HEAT TRANSFER - Computer Programming

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## Friday, April 1, 2011

HEAT TRANSFER

AIM:
To determine the overall heat transfer heat transfer coefficient ‘U’ from experiment and conforming the values using correlation.

THEORY:
Driving force for the heat transfer is the temperature difference between any two bodies. Two bodies at different temperatures when in contact tend to attain the same temperature by heat transfer. This phenomenon is used in reactors to heat or cool the medium to desired temperature. To determine the flow rate temperature of the heating or cooling substances, such that the operation of heating or cooling is performed effectively and efficiently. It is necessary to know the overall heat transfer coefficient ‘U’. The transferred is proportional to the temperature gradient and inversely proportional to the area.
Hence, Q α  A ΔT (or) Q = U A ΔT                                                                           (1)
Thus, by knowing the overall rate of heat transfer (Q) we can determine ‘U’
By a simple thermodynamic relation
Q = mf Cp (To – Ti )                      -----                                              (2)
Where,
mf – mass flow rate of heating or cooling substance, kg/m s
Cp – specific heat capacity of heat substance, J / kg K
To – the outlet temperature of substance for heating or cooling, K
Ti – the inlet temperature of substance for heating or cooling, K

mf Cp (To – Ti )
U =                                                                                                     (3)
A ΔT
How ΔT is defined in different ways. The best would possibly be log mean temperature difference (LMTD)

To – Ti
LMTD =                                                                                                                      (4)
ln ﴾(TF-To)/ TF-Ti﴿
Where Tf is the fermentation temperature. Also, the value of U depends on the nature of material across heat is being transferred, the systems geometry, the nature of fluid etc., the dependence of ‘U’ on all of the above is quite complex and is evaluated using empirically.
Calculation
1  =   1   + 1  . do  + Xw    .  do
U       ho     hi   di      kw     di

where,
ho – heat transfer coefficient of liquid (film) outside
hi – heat transfer coefficient of liquid (film) inside.

RESULT:
The overall heat transfer  coefficient ‘U’  was calculated using correlation n and experiment

U expt  =

U corr  =

An increase in value of heat transfer coefficient was seen with increase in rpm

INFERENCE

An increase in rpm allows better transfer of heat all through the liquid and hence the overall heat transfer coefficient is seems to be increased

Also the outer film transfer resistant (1/ho) decreases due to better and vigorous mixing

The correlation values are lesser than that by the experiment because of the assumption of water constant at temperate 290K

The diameter of the agitator and flow rate were also approximated which would have been the cause for difference in the experimental and correlation values