# Heat Transfer Co-Efficient Calculation

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Heat Transfer Co-efficient Calculation (Sheet HES_00002122)

The following calculation was carried out to calculate individual and overall heat transfer co-efficient for PHE1 and coil in RV1.

For PHE1

Table 1 Technical Data for Plate Heat Exchanger PHE1

 Parameters Units Value Heat Transfer Area One Plate (Ap) m2 0.086 Given Number of Plates (Np) 43 Given Effective Number of Plates (NEp) 41 = Np-2 Overall Heat transfer Area (AT) m2 3.506 =NEp*Ap Plate Thickness (Pt) mm 0.6 Given m 0.0006 Plate Gap (Pg) mm 4.27 Given m 0.004 Plate Width (Pw) mm 210 Given m 0.21 Plate Length (Pl) mm 570 Given m 0.57 Number of Channels of  Product (NCp) 21 =(NEp-1)/2 Number of Channels of Cooling Water (NCcw) 21 =(NEp-1)/2 Fouling Factor Cooling Water (fcw) W m-2 C-1 8000 C&R Vol 6 Fouling factor Product (fp) W m-2 C-1 6000 C&R Vol 6 Hydraulic Diameter (Dh) m 0.009 =Pg*2 Cross Sectional Area Plate (Sp) m2 0.019 =Pw*Pg*NCp Thermal Conductivity Stainless Steel (kss) W m-1 C-1 16.70

In the above data the fouling factor of product is considered that of saline water as the product is a NaCl solution with small amounts of other salt impurities. The values for fouling factors have been taken from Coulson and Richardson, Vol 6 , Chapter 12. Also as the temperature of the fluids is same as the temperature of the liquid between the plates, the ratio of viscosity of fluid to viscosity at the plate wall is considered negligible.

At time 1:28 PM:

Cooling Water Temperature (Tcw) = 33.50 °C

Product Temperature (Tp) = 37.87 °C

Cooling water flow rate (Fcw) = 4.78 l /min =  m3/s = 7.97E-05 m3/s[pic 1]

Channel velocity of cooling water (ucw) =  =  = 0.0042 m/s[pic 2][pic 3]

Product flow rate (Fp) = 4.47 l /min =  m3/s = 7.45E-05 m3/s[pic 4]

Channel velocity of product (up) =  =  = 0.0039 m/s[pic 5][pic 6]

To find the viscosity, density, specific heat capacity and thermal conductivity of both the product and cooling water following correlations were used:

For Viscosity, μ (N s/m2):

Equation 1[pic 7]

For Density, ρ (kg/m3):

Equation 2[pic 8]

For Specific Heat Capacity, Cp (J/ kg °C):

Equation 3[pic 9]

For Thermal Conductivity, k (W/ m °C):

Equation 4[pic 10]

The above correlation have been found by plotting the parameters values from steam table at specified temperature and a graph plotted (parameter (y-axis) against temperature (x-axis)) and the correlation is derived in terms of the specific parameters and x (temperature in °C). The details are attached. The physical properties of product is considers to be equivalent to cooling water properties as the product is 97% water.

For cooling water at temperature, Tcw = 33.50 °C:

Viscosity, μcw  = 7.44E-04 N s/m2[pic 11]

Density, ρcw   = 994.52 kg/m3[pic 12]

Specific Heat Capacity, Cpcw =   = 4178.62  J/kg °C                             [pic 13]

Thermal Conductivity, kcw =   =  0.62 W/m °C[pic 14]

Similarly, using equations 1,2,3 and 4 for product at temperature, Tp = 37.87°C:

Viscosity, μp = 6.83E-04 N s/m2

Density, ρp = 992.99 kg/m3

Specific Heat Capacity, Cpp = 4178.81 J/kg °C

Thermal Conductivity, kp = 0.63 W/m °C

For the above physical properties the dimensionless numbers can be calculated using the following equations (Coulson and Richardson, Volume 6):

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