserted into a furnace with one end exposed to the surrounding air, which is at 300 K. The temperatures measured at two points 7.6 cm apart are 399 K and 365 K, respectively. If the convective heat-transfer coefficient is 17 W/m2K, determine the thermal conductivity of the rod material. 8. Heat conduction in a nuclear fuel rod assembly: BSL 10B.3 (p. 322, 2nd Ed.)