1. The two faces of a thin metal sheet that is 3 units wide and 5 units long are insulated, and the sheet is so thin that the heat flow inside of it is essentially two-dimensional. The bottom edge is kept at zero degrees, and the top edge is kept at fifty degrees. The vertical edges are insulated. Determine the temperature distribution throughout the sheet in a steady state.

1. The two faces of a thin metal sheet that is 3 units wide and 5 units long are insulated, and the sheet is so thin that the heat flow inside of it is essentially two-dimensional. The bottom edge is kept at zero degrees, and the top edge is kept at fifty degrees. The vertical edges are insulated. Determine the temperature distribution throughout the sheet in a steady state.

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 2.4P: A plane wall 15 cm thick has a thermal conductivity given by the relation k=2.0+0.0005T[W/mK] where...

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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.
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.
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.
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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.
The side of a home can be modeled as a plane wall. The wall is 12 centimeters thick. If the outdoor temperature is 30oC and the indoor temperature is 220C, what is the temperature in the wall 1 cm from the inside surface? Assume a steady-state temperature distribution. Draw a schematic or diagram. Show all calculations.
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