1. A large plane wall has a thickness L = 50 cm and thermal conductivity k = 25 W/m∙K. On
the left surface (x = 0), it is subjected to a uniform heat flux ̇ while the surface temperature is constant. On the right surface, it experiences convection and radiation heat transfer while the surface temperature is = 225°C and the surrounding temperature is 25°C. The emissivity and the convection heat transfer coefficient on the right surface are 0.7 and 15 W/m2 ∙K, respectively. Show that the variation of temperature in the wall can be expressed as ( ) = ( ̇ / ) ( − ) + , where ̇ = 5130 W/m2, and determine the temperature of the left surface of the wall at x = 0.
FIGURE Q1 2. The wall of a refrigerator is constructed of fiber glass insulation (k=0.035 W⁄(m.℃) sandwiched between two layers of 1-mm-thick sheet metal (k =15.1 W/m· °C). The refrigerated space is maintained at 3°C, and the average heat transfer coefficients at the inner and outer surfaces of the wall are 4 W/m2 · °C and 9 W/m2 · °C, respectively. The kitchen temperature averages 25°C. It is observed that condensation occurs on the outer surfaces of the refrigerator when the temperature of the outer surface drops to 20°C. Determine the minimum thickness of fiberglass insulation that needs to be used in the wall in order to avoid condensation on the outer surfaces
FIGURE Q2 Heat Transfer (MEng4103) Assignment One
3. A 12-m-long and 5-m-high wall is constructed of two layers of 1-cm-thick sheetrock (k =
0.17 W/m·K) spaced 16 cm by wood studs (k = 0.11 W/m·K) whose cross section is 16 cm 35 cm. The studs are placed vertically 60 cm apart, and the space between them is filled with fiberglass insulation (k = 0.034 W/m·K). The house is maintained at 20°C and the ambient temperature outside is 29°C. Taking the heat transfer coefficients at the inner and outer surfaces of the house to be 8.3 and 34 W/m2·K, respectively. Determine (a) The thermal resistance of the wall considering a representative section of it (b) The rate of heat transfer through the wall. 4. In a pharmaceutical plant, a copper pipe (kc = 400 W/m·K) with inner diameter of 20 mm and wall thickness of 2.5 mm is used for carrying liquid oxygen to a storage tank. The liquid oxygen flowing in the pipe has an average temperature of 2200°C and a convection heat transfer coefficient of 120 W/m2 ·K. The condition surrounding the pipe has an ambient air temperature of 20°C and a combined heat transfer coefficient of 20 W/m2 ·K. If the dew point is 10°C, determine the thickness of the insulation (ki = 0.05 W/m·K) around the copper pipe to avoid condensation on the outer surface. Assume thermal contact resistance is negligible.
FIGURE Q4
5. A hot surface at 100°C is to be cooled by attaching 3-cm-long, 0.25-cm-diameter
aluminum pin fins (k = 237 W/m · °C) to it, with a center-to-center distance of 0.6cm. The temperature of the surrounding medium is 30°C, and the heat transfer coefficient on the surfaces is 35 W/m2 · °C. Determine the rate of heat transfer from the surface for a 1-m x 1-m section of the plate. Also determine the overall effectiveness of the fins. Heat Transfer (MEng4103) Assignment One
FIGURE Q5
6. A plane wall with surface temperature of 300°C is attached with straight aluminum triangular fins (k=236 W/m·K). The fins are exposed to an ambient air condition of 25°C and the convection heat transfer coefficient is 25 W/m·K. Each fin has a length of 55 mm, a base of 4 mm thick and a width of 110 mm. Using Table 3–4, determine the efficiency, heat transfer rate, and effectiveness of each fin.
