A dormitory at a large university, built 50 years ago, has exterior walls constructed of Ls a thermal conductivity of k, = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; = 0.029 W/m-k the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Lg = 5-mm-thick architect 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 25-mm-thick sheathing = 22°C and T = 0°C, respectively. The inner and outer convection heat transf coefficients are h; = 5 W/m2-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 Ls a thermal conductivity of k, = 0.1 W/m-K. To reduce heat losses in the winter, the university decides to encapsulate entire dormitory by applying an L; = 25-mm-thick layer of extruded insulation characterized by k; = 0.029 W/m-k the exterior of the original sheathing. The extruded insulation is, in turn, covered with an Lg = 5-mm-thick architect 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 25-mm-thick sheathing = 22°C and T = 0°C, respectively. The inner and outer convection heat transf coefficients are h; = 5 W/m2-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?.

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 2.3P: 2.3 The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal...

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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
One end of a 0.3-m-long steel rod is connected to a wall at 204C. The other end is connected to a wall that is maintained at 93C. Air is blown across the rod so that a heat transfer coefficient of 17W/m2 K is maintained over the entire surface. If the diameter of the rod is 5 cm and the temperature of the air is 38C, what is the net rate of heat loss to the air?
A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and 50C over the left and right surfaces, respectively. If the thermal conductivities of the wall materials are: kA=70W/mK,kB=60W/mK, kC=40W/mK, and kP=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces. Repeat Problem 1.34, including a contact resistance of 0.1 K/W at each of the interfaces.
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.
1.10 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.
A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6
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.
2.3 The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of . Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially from a value of at the inner surface to a value of at a distance of 12.5 cm from the interior surface. If the exterior surface is kept at 38°C by forced convection, determine the temperature at the inner surface of the field. Hint: First set up the differential equation for a system in which the heat generation rate varies according to .
2.51 Determine by means of a flux plot the temperatures and heat flow per unit depth in the ribbed insulation shown in the accompanying sketch.
Repeat Problem 1.35 but assume that instead of surface temperatures, the given temperatures are those of the air on the left and right sides of the wall and that the convection heat transfer coefficients on the left and right surfaces are 6 and 10W/m2K, respectively.
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.)