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I'm studying heat transfer at graduate level, and in the process of deriving LMTD of a heat exchanger, the book took the following assumption :

Any axial heat conduction will be neglected.

What that truly means?

Does it mean that the tube's temperature only changes along radial direction and remains constant axially?

Screenshot from the book

Book: Fundamentals of Heat Transfer by Incropera

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2 Answers 2

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What your book means is that axial heat conduction within the fluid is considered negligible compared to axial convection of heat caused by the axial fluid movement. This approximation has been validated for all typical fluids, but, for liquid metals, the axial conduction needs to be included. You can verify the validity of the approximation a postiori.

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  • $\begingroup$ The quote from the book is quite specific that it’s ignoring axial along the tubes, not along the fluid column $\endgroup$
    – Bob Jacobsen
    Commented Aug 12, 2021 at 22:39
  • $\begingroup$ @Bob Jacobsen Actually, the analysis neglects both. The is no term in the differential heat balance equation in the book for $k\frac{\partial ^2T}{\partial z^2}$ , where z is the axial coordinate. Anyone with any kind of practical heat transfer experience is aware of this. $\endgroup$
    – Chet Miller
    Commented Aug 12, 2021 at 22:54
  • $\begingroup$ @ChetMiller Yes that makes sense. The mean temperature at every cross section of the tube will vary and will give rise to axial heat transfer but we are neglecting that too. $\endgroup$
    – Harshit Rajput
    Commented Aug 13, 2021 at 6:11
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“Axial conduction along the tubes” refers to heat transfer along the material of the tubes themselves. In most exchangers, that’s negligible due to thin tubes and high flow rates.

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  • $\begingroup$ So that should imply temperature at the inner surface of the tube remains constant (uniform everywhere)? $\endgroup$
    – Harshit Rajput
    Commented Aug 12, 2021 at 18:54
  • $\begingroup$ No. Just that the amount of thermal energy transferring inside the tube due to that dT is negligible. $\endgroup$
    – Bob Jacobsen
    Commented Aug 12, 2021 at 18:55
  • $\begingroup$ @HarshitRajput Oh no, not at all. The temperature varies along the tube, so the inner surface temperature does too. $\endgroup$
    – Gert
    Commented Aug 12, 2021 at 18:56
  • $\begingroup$ The inner wall temperature is not important because that's not how LMTD is calculated anyway. $\endgroup$
    – Gert
    Commented Aug 12, 2021 at 19:06
  • $\begingroup$ Ohhh! So the temperature along the tube does vary, it's just that the temperature difference is small as we move along the tube and heat transfer due to that little temperature difference turns out to be negligible. Any corrections in my understanding? $\endgroup$
    – Harshit Rajput
    Commented Aug 12, 2021 at 19:14

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