[skp524]

A liquid fermentation medium at 90 degree Celsius is pumped at 1000kg/h through a double-pipe heat exchanger, where it is cooled to 40 degree Celsius by water. Water enters the exchanger at 15 degree Celsius and 1492.5 kg/h in opposite direction to the liquid medium. The heat exchanger has a total heat transfer area of 1.6 m^2. Mean heat capacity :4.06kJ/kg degree C. for liquid medium and 4.18kJ/kg degree C. for  water.

a) Deteremine the overall heat transfer coefficient(U) . (Done)
But I want to ask why log mean is used instead of arithmetic mean .
( Q=UA (delta T log mean) )

b) After a long time operation, fouling is formed in the medium side, which has a heat tranfer rate of 4800W/m^2*degree C.  In order to maintain the oulet temperature of medium unchangeed , what should be the medium flow rate now?(Assuming negligible effects by the change of flow rate in the heat exchanger.)

Can I simply calculate the medium flow by :
Q=mCdelta T = UA (delta T log mean)
m*4.06 * (90-50) = (4800* 1000/3600 )1.6* (delta T log mean)  ? ( Same log mean was used as part a)