Q3. 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 t1, t2, t3 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.

Q3. 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 t1, t2, t3 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.

Chapter2: Steady Heat Conduction

Section: Chapter Questions

Problem 2.6P: A plane wall of thickness 2L has internal heat sources whose strength varies according to...

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A plane wall of thickness 2L has internal heat sources whose strength varies according to qG=qocos(ax) Where qo is the heat generated per unit volume at the center of the wall (x=0) and a is a constant. If both sides of the wall are maintained at a constant temperature of Tw, derive an expression for the total heat loss from the wall per unit surface area.
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.
1.3 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.
1.10 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.
2.15 Suppose that a pipe carrying a hot fluid with an external temperature of and outer radius is to be insulated with an insulation material of thermal conductivity k and outer radius . Show that if the convection heat transfer coefficient on the outside of the insulation is and the environmental temperature is , the addition of insulation actually increases the rate of heat loss if , and the maximum heat loss occurs when . This radius, is often called the critical radius.
2.16 A standard 4-in. steel pipe (ID = 4.026 in., OD = 4.500 in.) carries superheated steam at 1200°F in an enclosed space where a fire hazard exists, limiting the outer surface temperature to 100°F. In order to minimize the insulation cost, two materials are to be (a) Specify the thickness for each insulating mate- rial. (b) Calculate the overall heat transfer coefficient based on the pipe OD. (c) What fraction of the total resistance is due to (1) steam-side resistance, (2) steel pipe resistance, (3) insulation (the combina- tion of the two), and (4) outside resistance? (d) How much heat is transferred per hour per foot length of pipe? used: first a high-temperature (relatively expensive) insulation is to be applied to the pipe, and then magnesia (a less expensive material) will be applied on the outside. The maximum temperature of the magnesia is to be 600°F. The following constants are known: steam-side coefficient h = 100 Btu/hr ft² °F high-temperature insulation conductivity k =…
A wall of a house is made from two layers of bricks enclosing a layer of insulation. A radiator is positioned to cover the whole internal surface, and used intermittently when the internal temperature is low. The external surface is exposed to the outside air. Which of the following assumptions could be used to identify the relevant reduced form of the conduction equation to find the temperature in the wall. a. Conduction is mainly in two directions. b. Conduction is mainly in one direction. c. The wall properties are homogeneous. d. Steady conditions exist. e. Unsteady conditions exist. f. There is an internal volumetric heat generation in the wall.
2.19 Consider a 300 mm x 300 mm window in an aircraft. For a temperature difference of 80°C from the inner to the outer surface of the window, calculate the heat loss through L = 10-mm-thick polycarbonate, soda lime glass, and aerogel windows, respectively. The thermal conductivities of the aerogel and polycarbonate are kag = 0.014 W/m-K and kpe = 0.21 W/m-K, respectively. Evaluate the thermal conductivity of the soda lime glass at 300 K. If the aircraft has 130 windows and the cost to heat the cabin air is $1/kW-h, compare the costs associ- ated with the heat loss through the windows for an 8-hour intercontinental flight.
A composite wall is formed by sandwiching a 0.1 m thickness material between two steel slabs. The thermal conductivity of steel is 20 W/mK. We need to calculate the thermal conductivity of the material. The thickness of each steel slab is 0.4 m. The heat flux given at steady state is 20KW/m^2. The inner temperature of this composite wall is 700 K and the outer temperature is 200 K. Also calculate the temperature at the interface.
A slender rod of length L, diameter d (L >> d) and thermal conductivity k1 is joined with another rod of identical dimensions, but of thermal conductivity k2, to form a composite cylindrical rod oflength 2L. The heat transfer in radial direction and contact resistance are negligible. Find the effectivethermal conductivity of the composite rod.
A composite wall of a refrigerator consists of three different materials; A, B, and C. Two of the used materials have known thermal conductivity, KA = 30 W/m. K and kc-45 W/m. K, and known thickness, LA=0.20 m and Lc = 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, LB = 0.15 m, but unknown thermal conductivity kB. Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o= 20°C, an inner surface temperature of Ts,i = 600°C, and a refrigerator air temperature of Too = 800°C. The inside convection coefficient h is known to be 25 W/m².K. (a) First, draw the thermal circuit for this wall. (b) What is the value of thermal conductivity for material B? Tsi Air To, h KA K₂ kc Lg Lc Figure 2: Composite wall configuration described in problem 3.
A hollow cylindrical copper conductor 1.27cm. i.d. and 5.1cm. o.d. carries a current density 5000 amp/cm². For copper K = .38 kW/m°K and electrical resistivity = 2 x 10-6 ohm cm. Find the position and magnitude of the maximum temperature and the internal and external heat removal when (a) the outside temperature is 37.8°c and no heat removal occurs on the inside and (b) the outside is at 37.6°C and the inside at 27.2°C.