Heat Transfer
Harmonic mean temperature difference is given by

(ΔT₁ - ΔT₂)/(ΔT₁ . ΔT₂)
2.(ΔT₁ . ΔT₂)/(ΔT₁ + ΔT₂)
√(ΔT₁ . ΔT₂)
2.(ΔT₁ . ΔT₂)(ΔT₁ - ΔT₂)

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Heat Transfer
In a shell and tube heat exchanger,

The temperature drops in the two fluids and the wall are proportional to individual resistances
There is no relationship between temperature drop and resistance
The relationship is not generalised
The temperature drop is inversely proportional to the resistance across which the drop occurs

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