Temperature change across a wall with respect to time

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SUMMARY

The discussion focuses on calculating the time it takes for the temperature on the inside of an aluminum wall to reach a specific temperature (Tr) after a change in temperature on the outside (To). The heat transfer rate is defined by the formula kA (T1 - T2) / d, where k is the thermal conductivity, A is the surface area, d is the wall thickness, T1 is the higher temperature, and T2 is the lower temperature. Given the initial temperatures of Ti = 90°C and To = 80°C, the calculated heat transfer rate is 1649.8 J/s. The user seeks to determine the time required for the inside wall temperature to rise from 80°C to 85°C.

PREREQUISITES
  • Understanding of heat transfer principles, specifically conduction.
  • Familiarity with the thermal conductivity coefficient (k).
  • Knowledge of the heat transfer rate formula: kA (T1 - T2) / d.
  • Basic algebra for solving time-related equations in thermal dynamics.
NEXT STEPS
  • Research the specific thermal conductivity values for aluminum at various temperatures.
  • Learn about transient heat conduction and how to apply it in practical scenarios.
  • Explore numerical methods for solving heat transfer problems over time.
  • Investigate the impact of wall thickness on heat transfer rates and time calculations.
USEFUL FOR

Engineers, physicists, and students studying thermodynamics or heat transfer, particularly those involved in materials science and thermal management applications.

ihaland
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Please help:

I need help to figure out the following:
Given:
An alluminum wall of thickness s.
T outside wall, To
T inside wall, Ti

If the temperature changes on one side of the wall To, how long will it take until the the other side of the wall Ti reaches Tr, where To < Tr <Ti

I appreciate all the help I can get.

Thanks!
 
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The rate od heat transfer is given with kA (T1 - T2) / d, where k is the thermal conductivity coefficient, A, the surface area of the transferred heat, d the thickness of the wall, T1 the higher and T2 the lower temperature. This should work.
 
Yes, I have already calculated the rate, but I seem to be stuck on what to do next.


If I have the following:

Ti - 90 C

To - 80 C

Then I have calculated my rate of heat transfer to be 1649,8 J/s.

How long will it take for To = 85 ?


I really appreciate the help, Thanks!
 

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