Thermal management

Requirement

Every component that carries power turns some of it into heat, and every component has a temperature above which it derates, drifts out of specification, or fails outright. A motor winding, a battery cell, and a power transistor all state a maximum temperature. The design task is to move the waste heat from where it is generated to the surrounding air fast enough that the component never crosses that limit, using no more space, noise, or cost than the product can bear.

Constraints

Six quantities bound the problem. The power dissipated, in watts, sets how much heat must leave. The ambient temperature sets the floor the heat is rejected into. The component's temperature limit sets the ceiling. The difference between ceiling and ambient is the entire temperature budget the design has to spend. Space, acoustic noise, and cost bound the means. State these first, because a cooling design that ignores any one of them is not a design but a wish.

Design choices

Model the heat path as a chain of thermal resistances in series. A thermal resistance R relates the temperature drop across a stage to the power flowing through it:

R = delta-T / P

with R in degrees Celsius per watt. This definition is not an analogy borrowed from circuits; it follows from the linearity of conduction and convection, where the heat rate is proportional to the temperature difference driving it, so their ratio is a constant for a given geometry. Radiation is the exception, linear only across a narrow temperature range, a caveat the limits section returns to. The stages add in series for a concrete reason from the first law: in steady state the same wattage crosses the source, the case, the interface, the sink, and the air, because energy is neither stored nor lost along the way, so the temperature drops across the stages simply add. The total is R_total = R_source-to-case + R_case-to-sink + R_sink-to-air.

Each stage is a design lever. Conduction from the source through a spreader or baseplate is set by material conductivity and cross-section, which is where material selection enters. The case-to-sink interface is set by mounting pressure and by thermal paste that displaces insulating air gaps. The sink-to-air stage is set by fin area and by airflow: natural convection when the enclosure is passive, forced convection when a fan is added, which can cut that stage's resistance severalfold. Radiation is often dismissed, but honesty requires the correction the Kordyban source insists on: under forced convection radiation is negligible, yet in a sealed passive enclosure it commonly carries a quarter to a third of the dissipation, and ignoring it oversizes the fan or undersizes the sink. Thermal mass, finally, does not change the steady state at all; it only buys time against transients, slowing how fast the temperature climbs toward its final value.

This entry does not re-teach the three transfer mechanisms themselves; conduction, convection, and radiation are developed in their own entry, which hands off to this one. The burden here begins at quantifying the chain and budgeting against it.

Calculations

A worked budget makes the method concrete. A component dissipates 12 watts, the air around it sits at 40 degrees Celsius, and the datasheet caps the component at 85 degrees. The temperature budget is 85 minus 40, which is 45 degrees. The allowable total resistance from source to air is 45 divided by 12, which is 3.75 degrees per watt. Suppose the source-to-case resistance is fixed by the part at 1.0 degree per watt and a good pasted interface adds 0.3 degrees per watt. The heat sink and its airflow must then supply the remaining 3.75 minus 1.3, which is 2.45 degrees per watt or better. That single number is the specification the heat sink must meet under the airflow actually available, and it is derived, not guessed.

Failure modes

Cooling fails in recognizable ways. Thermal runaway occurs when higher temperature raises dissipation, which raises temperature further, as in a battery whose internal resistance climbs as it heats. Blocked airflow and accumulated dust silently raise the sink-to-air resistance long after the design was validated clean. Contact resistance from a poorly mounted or paste-starved interface can dominate the whole chain while looking fine on paper. Treating radiation as negligible in a passive enclosure underpredicts the achievable cooling and leads to overdesign. And a steady-state budget is silent about transients: a component within its steady limit can still overheat during a brief power spike if the thermal mass is too small.

Limits and boundary conditions

The lumped series-resistance model has boundaries of its own. The convection coefficient it leans on is an empirical stand-in that shifts with geometry, orientation, and the temperature difference itself, so the resistances are approximate, not exact constants. Spreading resistance, not captured by a single series stage, dominates when a small heat source sits on a large plate. Radiation goes as the fourth power of absolute temperature, so treating it as one more linear resistance is a local approximation valid only over a modest temperature range. And the whole chain describes steady state; transient behavior needs the thermal mass the series model omits.

Build with it

Design the cooling for a sealed enclosure dissipating 12 watts at 40 degrees Celsius ambient with an 85 degree component limit. Compute the allowable total resistance from source to air, budget it across the source-to-case, interface, and sink-to-air stages, and choose a sink and airflow strategy whose sink-to-air resistance meets the remaining allowance. Then state in advance the measurement that would falsify the budget: where the thermocouple sits, how long you let the system soak before reading, and what temperature margin below the limit counts as a pass. Success is a budget whose stages sum inside the allowable total, together with a pre-stated falsification measurement you could actually run.