Heating of Water down the Length of a Pipe, Uniform Surface Temperature

Organized by textbook: learncheme.com/ A simulation of the heating of water down the length of a pipe is shown. The inner surface of the pipe is maintained at a uniform temperature. Made by faculty in the Department of Mechanical Engineering and processed by the Department of Chemical & Biological Engineering at the University of Colorado Boulder
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[@1morrel]

I'm able to reproduce your results fairly closely. A couple of observations: 1) Multiplying velocity by cross-sectional area times density gives 0.778 kg/s, I adjusted my velocity to 0.113 m/s in order to match your 0.0088 kg/s. However, adjusting velocity results in a slightly higher Reynolds number of 2100. Going back to 0.1 m/s gives the same Reynolds number you have. 2) I think some attention needs to be given for how the Nusselt number was calculated as it can vary by method. The only value I could get that was close to your 5.2 was to use the Sieder Tate relation assuming 1 for the viscosity ratio between bulk and wall conditions. My value was 5.9. This is important because I'm assuming that's how you found the average heat transfer rate, h. I got 380 W/m2 C. If I use your 330 W/m2 C I'm able to reproduce your results. It's probably worth noting to the viewer that the heat transfer correlations will vary depending on the Reynolds number which is clearly in the laminar flow regime for this problem. Thanks for posting the video.

[@hongnanhu3404]

Hi, I am wondering how do you do the simulation. Do you have your own MATLAB code or there is a software there?

[@robertaglarsen]

Brilliant! Thanks

[@orn6394]

Thanks, good explanation !

[@user-lo9oy9lj9o]

I've attempted to recreate your simulations in a spreadsheet using your parameters for reference and cannot achieve the same output. The initial value yielded by the formula in the spreadsheet is 99 C @ position '0' : [ T = 100 - (100 - 0) ^ 0 = 100 - 1 = 99, which then asymptotically approaches 100 C for larger values of Z. I've tried a number of variations / tweaks in my spreadsheet but nothing has proven successful. Any suggestions are welcome!

[@andriykumanovskyy5975]

Getting rid of the '-ln'/natural log yields T=Ts-(Ts-Tin)*e^(-h(per)(z)/cp*M(dot)) not T=Ts-(Ts-Tin)^(-h(per)(z)/cp*M(dot)). e being 2.718281828459045.

[@martingravel2098]

Exp refers to the exponential function "e". The function is Ts-(Ts-Tin)*e^(blob) and not Ts-(Ts-Tin)^(blob)