Heat Transfer in a Bank of Tubes

This Demonstration shows convective, steady-state heat transfer from a bank of tubes, which are at a constant temperature of 70 °C, to cross-flowing air, which enters at 15 °C. Align or stagger the tubes with buttons. The aligned configuration has flow lanes for the air, whereas the staggered configuration disrupts these flow lanes. When the air velocity increases, the rate of heat transfer increases and the outlet air temperature decreases. An average Nusselt number is calculated for the entire tube bank, and that number is used to calculate the outlet air temperature and the heat transfer rate per length of tube. Radiation is negligible and air properties are assumed independent of temperature. Use sliders to adjust the arrangement of the tubes. Due to ineffective heat transfer, aligned tubes should not be considered for a ratio of transverse pitch to longitudinal pitch less than 0.7. The tube diameter does not change when the tube arrangement changes, but the diameter displayed in the tube configuration figure changes so that all tubes are shown.


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The diagonal pitch of a bank of tube is:
where and are the longitudinal and transverse pitch (m).
A Nusselt correlation is used to calculate the average heat transfer coefficient:
If , , otherwise ,
where is the average Nusselt number for the entire bank of tubes, is the Reynolds number at the maximum fluid velocity, and are the Prandtl numbers at air and tube surface temperatures, is the maximum fluid velocity (m/s), is tube diameter (m), is the kinematic viscosity of air (), is velocity (m/s), is the average heat transfer coefficient (), is thermal conductivity (W/[m K]) and , and are constants from the following two tables:
If the number of columns , get from the following table, otherwise :
The heat transfer rate per unit length of tube is calculated from the found from the Nusselt correlation:
where is in W/m, is the total number of tubes in the bank, is the log-mean temperature difference (°C), is the tube surface temperature (°C), and are the temperatures at the inlet and outlet (°C), is air density (), is the number of tubes in each row and is heat capacity (J/[kg K]).
[1] T. L. Bergman, A. S. Lavine, F. P. Incropera and D. P. DeWitt, Introduction to Heat Transfer, 6th ed., Hoboken: John Wiley and Sons, 2011 pp. 447–451.
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