Compare thermal prototypes under matched conditions

Compare a device, not just an isolated number

Two fictional enclosures use the same heater and start at 20°C in surroundings maintained at 20°C. The target is 30°C. Which design should you prefer? A lower energy total is useful only if the enclosure also meets its temperature requirements. Start by writing a prediction for the standard and insulated hardware at gain 2 W/K. Do not change the gain while testing the hardware effect.

Both designs have heat capacity C = 100 J/K. Standard hardware has conductance G = 1 W/K and costs three fictional tokens; insulated hardware has G = 0.5 W/K and costs five. The conductance sets heat transfer to the surroundings per degree of temperature difference. These are original model assumptions, not measured material properties, prices or environmental impact ratings.

Keep the test conditions matched

The run lasts 120 seconds: twelve intervals of ten seconds, with thirteen temperature states including the initial state. The nominal scenario has no sensor offset or delay, and this lab fixes the correction at zero. Its six selectable combinations are two hardware choices and three proportional gains: 2, 6 and 12 W/K.

The controller asks for 10 + Kp × (30 − sensed temperature) watts. Here Kp is gain in W/K. The fixed 10 W is a feedforward contribution; it is not an integral controller. Requested power is clipped to the heater’s range of 0–20 W and held for each interval. At the initial 20°C, gain 2 requests 30 W but the heater applies only 20 W. Record both quantities when explaining the first step.

The ten-watt contribution stays the same when hardware changes. At the target, standard hardware loses G × (30 − 20) = 10 W, while insulated hardware loses only 5 W. Thus the same controller need not settle exactly at target on both designs. The hardware comparison deliberately preserves the controller rather than secretly retuning it to make insulation look uniformly better.

Check separate criteria

The supplied brief requires true temperature from 29 to 31°C at the samples 90, 100, 110 and 120 seconds; a peak no higher than 32°C over the run; heater input energy no more than 2,000 J; and cost no more than six tokens. These are stipulated design criteria. The energy ceiling reports compliance; exceeding it would not automatically switch the heater off.

Capture standard hardware at gain 2. Its four tail temperatures are approximately 29.359, 29.542, 29.673 and 29.766°C, and total input is 1,821.035 J. Now change only hardware. The insulated tail is approximately 30.798, 31.091, 31.313 and 31.481°C, with 1,624.625 J input. It uses about 196.411 J less, yet three tail samples exceed 31°C. Its peak remains below 32°C and cost remains below six; neither fact erases the tail failure.

Make a requirement table with pass/fail entries rather than a single preferred score. Add a sentence about the cause: the hardware change reduces heat loss while the controller retains its original feedforward term. The evidence supports this mechanism within the stipulated plant; it is not proof about every real insulation retrofit.

Distinguish the new plant from the opening panel

The earlier two-layer investigation had maintained surface temperatures and a steady spatial profile. This enclosure instead has one uniform temperature that changes as energy accumulates. It does not resolve temperature gradients through walls. COMSOL’s thermal-capacitance theory describes the conditional nature of treating a body as one temperature. Our fictional conductance and capacity are not a validation of that approximation for an actual device.

Transfer: a changed resource allowance

Suppose the token limit becomes four while every thermal criterion stays unchanged. Compare the two gain-2 captures. Could the insulated candidate become feasible merely because its heater energy is lower?

Check the changed-resource transfer

No. Its five-token cost exceeds four, and its tail temperatures still fail. Standard gain 2 costs three and satisfies the listed nominal requirements. This is a paper change to the brief, not a new widget setting. It supports a bounded feasibility decision, not a claim that standard hardware is always preferable.

Keep both captures and the failed rows. Continue to the changing-temperature energy balance to explain where the heater energy goes.