Question

Describe the considerations about a) flow behavior and b) temperature gradient that need to be taken into account for a bank of tubes. How are these considerations accounted for in the calculations?

Answer 1

Tube banks are employed in a wide range of heat exchangers. The average heat flux( q̇ ) is expressed as a linear function of the mean temperature difference between the bulk of the fluid in the tube bank and the wall, according to a rate equation

                                                                                

where (q̇) is the rate of heat transfer, Q̇ is an overall heat transfer coefficient, and ΔT_M is some representative temperature difference between the tube wall and the bulk of the fluid. A is the total heat transfer area, which for plain tubes is given by

                                                                                         

A NDL

where N is the number of tubes of outer diameter D and length L. The overall heat transfer coefficient, is non dimensionalised in terms of an average Nusselt Number,
Nu Ll
, according to

                                                                                                 where $\lambda$ is the fluid thermal conductivity

The choice of reference temperature is a matter for concern since in most situations, the engineer must use a mean value for thermal design/analysis. For constant T_w the appropriate temperature in the log-mean temperature difference,

$\Delta$Tm=$\Delta$Tlm=($\Delta$Tout-$\Delta$Tin)/(ln($\Delta$Tin/$\Delta$Tout))

where ΔT_in = T_in – T_w and ΔT_out = T_out − T_w are the differences between the fluid and wall temperatures at the inlet and outlet, respectively (see also Mean Temperature Difference.) The reference temperature, T_M, for ennumerating property values should be T_w + ΔT_LM. For constant the arithmetic-mean temperature should be used.

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