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Technology / Technical guide
Thermal Resistance, Heat Capacity & Transient RC Models
Heat generation and temperature are not the same quantity. Thermal resistance relates a temperature difference to a heat-flow rate, while thermal capacitance represents stored internal energy. Their combination explains delayed temperature response in a stated lumped model rather than an instantaneous jump to a steady temperature.
Separate the heat-flow path from the energy stored in a body.
An RC analogy uses thermal units and boundaries; it does not turn an electrical resistor or capacitor value into a physical temperature rating.
01 / Heat-flow relation
Thermal resistance connects a difference with a rate.
For a constant linear thermal resistance Rth between two nodes, heat-flow rate is their temperature difference divided by Rth.
For a constant linear thermal resistance Rth between two nodes, heat-flow rate is their temperature difference divided by Rth. Rth is expressed in K/W. A kelvin temperature difference has the same numerical size as a Celsius temperature difference.
MathWorks’ thermal-resistance model states that relationship with a defined heat-flow sign. It is a lumped approximation to a represented path, not a universal material property independent of geometry or boundary conditions. Temperature at one node does not name every temperature in an assembly.
02 / Storage relation
Heat capacity sets the rate of temperature change.
For a uniform lumped body with constant mass m and specific heat cp, thermal capacitance is Cth = m cp in J/K.
For a uniform lumped body with constant mass m and specific heat cp, thermal capacitance is Cth = m cp in J/K. Net heat entering that body is Cth dT/dt. Storage therefore allows input and outgoing heat-flow rates to differ during a transient.
The thermal-mass reference explains this internal-energy role. Thermal capacitance is not measured in electrical farads. A higher Cth in the same simplified model slows temperature change for a given net heat input; it does not alone establish a lower eventual steady temperature.
03 / Single-node model
Combine one body with one fixed ambient path.
Consider an invented single thermal node receiving constant dissipation P and connected through constant Rth to fixed ambient temperature Ta.
Consider an invented single thermal node receiving constant dissipation P and connected through constant Rth to fixed ambient temperature Ta. With constant Cth, its model is Cth dT/dt = P − (T − Ta)/Rth.
This model assumes the body has one representative temperature and the path remains linear. Its steady temperature rise is P Rth, while its time constant is τ = Rth Cth in seconds. Multiplying K/W by J/K gives J/W, which is seconds.
04 / Step illustration
One time constant closes a defined temperature gap.
If the hypothetical body starts at Ta and receives a constant power step, the model gives T − Ta = P Rth[1 − e^(−t/τ)].
If the hypothetical body starts at Ta and receives a constant power step, the model gives T − Ta = P Rth[1 − e^(−t/τ)]. At one τ, the rise is about 63.2% of the model’s final rise.
With different initial temperature, the complete response retains that initial state and approaches the new steady result exponentially. The percentage applies to the gap, not to an absolute Celsius temperature. It supplies no MARSTON time constant, heat capacity, dissipation or accepted heating duration.
05 / Several nodes
Different physical regions need not share one response.
A junction, package, enclosure and ambient can follow different thermal histories.
A junction, package, enclosure and ambient can follow different thermal histories. Several storage and transfer paths can produce several time scales. One apparent exponential over a limited interval should not automatically describe the entire assembly at every duration.
A fitted compact network can reproduce an observed boundary response without every internal node corresponding to a particular physical part. Its interpretation depends on how the model was obtained. The thermal-rating guide treats a different question about real rating conditions.
06 / Model scope
A calculated rise is not a product temperature allowance.
The loss guide describes heat generation, while the winding-class guide distinguishes material temperature terminology.
The loss guide describes heat generation, while the winding-class guide distinguishes material temperature terminology. Neither supplies the Rth/Cth needed to identify an actual converter’s transient temperature.
No MARSTON thermal-network parameters, junction limit, cooling function or transient rating is assigned. This explanation gives no heating test, fan modification, protective threshold or operating duration; it explains the unit-consistent first-order model and its limitations.
Related technical guides: Converter Instantaneous Power, Storage & Dissipation · Generator Core Loss: Magnetic Hysteresis & Eddy Currents · DC Capacitor Charging, Initial Voltage & Inrush Current.
General background: MathWorks: thermal resistance and temperature-difference/heat-flow relation · MathWorks: thermal mass, specific heat and stored-energy rate. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Heat-flow rate | P or heat rate in W | Different from temperature in K or °C. |
| Thermal resistance | Rth in K/W | Defined linear transfer path. |
| Thermal capacitance | Cth in J/K | Uniform lumped constant-capacity body. |
| Time constant | Rth Cth in s | Single-node constant-R/C model. |
| Steady rise | P Rth in K | Constant input and fixed ambient under the model. |
Engineering questions.
Is thermal capacitance measured in farads?
No. Its unit is J/K; electrical and thermal analogies use different physical units.
Does larger thermal capacitance lower the eventual steady rise?
Not by itself in the stated model. It changes the time response.
Does one τ give 63.2% of absolute temperature?
No. It closes that fraction of the stated model’s temperature gap.
Are ambient and junction temperature the same node?
Not generally. Different paths and storage separate them.
Does a fitted thermal node always identify one physical layer?
No. The model’s construction and interpretation determine that meaning.
Does this provide actual MARSTON thermal limits?
No parameters, allowed durations or protective settings are assigned.
Technical enquiry
Discuss the technical question.
Heat generation and temperature are not the same quantity. Share the model and applicable operating or design information for an engineering discussion.