# Need some helps for a Heat Exchanger Optimization project

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1. Dec 8, 2014

### danny_91

Hello fellow PF members,

My teammates and I are working on a project in our Heat Transfer class. It is extremely broad (open ended) and we are not very sure how we should get this project up and going.

1) Project description:
We are given an Air Cooled Rankine Cycle. Cooling water, at 70 °C (after it has cooled off the steam exiting the turbine) is pumped into the heat exchanger (HX) where it exchanges heat with an air stream.

2) Known: Water enters the HX at Th,i = 70 °C and needs to be cooled down to Th,o = 35 °C or less. Air enters HX at Tc,i = 30 °C
The heat amount to be transferred is q = 1 MW = 106 Watts
A list of fans and pumps with specifications (volumetric flow rate, static pressure, etc.) and charts with their performance

3) What we have to find: Based on the constraints from the selection of 1 fan and pumps, and select the configuration of the heat exchanger so that the volume of the heat exchanger is minimized.

4) What we understand and have done:
• To minimize volume, we need to minimize the surface area. Or we are minimizing the tube diameter and length, etc.
• We have chosen 2 possible designs:
1. Shell and Tube HX with circular tubes and counter flow (Currently working on this design)
2. Compact HX with fins, circular tube, and cross flow.
• We have calculated: $C_h = \frac{q}{T_{h,i} - T_{h,o}}$
• Finding some properties of air assuming the temperature is Tc,i
• Our analyzing method at the moment is the ε-NTU method. We have equation for ε and NTU already.
5) Where should we go?
We know that we have to pick one pump and fan to get the mass flow rates and the pressure drops of the air and water but are not entirely sure how we will make that pick yet. We also don't know what temperature we need to set for the air outlet temperature Tc,o yet. We also need to get the overall heat transfer coefficients from getting the Nusselt and Reynolds number which requires the inlet velocity.

It seems like picking one fan or pump is the way to go right now but there are so many of them that I think our professor wants us to use them as some parameters to optimize the volume. He also told us to use the shell diameter, tubes diameter, and number of tubes as parameters to run to get the minimized size for the HX.

Thank you so much if you read through my post and can put in some suggestions for me to get started. I am not asking for solution but more of a general guidelines that we could use for our project. FYI, we are using a software called EES (Engineering Equation Solver) to do most of our calculation, parametric tables and plots.

2. Dec 8, 2014

### danny_91

6) Some equations we have considered to use:
$q = C_h (T_{h,o} - T_{h,i}) = C_c (T_{c,i} - T_{c,o})$

$C_h = \dot m_{water} c_{ph}$ , $C_c = \dot m_{air} c_{pc}$, $c_{ph}$ and $c_{pc}$ are specific heat capacity of water and air respectively

$NTU = \frac{UA}{C_{min}}$ NTU is number of transfer unit

Effectiveness: $ε = \frac{q}{q_{max}}$

Reynolds number: $Re_D = \frac{ρv_{fluid}D}{μ}$

And Nusselt number: $Nu_D = \frac{hD}{k_{fluid}}$ , $k_{fluid}$ is thermal conductivity of the fluid and $h$ is the convective heat coefficient of the specific fluid