Optimizing heater power in a thermal process

Problem Statement

Laminar Inflow at 20°C

OutletH

eate

r 1

Hea

ter

2

Maximize the temperature at the outletBy changing the power at the two heatersConstrain the peak temperature at the heaters

Gravity

Air flow through a channel Two heaters raise the air temperatureThe buoyancy force accelerates the flow

Optimization Problem:

Air

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 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

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°CTemperature at outlet is 70°CHeater 1: 7.9 WHeater 2: 4.0 W