A dormitory at a large university, built 50 years ago, has exterior walls constructed of L, 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 T4 = 22°C and To O°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5W/m?-Kand h, 25-mm-thick sheathing with a thermal 00,4 25 W/m2-K, respectively.

A dormitory at a large university, built 50 years ago, has exterior walls constructed of L, 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 T4 = 22°C and To O°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5W/m?-Kand h, 25-mm-thick sheathing with a thermal 00,4 25 W/m2-K, respectively.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.1DP

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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
1.3 A furnace wall is to be constructed of brick having standard dimensions of Two kinds of material are available. One has a maximum usable temperature of 1040°C and a thermal conductivity of 1.7 W/(m K), and the other has a maximum temperature limit of 870°C and a thermal conductivity of 0.85 W/(m K). The bricks have the same cost and are laid in any manner, but we wish to design the most economical wall for a furnace with a temperature of 1040°C on the hot side and 200°C on the cold side. If the maximum amount of heat transfer permissible is 950 , determine the most economical arrangement using the available bricks.
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.)
Wearing layers of clothing in cold weather is often recommended because dead-air spaces between the layers keep the body warm. The explanation for this is that the heat loss from the body is less. Compare the rate of heat loss for a single 2-cm-thick layer of wool [k=0.04W/(mK)] with three 0.67-cm layers separated by 1.5 mm air gaps. The thermal conductivity of air is 0.024 W(mK).
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.
1.2 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.
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 L, = 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 Ti = 22°C and T0 -15°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5 W/m?-K and h, = 25 W/m²-K, respectively. The heat flux through the original walls is i W/m?. The heat flux through the retrofitted walls is i W/m?.
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 Ti = 22°C and T.0 -17.5°C, respectively. The inner and outer convection heat transfer coefficients are h; = 5W/m?-K and h, = 25 W/m²-K, respectively. The heat flux through the original walls is i W/m?. The heat flux through the retrofitted walls is i W/m?.
4. The section of a vertical wall is made up of fiberglass insulation slabs separated by wooden studs. The thermal conductivity of fiberglass and wood are 0.04 W/m-K and 0.18 W/m-K, respectively. The thickness of the wall is 160 mm. The temperatures of the inner and outer surfaces of the wall section are 22 °C and 4 °C, respectively. The ratio of the insulation area to the total wall area is 0.8. Calculate the total heat flow rate (in W/m2) through the wall per unit area. Wooden Stud Fiberglass Insulation Follow-up question to Question 4, calculate the rate of heat flow (in W/m2) through unit area of studs.
A dormitory at a large university, built 50 years ago, has exterior walls constructed of Ls a thermal conductivity of k, = 25-mm-thick sheathing with = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate the = 0.029 W/m:K to entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Lg = 5-mm-thick architectural glass with kg exterior air temperatures are T; 1.4 W/m-K. Determine the heat flux through the original and retrofitted walls when the interior and = 22°C and T. 0°C, respectively. The inner and outer convection heat transfer 0,i coefficients are h; = 5 W/m2.K and ho 25 W/m2-K, respectively. The heat flux through the original walls is i W/m?. The heat flux through the retrofitted walls is i W/m?.
An insulation layer of 20 mm thick refractory material is placed on top of a layer of mineral wool to insulate a hollow, spherical steel ball with an outside diameter of 60 mm and an internal diameter of 50 mm wool. The table below lists the thermal conductivities: Substance a. 6.0 mm above Steel Refractory Mineral wool b. 6.1 mm k (W/m-K) c. 6.2 mm 48 While the outside temperature is 30 °C, the temperature within the steel is 200 °C. Heat effects from convection and radiation are disregarded. Find the needed thickness of the mineral wool if the heat loss is 50 W. 0.346 0.047 d. 6.3 mm e. No to all of the