Heat and Mass Transfer
The heat transfer by conduction through a thick sphere is given by

Q = 2πkr1 r2 (T1 - T2)/ (r2 - r1)
Q = 6πkr1 r2 (T1 - T2)/ (r2 - r1)
Q = 4πkr1 r2 (T1 - T2)/ (r2 - r1)
Q = 8πkr1 r2 (T1 - T2)/ (r2 - r1)

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Heat and Mass Transfer
Film coefficient is defined as the ratio of

Thermal conductivity to the equivalent thickness of the film of fluid
Thickness of film of fluid to the temperature drop through the films of fluids
Temperature drop through the films of fluids to the thickness of film of fluids
Thickness of film of fluid to the thermal conductivity

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Heat and Mass Transfer
The logarithmic mean temperature difference (tm) is given by (where Δt1 and Δt2 are temperature differences between the hot and cold fluids at entrance and exit)

tm = loge (Δt1/Δt2)/ (Δt1 - Δt2)
tm = tm = (Δt1 - Δt2) loge (Δt1/Δt2)
tm = loge (Δt1 - Δt2)/ Δt1/Δt2
tm = (Δt1 - Δt2)/ loge (Δt1/Δt2)

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