What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness ti, t2, të respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab.

What is the analogical reason between heat transfer by conduction and flow of electricity through ohmic resistance? Use a composite wall of a building to illustrate the concept. A composite slab with three layers of thermal conductivities k1, k2, k3 and thickness ti, t2, të respectively, are placed in a close contact. Derive an expression from the first principle for the heat flow through the composite slab per unit surface area in terms of the overall temperature difference across the slab.

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.34P: A section of a composite wall with the dimensions shown below has uniform temperatures of 200C and...

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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
A hollow sphere with inner and outer radii of R1 and R2, respectively, is covered with a layer of insulation having an outer radius of R3. Derive an expression for the rate of heat transfer through the insulated sphere in terms of the radii, the thermal conductivities, the heat transfer coefficients, and the temperatures of the interior and the surrounding medium of the sphere.
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 kD=20W/mK, determine the rate of heat transfer through this section of the wall and the temperatures at the interfaces.
Heat is generated uniformly in the fuel rod of a nuclear reactor. The rod has a long, hollow cylindrical shape with its inner and outer surfaces at temperatures of TiandTo, respectively. Derive an expression for the temperature distribution.
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.
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.
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.
Both ends of a 0.6-cm copper U-shaped rod are rigidly affixed to a vertical wall as shown in the accompanying sketch. The temperature of the wall is maintained at 93C. The developed length of the rod is 0.6 m, and it is exposed to air at 38C. The combined radiation and convection heat transfer coefficient for this system is 34W/m2K. (a) Calculate the temperature of the midpoint of the rod. (b) What will the rate of heat transfer from the rod be?
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.)