1. Optimizing heater power in a thermal process

2. Problem Statement Laminar Inflow at 20°C Outlet Heater 1 Heater 2 Maximize the temperature at the outlet By changing the power at the two heaters Constrain the peak temperature at the heaters Gravity Air flow through a channel Two heaters raise the air temperature The buoyancy force accelerates the flow Optimization Problem: Air

3. 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

4. Step 2: Solve the problem and examine results Since we use the Open Boundary, the Non- Isothermal Flow interface automatically sets up a post-processing variable for us: comp1.nitf.open1.Tave 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

5. Step 3: Add Optimization to the Study Default Optimization Solver Settings

6. Step 4: Define the Objective Maximize the mass-flow-weighted average temperature at the outlet

7. 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.

8. Step 6: Define the Constraints Keep the maximum temperature at the heaters below 95°C

9. 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