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: ôu ốt 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: ôu ốt 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)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text: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:
ôu
ốt
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)
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