It is proposed to air-cool the cylinders of a combustion chamber by joining an aluminum casing with annu- lar fins (k = 240 W/m•K) to the cylinder wall (k = q," = 105 W/m². Assuming negligible contact resistance between the wall and the casing, determine the wall inner temperature T; and the base temperature Tp. Determine these temperatures if the interface contact resistance is 50 W/m·K). Cylinder wall Aluminum casing R", = 10-4 m².K/W. tc T T, t = 2 mm 8 = 2 mm 11 r; = 60 mm T, h r = 66 mm r2 = 70 mm = 95 mm The air is at 320 K and the corresponding convection coefficient is 100 W/m² ·K. Although heating at the inner surface is periodic, it is reasonable to assume steady-state conditions with a time-averaged heat flux of

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A thick-walled cylindrical tubing of hard rubber (k=0.151 W/m*K) having an inside radius of 5 mm and an outside radius of 20 mm is being used as a temporary cooling coil in a bath. Ice water is flowing rapidly inside, and the inside wall temperature is 275 K. The outside surface temperature is 300 K. A total of 20 W must be removed from the bath by the cooling coil. How many meter of tubing are needed?

40°C water with hwater = 800 W/m² K is flowing in a Pyrex tube. The inner and outer diameters of the tube are 25 mm and 35 mm. A thin metallic heater element bonded to the outer surface of the tube is being used to heat the water by transferring 600 W/m of thermal energy to the water flowing in the tube. The Pyrex tube and heater are covered with a 10-mm thick layer of foam insulation. The outer surface of the foam insulation is exposed to air at T = -5°C with hair = 12 W/m².K. The heater = air element must generate more than 600 W/m, because part of the heat being generated is lost to the air surrounding the foam insulation. Assume kp = 1.30 W/m K for Pyrex and k = 0.026 W/m K for the foam insulation. a) Find the temperature of the heater element needed to transfer 600 W/m of thermal energy to the water in the tube. b) Find the total rate at which the heater element must generate thermal energy. Water Pyrex tube, kp = 1.30 W/m.K = 40°C water hwater = 800 W/m².K Heater element Tair=…