The fin array shown below consists of 25 cylindrical pin-fins on a 10-mm thick, 50-mm x 50-mm base plate. Each fin is 25 mm long with a 4-mm diameter. The fin array is made of brass (30% Zn). The edges of the base plate are insulated. The surface of the array with the fins is exposed to air at T = 20°C with h=80 W/m² .K . The flat side of the array is exposed to water at T = 100°C with h=1600 W/m².K. Find the rate of heat transfer from the surface of the fin array to the air (answer: 50 W). 10 mm- 111 T = 100°C h = 1600 W/m².K - 25 mm 4 mm 111 T. = 20°C h = 80 W/m³-K 50 mm 50 mm

You can neglect radiation at the bottom of the plate; the bottom side of the plate has water flowing underneath it. Often, when dealing with liquids (rather than gases), one can neglect radiation because heat transfer due to convection is so much larger (liquids tend to have higher convection coefficient values than gases).

PROBLEM 4: A black thermocouple is inside a chamber with black walls. If the air around the thermocouple is at 20°C, the walls are at 100-C, and the heat transfer coefficient between the thermocouple and the air is 75 W/m²K, what temperature will the thermocouple read?

The Golden Gate Bridge in San Francisco has a main span of length 1.28 km, one of the longest in the world. Imagine that a steel wire with this length and a cross-sectional area of 4.10 x 106 m2 is laid in a straight line on the bridge deck with its ends attached to the towers of the bridge. On a summer day the temperature of the wire is 22.0°C. (a) When winter arrives, the towers stay the same distance apart and the bridge deck keeps the same shape as its expansion joints open. When the temperature drops to -10°C, what is the tension in the wire? (Take Young's modulus for steel to be 2.00 x 1011 N/m2, and the average linear expansion coefficient for steel to be 1.1 x 10-Soc-1.) (b) Permanent deformation occurs if the stress in the steel exceeds its elastic limit of 3.00 x 10° N/m2. At what temperature would the wire reach its elastic limit? (c) Explain how your answers to parts (a) and (b) would change if the Golden Gate Bridge were twice as long.