Heat Transfer
Harmonic mean temperature difference is given by

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

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Heat Transfer
In a gas-liquid shell and tube heat exchanger, the

All of these
Gases to be heated/cooled is normally routed through the shell side, because the corrosion caused by the cooling water or steam condensate remain localised to the tubes
Presence of a non-condensible gas decreases the condensing film co-efficient
Gases under high pressure are routed through the tube side, because high pressure gases are corrosive in nature

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Heat Transfer
A hollow sphere and a solid sphere of the same material and equal radii are heated to the same temperature. In this case,

Both the spheres will emit equal amount of radiation per unit time in the beginning
Both will absorb equal amount of radiation from the surrounding in the beginning
The cooling rate will be the same for the two spheres and hence the two spheres will have equal temperatures at any instant
Both B & C

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