Every time this page loads, the solver is checked against analytic solutions right here in your browser. The source code is public on GitHub.
In electronics cooling and battery thermal design, you need quick answers before ever running 3D CFD: how hot does the junction get? How much heat-sink thermal resistance do I need? This tool is a 1D thermal network (thermal circuit) solver built for exactly that stage. Wire up thermal resistances, capacitances, heat sources, convection and radiation like a circuit schematic, and every node temperature is computed instantly.
Heat conduction shares its mathematical structure with electrical circuits. Temperature difference maps to voltage, heat flow to current, thermal resistance to electrical resistance, and energy conservation at each node is Kirchhoff's current law. The solution method is the same too: assemble the nodal equations and solve them with Newton's method.
| Quantity | Electrical circuit | Thermal circuit |
|---|---|---|
| Across variable (potential) | Voltage V [V] | Temperature difference ΔT [K] |
| Through variable (flow) | Current I [A] | Heat flow q [W] |
| Resistance | R [Ω] | Thermal resistance Rth [K/W] |
| Capacitance | C [F] | Thermal capacitance Cth [J/K] |
Energy conservation is enforced at every node. In steady state:
Σ qout(T) − Pin = 0
Transient analysis adds the storage term from thermal capacitance, integrated in time with backward Euler:
C (Tn+1 − Tn) / Δt + Σ qout(Tn+1) − Pin = 0
Backward Euler is unconditionally stable, so stiff systems — an electronic component with millisecond time constants next to a chassis with hour-scale thermal mass — solve with large time steps without blowing up. Radiation is a nonlinear T4 term, so its 4εσA T3 contribution goes into the Jacobian and the system is solved with Newton's method.
| Component | Law | Typical use |
|---|---|---|
| Thermal resistance R | q = ΔT / R | Conduction, contact resistance, TIM |
| Convection h·A | q = hA·ΔT | Natural convection, forced air, liquid cooling |
| Radiation ε·A | q = εσA(T₁⁴ − T₂⁴) | Radiative share in passive cooling |
| Thermal capacitance C | q = C·dT/dt | Transients, thermal time constants |
| Heat source P | — | Chip losses, heaters |
| Fixed temperature T | — | Ambient, coolant temperature |
This tool solves lumped-parameter (1D) thermal networks. It does not resolve temperature fields inside a part, nor the flow field itself. That is exactly the point: for system-level sizing, heat-budget checks and sensitivity studies — the decisions you make before committing to a 3D run — it is sufficient, and the answer is instant. When you do need full 3D temperature fields, move on to the thermal analysis articles and finite-element or CFD tools.
This is v0.1 beta. On the roadmap: more component libraries (fluid and electrical branches), a sparse solver for large models, and further UI languages. Requests are welcome via the request form.