Question

Q3 Log mean temperature difference

Starting from energy balance of fluid inside a tube, derive a formula to show that the

following long mean temperature difference should be used to calculate the total rate of heat

transfer to or from a fluid flowing through a tube with a constant fluid temperate outside of

the tube.

qconv =UAs

Tlm ,Tlm = ?Ti ? ?To

?Ti = T? ?Tm,i

?To = T? ?Tm,o

Answer 1

For a parallel flow system

Assumptions are mass flow rate, overall heat transfer coefficient, specific heat capacity are constant

Heat flow rate

dQ = U x dA x dT

dA = elementary area of exchanger

Energy balance

dQ = - mh x Cph x dTh = mc x Cpc x dTc

h and c represents the hot and cold fluid respectively

Negative sign shows the decrease in temperature