Hello everybody,
i hope you're doing well,
please could you help me the question above using numerical calculations
Overall heat transfer equation
Q = UxAoverallxLMTD
where, Q = overall heat transfer rate U = Overall heat transfer coefficient AOverall = Overall heat transfer surface ares LMTD = Logarithmic Mean Temperature Difference
LMTD=ΔT1-ΔT2/ln(ΔT1/ ΔT2)
LMTD is valid only for heat exchanger with one shell pass and one tube pass. For multiple number of shell and tube passes the flow pattern in a heat exchanger is neither purely co-current nor purely counter-current. Hence to account for geometric irregularity, Logarithmic Mean Temperature Difference (LMTD) has to be multiplied by a Mean Temperature Difference (MTD) correction factor (FT) to obtain the Corrected Mean Temperature Difference (Corrected MTD).
LMTD=(ΔT1-ΔT2/ln(ΔT1/ ΔT2))xFT
The number of tubes needed in shell & tube exchanger (NT) based on Aoverlal from equation of Q
NT=Aoverall/ (πxODxL)
OD is the outside diameter of selected tube size L is the total tube length
Tubular Exchanger Manufacturers Association Standards https://www.ingeduca.com/wp-content/uploads/2020/11/TEMA-10th-Edition-2019.pdf
N = L1.L2/P1.P2, N(number of tubes), L1 (total length of flow normal to tube back), L2 (length of the no-flow side), P1 (distance between the center of one tube to the next in each column of tubes i.e., vertical separation distances), P2 (horizontal separation distance between two adjacent tubes)
see text: Heat Exchanger Design Handbook by T. Kuppan Chapter 4 section 3.2, pp 178-179
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