The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA = 20 W/m – K and kC = 50 W/m – K, and known thickness, LA = 0.30 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 600 oC, and an oven air temperatu

The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA = 20 W/m – K and kC = 50 W/m – K, and known thickness, LA = 0.30 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 600 oC, and an oven air temperatu

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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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.
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.)
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.
A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where T is in kelvin. If one surface of this wall is maintained at 150C and the other at 50C, determine the rate of heat transfer per square meter. Sketch the temperature distribution through the wall.
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.
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.
The composite wall of a furnace consists of three different materials, two of which have known thermal conductivity (ka = 20 W/m°C and kc = 50 W/m°C) and thicknesses La = 0.30 m and Lb = 0.15 m. The third material (B) is between A and C, with a thickness of 0.15 m, but its thermal conductivity (kb) is unknown. Under steady-state operating conditions, measurements reveal a temperature of 20 °C on the external surface, 600 °C on the internal surface, and a furnace ambient temperature of 800 °C. The internal convection coefficient is 25 W/m²°C. What is the value of kb?
Question 2: The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, kA 20 W/m K and kC50 W/m K, and known thickness, LA 0.30 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 an oven air temperature of T 800°C. The inside convection coefficient h is known to be 25 W/m2 K. What is the value of kB?
The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, ka = 20 W/m · Kand ke = 50 W /m · K, and known thickness, LA = 300 mm and Lc = 150 mm. The third material, B, which is sandwiched between materials A and C, is of known thickness, Lg = 150 mm, but unknown thermal conductivity kg. ka ke Air T., h Under steady-state operating conditions, measurements reveal an outer surface temperature of T, = 20°C, an inner surface temperature of T, = 600°C, and an oven air temperature of T = 800°C. The inside convection coefficient h is known to be 25 W/m? · K. What is the value of kg?
The composite wall of an oven consists of three materials, two of which has known thermal conductivity, kA = 40 W/m.K and kc = 30 W/m.K. The third material, B, sandwiched between these two has an unknown thermal conductivity kB. The thickness of the materials LA = 0.2 m, LB = Lc = 0.1 m. Under steady-state operating conditions, measurements reveal an outer surface temperature Ts,o = 40°C, an inner surface temperature Tsi = 550°C, and oven air temperature To = 700°C. The inside convection coefficient h = 25 W/m2.K. (a) Draw the thermal circuit and temperature profile across the wall. (b) Determine the heat flux through the wall. %3D %3D %3D (c) Find the value of kB. Draw sketch and show all calculations.
Question 2 The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, ka = 20 W/m•K and kc = 50 W/m•K, and known thickness, LA = 0.30 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 ke. Under steady-state operating conditions, measurements reveal an outer surface temperature of T0= 20°C, an inner surface temperature of T; = 600° C, and an oven air temperature of T= 800C. The inside convection coefficient h is known to be 25 W/m2 •K. a) Sketch the equivalent thermal resistance of the circuit b) What is the value of kg? Ts0 Ts, i S,0 kA kc kB Air To h LA LB Lc