Heat transfer and combustion correlations

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Discussion Overview

The discussion revolves around the correlations for heat transfer by natural convection from a horizontal pipe to the atmosphere, specifically focusing on the simplification of the Nusselt number equation and the calculation of the heat transfer coefficient. Participants explore the mathematical relationships and calculations involved, addressing uncertainties and challenges in deriving the correct coefficients.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on how two correlations for heat transfer can be similar and requests assistance in simplifying the given equation.
  • Another participant provides a detailed breakdown of the Nusselt number equation and suggests steps for simplification, indicating that the constants should lead to a specific form.
  • A participant notes discrepancies in their calculations, specifically not obtaining the expected coefficient of 1.34, and suggests verifying units.
  • There is a discussion about the treatment of the variable d in the simplification process, with some participants explaining how to handle the exponentiation and division.
  • Several participants express their struggles with the calculations and seek further assistance, indicating a lack of clarity in the steps required to reach the solution.
  • One participant mentions the need to clarify what is meant by "distributing through the exponents" and receives an explanation about combining like terms.
  • Another participant shares their algebraic expression for the heat transfer coefficient and seeks feedback on their approach.
  • There are multiple requests for help in progressing through the calculations, with some participants expressing frustration over their inability to resolve the problem.

Areas of Agreement / Disagreement

Participants generally do not reach a consensus on the simplification process and the calculations involved. Multiple competing views and approaches are presented, with some participants confirming the correctness of earlier contributions while others express ongoing confusion.

Contextual Notes

Participants mention specific constants and variables, but there is uncertainty regarding the values and their application in the equations. Some calculations appear to depend on assumptions about unit consistency and the treatment of variables, which remain unresolved.

Who May Find This Useful

This discussion may be useful for students and practitioners in engineering and physics who are dealing with heat transfer problems, particularly those involving natural convection and the application of Nusselt number correlations.

  • #31
Chestermiller said:
Any chance you can write this out using LaTex. https://www.physicsforums.com/help/latexhelp/

And please express your results first in terms of algebraic parameters, and then show how you substituted. I would like to see your whole derivation.

Is the above ok?
 
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  • #32
##h= \frac {2.816 \times 10^-5}{d} 0.53 ( \frac { (3.077 \times 10^-3) 1.086^2 d^3 (T_s - T_f) 9.81} {(1.962 \times 10^-5)^2})^{0.25} (0.915)##

The 0.915 at the end is my calculated Pr number to the power of 0.25.
 
  • #33
Rogue said:
##h= \frac {2.816 \times 10^-5}{d} 0.53 ( \frac { (3.077 \times 10^-3) 1.086^2 d^3 (T_s - T_f) 9.81} {(1.962 \times 10^-5)^2})^{0.25} (0.915)##

The 0.915 at the end is my calculated Pr number to the power of 0.25.
So, what is the problem?
 
  • #34
Chestermiller said:
So, what is the problem?

I realize it's probably going to be something daft, and I've done the hard part (hopefully), but I just can't seem to progress it from here?
 
  • #35
##0.0044h= \frac {(2.816\times 10^-5)}{d} 0.53 (0.2355 \times 1.0421 d^{0.75}(T_s - T_f)^{0.25} 1.7698 ) (0.915)##

Would this be a step in the right direction?
 
  • #36
Rogue said:
##0.0044h= \frac {(2.816\times 10^-5)}{d} 0.53 (0.2355 \times 1.0421 d^{0.75}(T_s - T_f)^{0.25} 1.7698 ) (0.915)##

Would this be a step in the right direction?
Yes. This is basic high school algebra.
 
  • #37
Chestermiller said:
Yes. This is basic high school algebra.

Bit harsh there Chet, but thanks.
I had just solved this, guess I need to try keep thinking straightforward rather than over complicating it. :)
 
  • #38
Rogue said:
Bit harsh there Chet, but thanks.
I had just solved this, guess I need to try keep thinking straightforward rather than over complicating it. :)
Sorry. I didn't mean to be harsh. I was just helping my grandson study for the SATs yesterday, and this kind of exponential algebra was one of the things the study guide touched upon.
 
  • #39
Chestermiller said:
Sorry. I didn't mean to be harsh. I was just helping my grandson study for the SATs yesterday, and this kind of exponential algebra was one of the things the study guide touched upon.
No worries.
 

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