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Steel is sequentially heated and cooled (annealed) to relieve stresses and to make it less brittle. Consider a 100-mm-thick plate
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Introduction to Heat Transfer
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- Problem 204. In an 11.2 dm high cylindrical container, whose base area is 1 dm², a frictionless piston of mass 8 kg is held at a height of 5.6 dm. The piston encloses 1 mol of helium at 273 °C. The wall of the container is insulated. Find the maximum height reached by the piston after being relcased. The molar specific heat of helium at constant volume is C. = 12.6 J/(molK), while at constant pressure it is C, = 21 J/(molK). The atmospheric pressure is 10.12 N/cm2.arrow_forwardA composite plane wall consists of a 4-in-thick layer of insulation (ks = 0.029 Btu/h-ft-°R) and a 0.75-in-thick layer of siding (ks = 0.058 Btu/h.ft.R). The inner temperature of the insulation is 67°F. The outer temperature of the siding is 8°F. Determine at steady state (a) the temperature at the interface of the two layers, in °F, and (b) the rate of heat transfer through the wall in Btu/h-ft² of surface area.arrow_forwardQ2-A hollow stainless-steel cylinder having an inside diameter of 4 cm and thickness of 1 cm is exposed to a convection environment at 30 C, h=50 W/m2 C. Heat is generated uniformly in the cylinder at the rate of 1 MW/m3. Determine the steady state temperature distribution in the cylinder. What are (1)-the location and (2)-the value of the maximum temperature in the cylinder? Assume the inside surface is insulated.arrow_forward
- A food product with 85% moisture content is being frozen. Estimate the specific heat of the product at -10°C when 80% of the water is in a frozen state. The specific heat of dry product solid is 2 kJ/(kg °C). Assume specific heat of water at -10°C is similar to specific heat of water at 0°C. And the heat of the types of ice follow the function of Cp ice = 0.0062 Tfrozen + 2.0649. Cp frozen product = ... kJ/kg °C.arrow_forward2.34 Show that the temperature distribution in a sphere of radius . made of a homogeneous material in which energy is released at a uniform rate per unit volume , isarrow_forwardA composite plane wall consists of a 5-in.-thick layer of insulation (ks = 0.029 Btu/h ft. "R) and a 0.75-in.-thick layer of siding (ks = 0.058 Btu/h-ft- ºR). The inner temperature of the insulation is 67°F. The outer temperature of the siding is 0°F. Determine at steady state (a) the temperature at the interface of the two layers, in °F, and (b) the rate of heat transfer through the wall in Btu/h-ft² of surface area.arrow_forward
- The initial state of 1.00 mol of a dilute gas is P1 = 3.00 atm, V1 = 1.00 L, and Eint 1 = 456 J and its final state is P2 = 2.00 atm, V2 = 3.00 L, and Eint2 = 912 J. The gas is first cooled at constant volume until it reaches its final pressure. It is then allowed to expand at constant pressure until it reaches its final volume. (a) Illustrate this process on a PV diagram and calculate the work done by the gas. (b) Find the heat absorbed by the gas during this process.arrow_forwardSolar heating of a house is much more efficientif there is a way to store the thermal energy collected during theday to warm the house at night. Suppose one solar-heated homeutilizes a concrete slab of area 12 m2and 25 cm thick. (a) If thedensity of concrete is 2400 kg>m3, what is the mass of the slab?(b) The slab is exposed to sunlight and absorbs energy at a rate of1.4 * 107J>h for 10 h. If it begins the day at 22 °C and has a specificheat of 750 J>1kg # K2, what is its temperature at sunset? (c) Modelthe concrete slab as being surrounded on both sides (contact area24 m2) with a 2.0-m-thick layer of air in contact with a surface thatis 5.0 °C cooler than the concrete. At sunset, what is the rate atwhich the concrete loses thermal energy by conduction throughthe air layer? (d) Model the concrete slab as having a surface areaof 24 m2and surrounded by an environment 5.0 °C cooler thanthe concrete. If its emissivity is 0.94, what is the rate at which theconcrete loses thermal…arrow_forwardA radioactive material can be considered as a sphere of ro = 0.04 m. the sphere is generating heat at a constant rate of 4x107 W/m³. The heat generated is dissipated to the environment in a steady state. The thermal conductivity of the sphere is k=15 W/m.°C and the surface of the sphere is maintained at a constant temperature of 80°C. Assuming steady one-dimensional heat transfer, (a) drive the differential equation and the express boundary conditions for heat conduction through the sphere, (b) Get a relation for the variation of temperature in the sphere by solving the differential equation, and (c) Calculate the temperature at the center of the sphere.arrow_forward
- The attached figure shows a gas contained in a vertical piston– cylinder assembly, where D = 10 cm. A vertical shaft whose cross-sectional area is 0.8 cm2 is attached to the top of the piston. The total mass of the piston and shaft is 25 kg. While the gas is slowly heated, the internal energy of the gas increases by 0.1 kJ, the potential energy of the piston–shaft combination increases by 0.2 kJ, and a force of F = 1668 N is exerted on the shaft as shown in the figure. The piston and cylinder are poor conductors, and friction between them is negligible.The local atmospheric pressure is 1 bar and g = 9.81 m/s2. (Patm = 1 bar) Determine, (a) the work done by the shaft, (b) the work done in displacing the atmosphere, and (c) the heat transfer to the gas, all in kJ.arrow_forwardIf 90 g of molten lead at 327.3°C is poured into a 300 g casting form made of iron that is initially at 20°C, what is the final temperature of the system? Assume no energy is lost to the environment. Other information for Iron: Specific heat capacity = 448 J/kg-°C Other information for Lead: Melting point = 327.3°C Latent heat of fusion = 2.45x104 J/kg Specific heat capacity = 128 J/kg-°C Required: t2arrow_forwardA long aluminum cylinder (p= 170 lbm/ft3, c= 0.22 Btu/lbm F, k = 140 Btu/h ft F) has a diameter of 3 inches. It initially has a uniform temperature of 600 F. It is suddenly quenched in a water bath for 2 min. The water bath is at 120 F and the convective coefficient is 100 Btu/h ft² F. What is the temperature of the cylinder when it leaves the water bath?arrow_forward
- Principles of Heat Transfer (Activate Learning wi...Mechanical EngineeringISBN:9781305387102Author:Kreith, Frank; Manglik, Raj M.Publisher:Cengage Learning