A single-cylinder air-cooled lawn mower engine operates under steady conditions. The cylinder temperature cannot exceed 300 ⁰C. To cool the engine, annular fins are placed around the cylinder. The fins are 0.3 cm thick and are 2 cm long from base to tip. The fins are made of cast iron (k = 52 W/mK). The outside diameter of the engine cylinder at the base of the fin is 0.3 m. Assume that the engine operates in 30 ⁰C air and that the heat transfer coefficient on the sides and tip of the fin is 12 Wm^-2K^-1. Determine the number of fins needed to cool a 3 kW engine to the given temperature if the engine has an efficiency of 30 % and 50 % of the total heat given off by the engine actually is dissipated through the fins ?

A wood stove heats a small cabin with the following dimensions 8 m x 6 m x 3 m (length x width x height) to 25°C. Of the heat generated by burning wood, 60% is lost up the chimney. The cabin also loses heat through walls, ceiling and floor. Assume that all sides of the house except the floor are insulated with a 10 cm thick polyethylene foam layer having a thermal conductivity htc = 0.038 W/(m•°C). The heat loss through the floor is 1/5 of the heat loss through the ceiling. Outside air is at -5°C. a) How much heat is lost in total from the ceiling, walls, and floor? b) How many kg of wood per hour is needed as fuel for the cabin to maintain its temperature if heat value of wood is AH = 18,000 kJ/kg?

= 31. A circular fin of diameter D = 0.25 inches and length L 4 inches transfers heat at a rate Q = 5.66 Btu/hr to air. The convective heat transfer coefficient is 3.62 Btu/hr-ft²- °F and the temperature difference between the fin-wall interface and the air is 100 °F. What is the thermal conductivity of the fin? What is the temperature of the fin tip?

Question #7 Steam at 320°C flows in a stainless steel pipe (k-15W/m K) whose inner and outer diameter are 5cm and 5.5cm respectively. The pipe is covered with 3cm thick glass wool insulation (-0.038W/mK). Heat is lost to the surroundings at 5°C by natural convection and radiation, with a combined natural convection and radiation heat transfer coefficient of h 15W/m² K. Taking the heat transfer coefficient inside the pipe to be happe = outside pipe = 80 W/m²K. (A) Draw the schematic diagram of this problem and label all quantities. (B) Draw the thermal network diagram of this problem and label all thermal resistors and the direction of heat flow. (C) Determine the (i) inner surface area (ii) outer surface area (iii) inner thermal resis- tance (iv) outer thermal resistance (v) thermal resistance across pipe and (vi) thermal resistance across insulation. (D) Determine the total thermal resistance for the unit length of pipe. (E) Determine the rate of heat loss from the steam per unit…