G r o u p I | 63
�
�=
����
��
(52)
Where Ds is the user defined shell diameter, C is the clearance previously calculated, B is the
baffle spacing also previously calculated, and Pt is the user defined tube pitch.
The tube flow area can be calculated as followed:
�
�=
���(��
�
2
)
4��
(53)
Nt is the number of tubes within the exchanger which is reliant upon the shell diameter and the
number of passes. IDt is the inner tube diameter which is user defined along with Np which is
the number of passes.
With the flow areas calculated, the shell and tube velocities can now be found:
�
�=
�̇
�
���
(54)
Where ms is the water flow rate into the shell, � is the density of the water, As is the flow area of
the water into the shell.
The flow velocity can also be calculated for the tube fluid as followed:
�
�=
�̇
�
���
(55)
Where mt is the mass flow rate of the refrigerant passing through the tubes, � is the density of the
vapor within the two phase flow of refrigerant, and At, as previously defined, is the tube flow
area.
The next value to calculate is the equivalent diameter. The calculation of this value depends on
the pitch chosen, triangular or square. For our design, as previously mentioned, a square pitch
was chosen. Therefore, the calculation is as followed:
�
�=
4��
2
−�??????(���
2
)
�??????(���)
(56)
Where Pt is the tube pitch and ODt is the outer diameter of the tubes.
The next value to calculate are the Reynolds number for the shell and tube. These are calculated
using the following formulas:
��
�=
������
??????
(57)
And,
��
�=
�����
??????
(58)
Where Ret is the Reynolds number for the tube and Res is the Reynolds number for the shell. For
the tube, Vt is the tube fluid velocity, IDt is the inner tube diameter, � is the density of the
refrigerant vapor, and ?????? is the dynamic viscosity of the vapor. For the shell Reynolds number, Vs
is the fluid in the shell, De is the equivalent diameter, � is the density of the water, and ?????? is the
dynamic viscosity of the water within the shell.
The Nusselt number is then calculated after the Reynolds number. The shell side is the easier
calculation and is found using the following equation:
��
�=
ℎ���
�
�
=0.36��
�
0.55
��
1
3 (59)
Where ho is the heat transfer coefficient in the tube, De is the equivalent diameter, and kf is the
thermal conductivity.