Collection of exercises

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Exercises for the HTTA course - A.Y. 2013-14 (version 2014/06/24) Heat Transfer and Thermal Analysis A.Y. 2013-14 Exercise Lectures 1 Exercises for the HTTA course - A.Y. 2013-14 (version 2014/06/24) 2 Radiation Exercise 1 Topic: Shielded thermocouple / equivalent electric network Draw the equivalent electric network for a system constituted by a shielded thermocouple inserted in a duct. Exercise 2 Topic: Intensity, solid angles, irradiation Example 12.1 of the textbook Incropera et al., Fundamentals of Heat and Mass Transfer, 7th ed. A small surface of area A1 = 10 −3 m2 is known to emit diffusely, and from measurements the total intensity associated with emission in the normal direction is In = 7000 W/m 2sr. Radiation emitted from the surface is intercepted by three black surfaces of area A2 =A3 =A4 = 10−3 m2, which are at a distance r = 0.5 m from A1 and are oriented as shown in the figure. Calculate: 1. the intensity of emission in each of the three directions; 2. the solid angles subtended by the three surfaces; 3. the rate at which radiation is intercepted by the three surfaces; 4. the irradiation G at each of the three surfaces. 3 Exercises for the HTTA course - A.Y. 2013-14 (version 2014/06/24) Solution: 1. The emission is diffuse, therefore the intensity of the emitted radiation is independent on the direction, and equal to I = 7000 W/m 2sr for all the three given directions. 2. Treating the three surfaces A2,A3 andA4 as differential surfaces areas, the solid angles may be computed as: dω1→i = dAin r2 i = dAi cosθi→1 r2 i wheredAin is the projection of the i th-surface normal to the direction of the radiation and θi→1 is the angle between the direction of the radiation incident onto the i th-surface and the normal to that surface. Since surfaces A3 and A4 are…