Convective and conductive heat transfer

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Discussion Overview

The discussion revolves around a heat transfer problem involving a cylindrical copper block subjected to both convective and conductive heat transfer. Participants explore the calculation of the final temperature of the block and the time required to cool it from an initial temperature, considering assumptions about uniform temperature and heat transfer coefficients.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a problem involving a cylindrical copper block and seeks to establish an energy balance for heat transfer.
  • Another participant notes that the assumption of uniform temperature throughout the block contradicts the principles of heat conduction.
  • A participant questions how to incorporate the initial temperature of 60°C into their calculations.
  • One participant claims to have solved the first part but struggles with the second part of the problem, using a specific formula to relate mass, specific heat, and temperature change.
  • There is a suggestion that the participant may be miscalculating or misinterpreting parts of the equation used for the second part of the problem.

Areas of Agreement / Disagreement

Participants express differing views on the validity of assuming uniform temperature in the block. There is no consensus on the correct approach to solving the second part of the problem, as participants are still exploring their calculations and assumptions.

Contextual Notes

Participants have not reached a resolution regarding the assumptions necessary for the calculations, particularly concerning the uniform temperature and the implications for heat conduction. There are also unresolved elements in the mathematical steps taken for the second part of the question.

Who May Find This Useful

This discussion may be useful for students studying heat transfer, particularly those grappling with concepts of convective and conductive heat transfer in practical problems.

DarkBlitz
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Hey, I was doing some revison for a test and i came across this question which I can't get my head around

a clyndrical copper block, 0.3m in diameter and 0.4m long is initially at a uniform temp of 60°C and half its curved surface is exposed to a heat flux of 450w/m^2. If the complete surface is being cooled by convection heat transfer to the surrounding air at 20°C, determine the final temperature of the block, assuming it is uniform throughout.

Determine the time to cool the block from 60 degrees to the final temperature. assuming the convective heat transfer is constant throughout the cooling process and can be calculated using the average temperature of the block during the cooling process.

For each case, identify an appropriate system and energy balance and use the following date: p(copper) =8900 kg/m^3
C(copper) =400j/kg
convective heat transfer coefficient = 20w/m^2k

I'm haven't tried the second half of the question as I can not get the first part.
So far, i have said that:
Qdotin=Qdotout
flux*Half curved surface= h* Atotal * (Tsurface - Tair)
But my problem with this equation is to find an expression for T surface in terms of the final and initial temperature.

Am I on the right track?

Thanks
 
Last edited:
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The first part says
determine the final temperature of the block, assuming it is uniform throughout.
That is telling you to assume Tsurface is equal the the uniform final temperature.

It is physically impossible for the temperature to be uniform throughout, because there would be no heat conduction in the block. But you have to use the assumptions the question tells you to use.
 
ah ok, but then what do i do with the initial 60 degree temperature?
 
oh, that might be for the second part of the question, ill give it a go thanks!
 
I got the first part, but for the second part of the question,
I used the formula:
m*c*deltaT/t = hA(Ts-Tf)
Where Ts is the average temperature of the copper during cooling and we are solving for T, however i do not get the right answer. The answer is 5.4hours.

Which part of the equation is wrong?
 
DarkBlitz said:
oh, that might be for the second part of the question

Yup, that's right. Give it a go...
 

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