Q6 A 1.0 m length copper bar with a constant cross section area of 0.0001 m² have the values of density, thermal conductivity and specific heat of 8960 kg/m², 385 W/m.K and 389 J/kg.K respectively. The copper bar is perfectly insulated laterally, with ends kept at temperature 0°C. The one-dimensional heat equation, with u(x,t) as the temperature is given as: ди = 0 k a? is the thermal diffusivity of the material, where; k = thermal conductivity, o=specific op heat, and p=density of material. (i) By using the method of separation of variable, derive the expression for the heat conduction through the copper bar If the initial uniform temperature, f(x)=100sin Ax, how long will it take for the (ii) maximum temperature in the bar to drop to 50°C. (Hint: maximum temperature occurs at the center of the bar)

Q6 A 1.0 m length copper bar with a constant cross section area of 0.0001 m² have the values of density, thermal conductivity and specific heat of 8960 kg/m², 385 W/m.K and 389 J/kg.K respectively. The copper bar is perfectly insulated laterally, with ends kept at temperature 0°C. The one-dimensional heat equation, with u(x,t) as the temperature is given as: ди = 0 k a? is the thermal diffusivity of the material, where; k = thermal conductivity, o=specific op heat, and p=density of material. (i) By using the method of separation of variable, derive the expression for the heat conduction through the copper bar If the initial uniform temperature, f(x)=100sin Ax, how long will it take for the (ii) maximum temperature in the bar to drop to 50°C. (Hint: maximum temperature occurs at the center of the bar)

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.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.10P: 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder...

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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.
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