Concept explainers
Functionally graded materials are intentionally fabricated to establish a spatial distribution of properties in the final product. Consider an
- Determine the spatially averaged value of the thermal conductivity k. Use this value to estimate the heat rate per unit length for cases I and 2.
- Using a grid spacing of 2 mm. determine the heat rate per unit depth for case 1. Compare your result to the estimated value calculated in part (a).
- Using a grid spacing of 2 mm, determine the heat rate per unit depth for case 2. Compare your result to the estimated value calculated in part (a).
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Chapter 4 Solutions
Fundamentals of Heat and Mass Transfer
- The heat conducts through the shape below. The temperature of the right face is 93 °C, while the left face is at 23 °C. If the top and bottom faces are completely insulated, and the thermal conductivity of the material decreases with decreasing temperature. * Assume that the thermal conductivity is 100 at 23, decreased to 10 at 93. A) Sketch the temperature profile inside the plate. B) If both sides of the plate in the above problem is exposed to air: Left side (h = 20 W/m2K, TL = 20 °C) and right side (h = 90 W/m2K). Calculate the temperature of the air on the right side.arrow_forwardA steel pipe (outside diameter 100 mm) is covered with two layers of insulation. The inside layer, 40 mm thick, has a thermal conductivity of 0.07 W/(m K). The outside layer, 20 mm thick, has a thermal conductivity of 0.15 W/(m K). The pipe is used to convey steam at a pressure of 600 kPa. The outside temperature of insulation is 24°C. If the pipe is 10 m long, determine the following, assuming the resistance to conductive heat transfer in steel pipe and convective resistance on the steam side are negligible: a. The heat loss per hour. b. The interface temperature of insulation.arrow_forwardSome sections of the Alaska pipeline above ground are supported by vertical steel supports (k = 25 W/mK), which have a length of 1 m and a cross-sectional area of 0.05 m². Under normal operating conditions, the temperature variation along the length of the steel support is given by the expression T = 100 – 150x + 10x², where T and x have units of °C and m, respectively. Temperature variations in the cross-sectional area of the support are negligible. Evaluate the temperature and the heat conduction rate at the pipeline-support junction (x = 0) and at the support-soil interface (x = 1 m). Explain the difference in heat rates.arrow_forward
- Clothing made of several thin layers of fabric with trapped air in between, often called ski clothing, is commonly used in cold climates because it is light, fashionable, and a very effective thermal insulator. So it is no surprise that such clothing has largely replaced thick and heavy old-fashioned coats. Consider a jacket made of five layers of 0.1-mm-thick synthetic fabric (k = 0.13 W/m·K) with 1.5-mm-thick air space (k = 0.026 W/m·K) between the layers. Assuming the inner surface temperature of the jacket to be 28°C and the surface area to be 1.25 m2, determine the rate of heat loss through the jacket when the temperature of the outdoors is 0°C and the heat transfer coefficient at the outer surface is 25 W/m2·K. What would your response be if the jacket is made of a single layer of 0.5-mm-thick synthetic fabric? What should be the thickness of a wool fabric (k = 0.035 W/m·K) if the person is to achieve the same level of thermal comfort wearing a thick wool coat instead of a…arrow_forwardSteel pipe 1 cm thick, 1.0 m long and 12 cm deep, covered with 8 cm thick insulation. The wall temperature in the steel pipe is 100 ° C. The ambient temperature around the insulated pipe is 24 ° C. The convection heat transfer coefficient outside the insulation surface is 50 W / (m² K). The thermal conductivity of steel is 54 W / (m K), and the thermal conductivity of the insulation is 0.04 W / (m K). Count; a. Heat loss per meter of pipe = Answer watts. b. Temperature between steel pipe and insulation. = Answer ° C.arrow_forwardThe cylindrical pipe with a thread diameter of 0.070 m and an internal diameter of 0.050 m is insulated both internally and externally. Calculate the heat loss per unit length of the pipe (1 m) when the inner surface temperature of the pipe is kept at 50 °C and the outer surface temperature at 20 °C (Average thermal conductivity constant = Km= 0.172 J/cm.s.K).arrow_forward
- The diagram below shows a composite wall 1 m deep. The first layer of thickness LA is made of special refractory material (kA=0.50 W/m.K). The second layer, 0.30 m thick, consists of insulating material A (kB=0.1 W/m.K) and insulating material B (kC = 0.35 W/m.K). The temperature on the inner face of A (Tsup) is equal to 900°C and the ambient temperature (Tamb) is equal to 25°C. The heat transfer coefficient h is equal to 10 W/m2.K. The rate of heat through the oven wall is constant and equal to 2500 W. Determine the thickness of the layer LA that forms wall A.arrow_forwardThe diagram below shows a composite wall 1 m deep. The first layer of thickness LA is made of special refractory material (kA=0.50 W/m.K). The second layer, 0.30 m thick, consists of insulating material A (kB=0.1 W/m.K) and insulating material B (kC = 0.35 W/m.K). The temperature on the inner face of A (Tsup) is equal to 900°C and the ambient temperature (Tamb) is equal to 25°C. The heat transfer coefficient h is equal to 10 W/m2.K. The rate of heat through the oven wall is constant and equal to 2500 W. Determine the thickness of the layer LA that forms wall A. What is the correct option? Present the calculation. a. 1,02 m b. 56 cm c. 27 cm d. 70 cm e. 12 cmarrow_forwardYou are asked to determine the heat loss from a very thin spherical cap containing a hot fluid at a temperature of 140.0°C. The outside diameter of the cap is 40.0 m and it is insulated by three layers of insulation of thickness 50.0 m each. The thermal conductivities of each layer are:?1 = 0.02 ?⁄??; ?2 = 0.06 ?⁄??; ?3 = 0.16 ?⁄?? These thermal conductivities are indicated from the inside out in the spherical space coordinate. On the other hand, the external temperature of the system is 30.0°C. Additionally, you are asked to determine the temperatures at the contact interfaces between the different materials. Finally, you are asked to make a freehand diagram of the system, indicating the temperatures obtained by you for each interface and the heat flux.arrow_forward
- a pipe with an outside diameter of 2.5 inches is insulated with 2 inches layer of asbestos ( K= 0.396(btu-in)/(hr-ft-F) followed by a layer of cork 1.5 inches thick ( K= 0.30 (btu-in)/ft (hr-ft-F). if the temperature of the outer surface of the cork and pipe is 90 F and 290 F RESPECTIVELY, calculate the heat loss per 100 ft of insulated pipe in btu/hrarrow_forwardWhat is the rate of heat transfer, temperature gradient, and the direction of the heat transfer through a piece of Celotex 3 ft by 8 ft by 1 in. in thickness, if the temp of one surface is 80°F and of the other side is 60°F? - thermal conductivity of Celotex in AES = 0.028.arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning