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Optimizing heater power in a thermal process
Problem Statement
Heater 2
Air flow through a channel
Two heaters raise the air temperature
The buoyancy force accelerates the flow
Heater 1
Optimization Problem:
Maximize the temperature at the outlet
By changing the power at the two heaters
Constrain the peak temperature at the heaters
Laminar Inflow at 20°C
Step 1: Set up a Non-Isothermal Flow model
Define the flow conditions at the inlet
Fix the inlet temperature
Open boundary at the outlet
Two different heater flux conditions
for the two heaters
Buoyancy force
Step 2: Solve the problem and examine results
Since we use the Open Boundary, the NonIsothermal Flow interface automatically sets
up a post-processing variable for us:
This variable takes the mass-flow-weighted
temperature average at the open boundary
and accounts for the non-uniform velocity and
any change in density over the outlet.
This weighted outlet temperature is ~61°C
and is what we want to improve
Step 3: Add Optimization to the Study
Default Optimization Solver Settings
Step 4: Define the Objective
Maximize the mass-flow-weighted
average temperature at the outlet
Step 5: Define the Control Variables
Choose reasonable initial values, and apply
boundary to the variables.
A lower bound of 0 is physically reasonable.
An upper bound is not necessary for this case.
Step 6: Define the Constraints
Keep the maximum temperature
at the heaters below 95°C
Solve & Evaluate Results
Peak temperature at heaters in 95°C
Temperature at outlet is 70°C
Heater 1: 7.9 W
Heater 2: 4.0 W
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