Thermal conductivity of a metalic bar

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SUMMARY

The discussion centers on the thermal conductivity of a metallic bar with a thermal conductivity of 200 W/(m·K), an area of 20 cm², and a thickness of 1 cm, which is in contact with a heater delivering 200 W at 300ºC. The key questions involve determining the temperature on the side of the bar not in contact with the heater and calculating the heat flux through the bar. The heat flux equation J = -k * grad(T) is utilized, leading to the conclusion that the non-heated side will not reach 300ºC in a stationary state, as this would result in zero heat flux.

PREREQUISITES
  • Understanding of thermal conductivity and its units (W/(m·K))
  • Familiarity with heat flux equations, specifically J = -k * grad(T)
  • Knowledge of stationary state conditions in thermal systems
  • Basic principles of heat transfer and temperature gradients
NEXT STEPS
  • Calculate the temperature difference across the metallic bar using the heater power and thermal conductivity
  • Explore the concept of thermal equilibrium and its implications on temperature distribution
  • Learn about Fourier's law of heat conduction and its applications
  • Investigate the effects of varying cross-sectional areas on heat transfer rates
USEFUL FOR

Students studying thermodynamics, engineers involved in heat transfer analysis, and anyone interested in the practical applications of thermal conductivity in materials.

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Homework Statement



we have a metalic bar with thermal condutivity of 200w/(m*k) it has an area of 20 cm^2 which is in contact with with an heater that delivers 200 W and is at 300ºC. the metalic bar has a thickness of 1cm

The two questions are:
a) once the system have entered a stationary state what's the temprature of the other of the side of the bar that is not in contact with the heater?
b) calculate the flux going through the metalic bar

Homework Equations





The Attempt at a Solution



well I haven't got far, I know that the flux of heat going to a surface is J=-k*grad(T) and from that I get that there is no flux going out the side walls of the bar.
I also concluded that at the stationary state the side of the bar which is not in contact with the heater won't be at 300ºC for in that case the flux of heat would be zero.
I think that if the board is in contact with something at the other end then it should be always at roam temperature because if it goes above that temperature there will be a discontinuity in the temprerature and it will result in an infinite flux.

Now I don't know what else to do.

Thank you
 
Physics news on Phys.org
You're on the right track. How do you calculate grad(T)? How does this relate the temperature difference across the bar to the heater power?
 

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