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# Heat Transfer in a Bank of Tubes

This Demonstration shows convective, steady-state heat transfer from a bank of tubes to cross-flowing air. This depends on the configuration of the tubes and when the inlet air velocity changes. Two tube configurations are considered: aligned and staggered. The aligned configuration has flow lanes for the air, whereas the staggered configuration disrupts these flow lanes. The air enters at 15 °C at a constant velocity, with the tubes at a constant temperature of 70 °C. 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 rate per length of tube. Radiation effects are assumed negligible and the air properties are assumed independent of temperature. The sliders can adjust the arrangement of the tubes, but for a ratio of transverse pitch to longitudinal pitch less than 0.7, aligned tubes should not be considered due to ineffective heat transfer. 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 can be shown.

### DETAILS

Air Properties
tempin = 15°C = air inlet temperature
= air density
= air heat capacity
= air viscosity
= air thermal conductivity
= air Prandtl number at inlet temperature
= air Prandtl number at tube surface temperature
Bank of Tubes
= transverse pitch (m)
= longitudinal pitch (m)
= diagonal pitch (m)
= tube diameter
= number of rows
= number of columns
Nusselt Correlations
= average Nusselt number for bank of tubes
= Reynolds number
= heat transfer coefficient ()
and are extracted from the following table.
 Configuration Rediam,max C1 m Aligned 10-102 0.8 0.4 Staggered 10-102 0.9 0.4 Aligned 102-103 0.683 0.466 Staggered 102-103 0.683 0.466 Aligned (ST/SL>0.7) 103-2*105 0.27 0.63 Staggered (ST/SL<2) 103-2*105 0.35(ST/SL)0.2 0.6 Staggered (ST/SL>2) 103-2*105 0.4 0.6 Aligned 2*105-2*106 0.021 0.84 Staggered 2*105-2*106 0.022 0.84
If the number of columns is less than 20, may be found in the following table; otherwise, a value of 1 is used.
 NL 1 2 3 4 5 7 10 13 16 Aligned 0.7` 0.8` 0.86` 0.9` 0.92` 0.95` 0.97` 0.98` 0.99` Staggered 0.64` 0.76` 0.84` 0.89` 0.92` 0.95` 0.97` 0.98` 0.99`
Temperature
= outlet air temperature (°C)
= log-mean temperature difference (°C)
Heat Transfer
= heat transfer rate per unit length of tube ()

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