Heat and Mass Transfer
Upto the critical radius of insulation,

Added insulation will increase heat loss
Heat flux will decrease
Convective heat loss will be less than conductive heat loss
Added insulation will decrease heat loss

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

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