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I have 2 pipe lines, both water . that combine to heat up water.

Assuming at steady state ,

Heat gained by cold water = heat lost by hot water

Let's say , according to formula , I calculated the combined temperature to be 62.94 degrees C.

However , the temperate transmitter tells me that it's 63.06 degrees C, slightly higher than 62.94.. why is that the case ?

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    $\begingroup$ Does it matter? what is the application here? you practically have a very nice agreement between calculations and actual result. And, you should add more details about your set up. $\endgroup$ – Algo Nov 11 '17 at 5:42
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Which formula you used? Are they distilled water or tap? Remember heat transfer formulas are based upon assumptions and there is always heat loss due to transfer to the surface of the tube and turbulence generates heat.

The more exact you want it to be the more complex you will make the problem, and heat transfer in a tube is actually a chaotic equation I cannot remember the guy who did that experiment. Will post the name if I remember

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The problem statement, proposed solution, and evaluation are incomplete.

  • The problem statement does not tell us the complete picture of the system. Are the tubes perfectly insulated or not? What kind of water is in the tubes? Is the flow laminar or turbulent? We must know all of these factors to create a proper model of the real system.

  • The proposed solution is a simple mixing equation based on assumptions that may or may not apply to the actual mixing system. See the notes above.

  • The evaluation quotes a number to four significant digits without reference to whether this level of precision is justifiable by all other values in the calculation. By example, when the specific heat of the water is used to only three significant digits in the calculations, the final answer is only valid as 62.9$^o$C.

  • The comparison is made to a measured value with four significant digits without reference to whether the measurement device has been calibrated to this level of accuracy and is precise to this level. By example, when the device has an overall $\pm 1$% calibration + measurement uncertainty, the measured value is reliable at best only as $63.1^o$C $\pm 0.6^o$C.

In summary, the answer to "Why is (temperature B slightly higher than temperature A)?" is this: Absent further information, the best we can say is, it is higher only because you think it is.

We cannot say anything about a proposed difference of 0.2$^o$C until all of the above issues are rectified.

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