Chapter 1, Problem 1.59P

1.10 A heat flux meter at the outer (cold) wall of a concrete building indicates that the heat loss through a wall of 10-cm thickness is . If a thermocouple at the inner surface of the wall indicates a temperature of 22°C while another at the outer surface shows 6°C, calculate the thermal conductivity of the concrete and compare your result with the value in Appendix 2, Table 11.

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.

1.4 To measure thermal conductivity, two similar 1-cm-thick specimens are placed in the apparatus shown in the accompanying sketch. Electric current is supplied to the guard heater, and a wattmeter shows that the power dissipation is 10 W. Thermocouples attached to the warmer and to the cooler surfaces show temperatures of 322 and 300 K, respectively. Calculate the thermal conductivity of the material at the mean temperature in W/m K. Problem 1.4

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.)

The figure shows the cross section of a wall made of three layers. The thicknesses of the layers are L1. L2 =0.500 L1. and L3 = 0.350 L1. The thermal conductivities are k1, k2 = 0.800 k1, and k3 = 0.680 k1. The temperatures at the left and right sides of the wall are TH = 20 °C and Tc = -10 °C, respectively. Thermal conduction is steady. (a) What is the temperature difference AT2 across layer 2 (between the left and right sides of the layer)? If k2 were, instead, equal to 1.100 k1, (b) would the rate at which energy is conducted through the wall be greater than, less than, or the same as previously, and (c) what would be the value of AT2? k1 ko k3 TH Tc L1 L9 L3 (a) AT2 = i (b) (c) AT2= i

3. A cylindrical pipe of negligible thickness holding a hot fluid at 140°C and having an outer diameter of 0.4 m is insulated with three layers of each 70 mm thick insulation of K₁ = 0.02: k2 = 0.06 and k3= 0.16 W/m-K (starting from inside). The outside surface temperature is 30°C. Solve for the value of T2.

A team of students tests a material for its thermal conductivity (k).  After 20 minutes in a heat box, the temperature is 48° C inside the box and 28° C on top of the material.  The following data is true about this test: Area of material = .0225 m2      Thickness of material = .0127 m        Light bulb = 25 W What is the thermal conductivity constant for the material?  Calculate the amount of energy transferred through the material.  Determine the R-value of the material.  Based on your calculations, would the material be a reasonable choice for home insulation? Yes of No

X Your answer is incorrect. A dormitory at a large university, built 50 years ago, has exterior walls constructed of L, = 25-mm-thick sheathing with a thermal conductivity of k, = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate the entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; = 0.029 W/m-K to the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Lg = 5-mm-thick architectural glass with kg = 1.4 W/m-K. Determine the heat flux through the original and retrofitted walls when the interior and exterior air temperatures are T = 22°C and To = O°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5 W/m?-Kand h, 00, 25 W/m2-K, respectively. The heat flux through the original walls is 1.46 W/m?. The heat flux through the retrofitted walls is 0.92 W/m?.

A wall of a house, shown in the figure, consists of the items in the accompanying table. If the inside and outside room temperature are 35"C and 15"C, with an exposed area of 150 m2. The total R-factor, Heat transfer through the wall and total thermal resistance in the sequence is given by option No Items Thermal resistance (R') (C/W) 0.5 Outside film resistance Face brick 1 1.8 2.7 2. Cement mortar 2.5 Cinder block Air space 6. 1.5 Gypsum board Inside film resistance 0.9 17 0.7 1. 2. 3. 4. 5. 6. 7. laall list a. 7837 m2-CW, 9.1540 Watt, 91.9 oCW O b. 5645 m2-C/W, 14145 Watt. 158 oC/W O c 6528 m2-C/W, 0.5487 Watt 194 oC/W O d. 1590 m2-CAW, 1.8867 Watt 106 oC/W احل اختداریا 345