1. The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, k₁ = 20 W/m • K and kc = 50 W/m • K, and known thickness, L₁ = 0.30 m and Lc = 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, Lâ = 0.15 m, but the unknown thermal conductivity kú. -Tsp Ts.i KA kB kg kc Air T, h Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o = 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/m² • K. What is the value of k¸? Answer: KB=1.53W/m*K

1. The composite wall of an oven consists of three materials, two of which are of known thermal conductivity, k₁ = 20 W/m • K and kc = 50 W/m • K, and known thickness, L₁ = 0.30 m and Lc = 0.15 m. The third material, B, which is sandwiched between materials A and C, is of known thickness, Lâ = 0.15 m, but the unknown thermal conductivity kú. -Tsp Ts.i KA kB kg kc Air T, h Under steady-state operating conditions, measurements reveal an outer surface temperature of Ts,o = 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/m² • K. What is the value of k¸? Answer: KB=1.53W/m*K

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 1.37P: 1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm...

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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.
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.
1.4 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
1.37 Mild steel nails were driven through a solid wood wall consisting of two layers, each 2.5-cm thick, for reinforcement. If the total cross-sectional area of the nails is 0.5% of the wall area, determine the unit thermal conductance of the composite wall and the percent of the total heat flow that passes through the nails when the temperature difference across the wall is 25°C. Neglect contact resistance between the wood layers.
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.
2.30 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.)
The composite wall of an oven consists of three materials, two of which are ofknown thermal conductivity, kA = 25 W/m ⋅ K and kC = 60 W/m ⋅ K, and knownthickness, LA = 0.40 m and LC = 0.20 m. The third material, B, which is sandwichedbetween materials A and C, is of known thickness, LB = 0.20 m, but unknownthermal conductivity kB. Under steady-state operating conditions, measurementsreveal an outer surface temperature of Ts,o = 20°C, an inner surface temperature ofTs,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. Neglecting convection transfer effect,what is the value of kB?
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?
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.
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