Chapter 1, Problem 1.59P

2.30 An electrical heater capable of generating 10,000 W is to be designed. The heating element is to be a stainless steel wire having an electrical resistivity of ohm-centimeter. The operating temperature of the stainless steel is to be no more than 1260°C. The heat transfer coefficient at the outer surface is expected to be no less than in a medium whose maximum temperature is 93°C. A transformer capable of delivering current at 9 and 12 V is available. Determine a suitable size for the wire, the current required, and discuss what effect a reduction in the heat transfer coefficient would have. (Hint: Demonstrate first that the temperature drop between the center and the surface of the wire is independent of the wire diameter, and determine its value.)

A composite refrigerator wall is composed of 5 cm of corkboard sandwiched between a 1.2-cm-thick layer of oak and a 0.8-mm-thick layer of aluminum lining on the inner surface. The average convection heat transfer coefficients at the interior and exterior wall are 11 and 8.5W/(m2K) respectively. (a) Draw the thermal circuit. (b) Calculate the individual resistances of the components of this composite wall and the resistances at the surfaces. (c) Calculate the overall heat transfer coefficient through the wall. (d) For an air temperature of 1C inside the refrigerator and 32C outside, calculate the rate of heat transfer per unit area through the wall.

1.2 The weight of the insulation in a spacecraft may be more important than the space required. Show analytically that the lightest insulation for a plane wall with a specified thermal resistance is the insulation that has the smallest product of density times thermal conductivity.

2.38 The addition of aluminum fins has been suggested to increase the rate of heat dissipation from one side of an electronic device 1 m wide and 1 m tall. The fins are to be rectangular in cross section, 2.5 cm long and 0.25 cm thick, as shown in the figure. There are to be 100 fins per meter. The convection heat transfer coefficient, both for the wall and the fins, is estimated to be K. With this information determine the percent increase in the rate of heat transfer of the finned wall compared to the bare wall.

1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.

A computer room located on the second floor of a five-storey office building is 10m x 7m. The exterior wall is 3.5m high and 10m long; it is a metal curtain wall (steel-backed with 10mm of insulating board), 75mm of glass fiber insulation, and 16mm of gypsum board. The single-glazed window (U=5.9 W/m^2-K) make-up 30% of the exterior wall. Three (3) computer sets at 500 Watts each and 500 Watts of total lightning power in the room operate 24 hours per day. The indoor temperature is 20°C. Determine the following: 1. Heat load in KW if the outdoor condition is 32°C DBT and 23°C WBT 2. What would be the load in kilowatts if the windows were double-glazed (U=3.5 W/m^2-K)

Two plates, one of aluminum with a tickness of 14mm and one of brass with thickness of 9mm were attached to each other. Determine the thickness of a board of another metallic material with thermal conductivity λ= 79W / mK so that it conducts an equal heat flow as together fasten the boards at the same total temperature drop across the structure. The thermal conductivity for aluminium is λAI = 238W / mK and for brass λm = 111W / mK.

For a flat corrugated galvanized steel (conductivity = 26 W/m.K) roof 1/32 in. thick lined with a ¼ in. asbestos-cement (conductivity = 1.2 W/m.K) ceiling 6 inches below the roof, with downward heat flow, calculate the overall thermal transmittance of the roof.

To maximize production and minimize pumping costs, crude oil is heated to reduce its viscosity during transportation from a production field. (1) Consider a pipe-in-pipe configuration consisting of concentric steel tubes with an intervening insulating material. The inner tube is used to transport warm crude oil through cold ocean water. The inner steel pipe (ks= 40 W/m·K) has an inside diameter of  Di, 1= 150 mm and wall thickness ti= 20 mm while the outer steel pipe has an inside diameter of  Di, 2= 250 mm and wall thickness to=ti. Determine the maximum allowable crude oil temperature to ensure the polyurethane foam insulation (kp= 0.0675 W/m·K) between the two pipes does not exceed its maximum service temperature of  Tp, max= 70°C. The ocean water is at ∞ T∞, o= -5°C and provides an external convection heat transfer coefficient of ho= 500 W/m2·K. The convection coefficient associated with the flowing crude oil is hi= 450 W/m2·K. (2) It is proposed to enhance the performance of the…