Heat Transfer

Description

Answer the questions (see ther file):

• Consider a house with a floor space of 200 m2 and an average height of 3 m at sea level where the standard atmospheric pressure is 101.3 kPa. Initially the house is at a uniform temperature of 100C. Now the electric heater switched on, and the heater runs until the air temperature in the house rises to an average value of 22 0C. Determine how much heat the air absorbs. Also, determine the cost of this heat if the unit cost of electricity in area is $0.075/kWh. [5 marks]
• Water heated in an insulated, constant diameter tube by a 5-kW electric resistance heater. If the water enters the heater steadily at 15 0C and leaves at 60 0C, determine the mass flow rate of water. [5 marks]
• Air enters the duct of an air conditioning system at 100 kPa and 100C at a volume flow rate of 15 m3/min. The diameter of the duct is 24 cm and heat is transfer to the air in the duct from the surroundings at a rate of 2 kW. Determine (a) the velocity of the air at the duct inlet and (b) the temperature of the air at the exit. [5 marks]
• Consider a large plane wall of thickness L=0.4 m, thermal conductivity k =1.8 W/m.K, and surface area A=30 m2. The left side of the wall is maintained at a constant temperature of T1= 900C while the right side loses heat by convection to the surrounding air at T∞= 250C with a heat transfer coefficient of h = 24 W/m2.K. Assuming constant thermal conductivity and no heat generation in the wall, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the wall.. (b) Obtain a relation for the variation of temperature in the wall by solving the differential equation and (c) evaluate the rate of heat transfer through the wall. [5 marks]
• Consider a steam pipe of length L= 9 m, inner radius r1 = 5 cm, outer radius r2 = 6 cm, and thermal conductivity k = 12.5 W/m.C. steam is flowing through the pipe at an average temperature of 1500C, and the average convection hat transfer coefficient on the inner surface is given to be h = 70 W/m2.C. If the average temperature on the outer surfaces of the pipe is T2= 800C, (a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the pipe. (b) Obtain a relation for the variation of temperature in the pipe by solving the differential equation and (c) evaluate the rate of heat loss from the steam through the pipe. [5 marks]