Energy loss-heat transfer-lumped-capacity method

Question

Question 1: A 50 cm diameter pipeline in the Arctic Carries hot oil at 30 ⁰C and exposed to a surrounding temperature of around -20 ⁰C. Special powder insulation 5 cm thick surrounds the pipe and has a thermal conductivity of 7 mW/m.⁰C. Convective heat transfer coefficient on the outside of the pipe is 9 W/m2. ⁰C. Find out the energy loss from the pipe per meter of length.

Question 2: A house wall might be approximated as two 1.2 cm layers of fiber insulating board, an 8 cm layer of loosely packed asbestos, and 10 cm layer of common brick. Supposing convective heat transfer coefficient 12 W/m2. ⁰C on both side of the wall. Compute the overall heat transfer for this arrangement.

Question 3: Heat produced uniformly in Stainless steel plate having k = 20 W/m.⁰C. The thickness of the plate is 1cm and the heat generation rate is 500 MW/m³. If the two sides of the plate are maintained at 100 and 200 ⁰C correspondingly, compute the temperature at the center of the pipe?

Question 4: A circumferential fin rectangular profile is constructed of Cu and surrounds a tube containing a diameter of 1.25 cm. The fin length is 6 mm and its thickness is 0.3 mm. The fin is exposed to the convection environment a 20 ⁰C with h= 55 W/m².⁰C base temperature.

Question 5: A tube assembly constructed of Cu with an inside diameter of 1.25 cm, wall thickness of 0.8 mm and circumferential fins about the periphery. The fins have thickness of 3 mm, and are spaced 6 mm apart. If the convective heat transfer coefficient from tube and fins to the surrounding air is 50 W/m2. ⁰C, compute the thermal resistance for a 30 cm length of the tube fin combination. Find out the fin efficiency for this arrangement? If the inside tube temperature is 100 0C and surrounding temperature is 20 ⁰C, Find out the heat loss per meter length of the tube? What fraction of heat loss by the fin?

Question 6: A piece of Al weighing 6 kg and initially at temperature of 300^OC is abruptly immersed in a fluid at a temperature of 20^OC. The convective heat transfer coefficient is 58 W/m2. ⁰C. Taking the Aluminum as a sphere containing the same weight as that given, estimate the time need to cool the aluminum to 90 ⁰C by using the lumped-capacity method of analysis.

Question 7: A 4 cm diameter Cu sphere is initially at uniform temperature of 400 ⁰C. It is abruptly exposed to a convection environment at 30 ⁰C with h = 20 W/m².⁰C. Compute time necessary for the center of the sphere to reach a temperature 80 ⁰C.

Question 8: A steel cylinder 10 cm in diameter and 10 cm long is initially at 300 ⁰C. It is immersed in an oil bath that is maintained at 40 ⁰C, with h = 280 W/m². ⁰C. Find out the temperature at the center of solid after 2 min.

Question 9: Air at 1 atm, 300K, and Re = 50,000:

a) Flow across the cylinder with a diameter of 10 cm.
b) Flow inside a tube with diameter of 10 cm.
c) Flow all along the flat plate of length 10 cm.

Compute the Average Heat transfer coefficient for each of above cases and comment on outcome.

Question 10: A smooth glass plate is coated with the special electrically conductive film which might be used to produce a constant heat flux on the plate. Find out the air flow velocity which must be employed to remove 850 W from a 0.5-m-square plate, maintained at an average temperature of 65 ⁰C and dissipating heat to air at 1 atm and 20 ⁰C. Assume that the plate as well radiated like black surface to the surrounding 20 ⁰C. What flow velocity would be essential to dissipate the 850 W under this condition?