Thermal Generation of Electricity: TEG Thermal Path Math & Sizing

To maximize the thermal generation of electricity using a Thermoelectric Generator (TEG), you must aggressively manage the cold-side thermal resistance. A TEG does not generate power from absolute heat; it generates power from a temperature differential ($\Delta T$). If your cold-side heatsink is undersized, the module reaches thermal equilibrium, $\Delta T$ collapses to near zero, and your electrical output flatlines. For a standard 50x50mm Bismuth Telluride (Bi2Te3) module harvesting 10W of waste heat, maintaining a $\Delta T$ above 100°C requires a cold-side thermal resistance ($R_{\theta SA}$) of 3.0 °C/W or lower.

The Physics of Thermal Generation and Temperature Limits

The thermal generation of electricity in solid-state modules relies on the Seebeck effect. When a temperature gradient is applied across dissimilar semiconductors (typically n-type and p-type Bi2Te3 legs), charge carriers diffuse from the hot side to the cold side, creating an open-circuit voltage ($V_{oc}$). The voltage is strictly proportional to the $\Delta T$ across the module.

How hot is too hot? This is the most common bench mistake. Standard Peltier coolers (like the ubiquitous TEC1-12706) repurposed as generators use low-temperature solder that melts around 138°C. Dedicated TEG modules (such as the SP1848-27145 or Laird Thermal Systems PowerSeries) use high-temperature lead-free solder (like SAC305) and can survive hot-side temperatures up to 200°C–250°C. Pushing a standard module past 150°C will liquefy the internal interconnects.

Failure signatures of thermal stress: When a TEG is subjected to excessive heat or rapid thermal cycling, it rarely fails open. Instead, you will see a massive spike in Equivalent Series Resistance (ESR). A healthy 50x50mm module might have an internal resistance of 2.5 $\Omega$; a thermally degraded module will jump to 10 $\Omega$ or higher, crushing your load current. Physically, look for delamination of the alumina ($Al_2O_3$) ceramic plates, which manifests as visible bulging or a hollow sound when tapped lightly with a plastic spudger.

Thermal Path Math: Junction-to-Ambient $R_{\theta}$ Calculations

To engineer a reliable energy harvesting circuit, we treat the TEG hot-side ceramic plate as the "junction" in standard semiconductor thermal math. The goal is to calculate the exact temperatures on both sides of the module to find our operating $\Delta T$.

The fundamental thermal path equations are:

• $T_{hot} = T_{source} - (Q \times R_{\theta\_source\_to\_hot})$
• $T_{cold} = T_{ambient} + (Q \times (R_{\theta\_cold\_to\_sink} + R_{\theta\_SA}))$
• $\Delta T = T_{hot} - T_{cold}$

Where $Q$ is the heat flow in Watts, and $R_{\theta}$ values are in °C/W. Below is a realistic thermal resistance budget for a 50x50mm TEG harvesting 10W of waste heat from an industrial power resistor.

Let us run the math assuming a heat source ($T_{source}$) of 180°C and an ambient room temperature ($T_{ambient}$) of 25°C:

• $T_{hot} = 180°C - (10W \times 0.15 °C/W) = 178.5°C$
• $T_{cold} = 25°C + (10W \times 4.85 °C/W) = 73.5°C$
• $\Delta T = 178.5°C - 73.5°C = 105°C$

With a $\Delta T$ of 105°C, a typical 50x50mm TEG will generate roughly 3.5V open-circuit and deliver about 1.2W of electrical power to a matched load. While functional, we are leaving power on the table due to the passive heatsink's high thermal resistance. For deeper theory on matching the electrical load to the thermal impedance, refer to the Laird Thermal Systems application notes on thermoelectric harvesting.

Heatsink Selection, Airflow, and Derating Curves

The cold-side heatsink is the single most critical variable you control. When selecting a heatsink, you must look past the marketing claims and read the manufacturer's derating curves. A heatsink's $R_{\theta SA}$ is not a static number; it is highly dependent on airflow velocity and the temperature differential between the fins and the ambient air.

Real-World Heatsink Selection: For our 50x50mm module, the Wakefield Vette 680-125P is a benchmark extruded aluminum profile. Measuring 125mm long with high-density fins, its datasheet provides a derating curve showing $R_{\theta SA}$ dropping from roughly 4.5 °C/W in natural convection (0 m/s) down to 1.8 °C/W at a forced airflow of 2.0 m/s.

What airflow and enclosure changes buy you: If we mount a 40x40x10mm fan (such as the Noctua NF-A4x10 FLX) to the end of the 680-125P heatsink, we shift the operating point on the derating curve. Let us recalculate the cold side temperature with forced air:

• New $R_{\theta SA}$ = 1.8 °C/W
• New $T_{cold} = 25°C + (10W \times (0.35 + 1.8) °C/W) = 25°C + 21.5°C = 46.5°C$
• New $\Delta T = 178.5°C - 46.5°C = 132°C$

By spending $15 on a small fan and dropping the cold-side temperature by 27°C, our $\Delta T$ increases from 105°C to 132°C. Because the Seebeck coefficient is roughly linear in this range, this 25% increase in $\Delta T$ yields a proportional 25% increase in open-circuit voltage, and roughly a 50% increase in maximum harvestable electrical power (since $P = V^2 / R$).

Enclosure Gotchas: If you are mounting this TEG inside a sealed NEMA enclosure, the "ambient" temperature for your cold-side heatsink is no longer the room temperature; it is the trapped air inside the box. A 10W heat load dissipated into a small, unventilated enclosure will raise the internal ambient temperature by 10°C to 15°C over a few hours. This directly eats into your $\Delta T$. To fix this, you must either duct the cold-side heatsink fins to the outside air through a filtered bulkhead, or use a liquid cold plate (like the CoolIT or CoolerMaster liquid loops adapted for industrial use) to transport the waste heat entirely out of the enclosure.

Mastering the thermal generation of electricity is ultimately an exercise in thermal plumbing. The electrical output is merely a byproduct of how efficiently you can move photons and phonons from the hot source, through the semiconductor legs, and out into the ambient environment via a properly derated heatsink.