The rod A has a cross sectional area 2376 mm2, modulus of elasticity 68 Gpa and thermal expansion coefficient 0.000022 1/C. The rod B has a cross sectional area 874 mm2, modulus of elasticity 176 Gpa and thermal expansion coefficient 0.000019 1/C. When the temperature T1=24 C a 0.5 mm gap exists between the ends of the rods, If the temperature T2=182 C. Answer the

The rod A has a cross sectional area 2376 mm2, modulus of elasticity 68 Gpa and thermal expansion coefficient 0.000022 1/C. The rod B has a cross sectional area 874 mm2, modulus of elasticity 176 Gpa and thermal expansion coefficient 0.000019 1/C. When the temperature T1=24 C a 0.5 mm gap exists between the ends of the rods, If the temperature T2=182 C. Answer the

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.

Chapter3: Transient Heat Conduction

Section: Chapter Questions

Problem 3.13P

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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.
1.63 Liquid oxygen (LOX) for the space shuttle is stored at 90 K prior to launch in a spherical container 4 m in diameter. To reduce the loss of oxygen, the sphere is insulated with superinsulation developed at the U.S. National Institute of Standards and Technology's Cryogenic Division; the superinsulation has an effective thermal conductivity of 0.00012 W/m K. If the outside temperature is on the average and the LOX has a heat of vaporization of 213 J/g, calculate the thickness of insulation required to keep the LOX evaporation rate below 200 g/h.
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
To determine the thermal conductivity of a structural material, a large 15-cm-thick slab of the material is subjected to a uniform heat flux of 2500 W/m2 while thermocouples embedded in the wall at 2.5 cm. intervals are read over a period of time. After the system had reached equilibrium, an operator recorded the thermocouple readings shown below for two different environmental conditions: Distance from the Surface (cm) Temperature (C) Test 1 0 40 5 65 10 97 15 132 Test 2 0 95 5 130 10 168 15 208 From these data, determine an approximate expression for the thermal conductivity as a function of temperature between 40 and 208C.
3.9 The heat transfer coefficients for the flow of 26.6°C air over a sphere of 1.25 cm in diameter are measured by observing the temperature-time history of a copper ball the same dimension. The temperature of the copper ball was measured by two thermocouples, one located in the center and the other near the surface. The two thermocouples registered, within the accuracy of the recording instruments, the same temperature at any given instant. In one test run, the initial temperature of the ball was 66°C, and the temperature decreased by 7°C in 1.15 min. Calculate the heat transfer coefficient for this case.
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
In 2012, a new fiber-optic cable of handling 40,000 telephone calls simultaneously was laid under the Pacific Ocean from California to Japan, a distance of 13,300 km. The cable was unreeled from shipboard at a mean temperature of 22oC and dropped to the Ocean floor having a mean temperature of 5oC. The coefficient of linear expansion of the cable is 75×10-6 /degree celsius. Determine the length of cable that must be carried on the ship to span the 13,300 Km. Also, find the percent change in length
Made of pure aluminum (k=2.37 W/m.K) with a diameter of 59 mm and a length of 15 mHeat is produced uniformly at a rate of 590000 W/m3 in a cylindrical reactor. Thisreactor transport coefficient 59000 W/m2.K and a temperature of 69°C.exists in the environment. Explain where the highest and lowest temperature will occurand calculate the values
A steam pipe carrying steam at 380 kPa pressure for a distance of 120 m in a chemical plant is not insulated. Estimate the Amount of heat saved if 16 cm steam line were covered with 85% magnesia pipe covering 5 cm thick. Take room temperature to be 36 ℃. Thermal conductivity of 85% magnesia is 0.0745 W/m−K , unit convective coefficient of room air, ho = 12 W m2−K .Take the steam temperature as 142℃. Use atleast 4 decimal places in every computation
How long must a 0.4 cm cylindrical copper fin be if the temperature of its insulated tip exceeds thesurrounding air temperature by 20% of T0 – T∞? Consider air temp to be 20°C and ℎ̅ = 28 W/m2K. Book gives answerof 27.3 cm.• You can use figure 4.9a or equation 4.45 in the book to find the right mL for the desired  at the tip. • Recall the nondimensional temperature is  = (T – T∞)/(T0 – T∞)
A cantilever beam, made of cold drawn AISI C1025 steel of circular cross section as shown in the figure below, is subjected to a load which varies from –F to 3F. Determine the maximum load that this member can withstand for an indefinite life using factor of safety N=2. A photoelastic model indicates a theoretical stress concentration factor of Kt=1.42 and the notch sensitivity for a 1/8 in. radius for this material is q=0.9. Analyze at the change of cross section only
A steel rod, 12 mm in diameter, passes centrally through a copper tube 2.5 m long and having 36 mm and 48 mm as internal and external diameters respectively. The tube is closed at each end by 24 mm thick steel plates which are secured by nuts. The nuts are tightened until the copper tube is reduced in length by 0.50. The whole assembly is then raised in temperature by 60 degrees Celsius. Steel: Coefficient of expansion = 1.2x10^-5/degrees Celsius, Es = 200 GPa Copper: Coefficient of expansion = 1.75x10^-5/degrees Celsius, Ec = 100 GPa Calculate the stress in copper and stress in steel after the rise of temperature if the thickness of the plates remains unchanged. Indicate if the answer is tensile, tension, compression.