Internal Heat Generation & Heat Sources
How the magnitude, location and timing of internally generated heat influence thermal response.
What Is It?
Internal heat generation is heat produced within a material or component rather than applied at a surface. It includes electrical dissipation (Joule heating in resistors, electronics, wires), battery heating, frictional heating (bearings, brakes, sliding contacts), chemical reaction heat and aerodynamic heating. The heat generation may be volumetric (distributed throughout a volume) or localised (concentrated in a small region). The magnitude, the spatial distribution and the temporal profile of the heat generation all affect the resulting temperature field. Understanding how to represent heat sources accurately is essential for credible thermal analysis.
Why It Matters
The temperature field is driven by the heat sources. An incorrect heat source — wrong magnitude, wrong location, wrong timing — produces an incorrect temperature, regardless of the accuracy of the thermal model. The same total heat load can produce very different temperatures depending on where it is generated. Heat generated in a small, isolated component produces a higher local temperature than the same heat distributed over a large area. Heat generated in a component with good thermal paths to a heat sink produces a lower temperature than heat generated in an isolated component. The location, distribution and timing of the heat sources are as important as the total heat load.
The same total heat load can produce very different temperatures depending on where it is generated. A concentrated heat source in an isolated region produces a higher local temperature than the same heat spread over a large area or located near a heat sink. The heat source location matters as much as the magnitude.
Volumetric Heat Generation
Volumetric heat generation is heat produced per unit volume within a material. It is represented as a source term in the heat conduction equation. The units are power per unit volume (W/m³). Volumetric heat generation occurs in electrical conductors (current through resistance), in nuclear fuel, in chemical reactors and in any process that converts energy to heat within a volume. The generation may be uniform (constant throughout the volume) or non-uniform (concentrated in specific regions).
Volumetric heat generation: q''' = heat generated per unit volume (W/m³) Total heat: Q = ∫∫∫ q''' dV (integrated over volume) Examples: Electrical: q''' = J² / σ (current density² / conductivity) = I²R / V (for uniform current in volume V) In the heat conduction equation: ρ c_p ∂T/∂t = ∇·(k∇T) + q''' q''' is the source term — drives the temperature rise
Localised vs Distributed Sources
A localised heat source — concentrated in a small region — produces a high local temperature with steep gradients away from the source. A distributed heat source — spread over a large volume — produces a lower, more uniform temperature. The difference is important for engineering: a single high-power component on a circuit board produces a hot spot that may exceed the component temperature limit, while the same total power distributed across many components produces a lower, more manageable temperature. The thermal design must account for the spatial distribution of the heat sources, not just the total.
| Source Type | Spatial Character | Thermal Effect |
|---|---|---|
| Point source | Heat at a single point | Very high local temperature; steep gradient |
| Localised (small area) | Heat in a small region | High local temperature; moderate gradient |
| Distributed (large area) | Heat spread over large region | Moderate temperature; gentle gradient |
| Volumetric (uniform) | Heat throughout the volume | Uniform temperature rise; minimal gradient |
| Surface source | Heat applied at a surface | Gradient into the material; surface is hottest |
Spatial and Temporal Distribution
Heat sources may vary in space and time. A spatially varying source — more heat in one region, less in another — creates a non-uniform temperature field. A temporally varying source — pulsed, ramped, cyclic — creates a transient temperature response. The spatial distribution determines the temperature distribution at any time; the temporal profile determines how the temperature evolves. Both must be represented accurately. A common simplification is to use a uniform, steady heat source when the actual source is non-uniform and transient — this can miss hot spots and transient peaks.
Electrical Dissipation
Electrical dissipation is one of the most common internal heat sources. Current flowing through a resistance generates heat (Joule heating): P = I²R. The heat is generated within the resistive material — the wire, the resistor, the semiconductor junction, the trace on a circuit board. The heat generation is proportional to the square of the current and the resistance. For non-uniform current distribution (skin effect, current crowding at corners), the heat generation is non-uniform. The total heat load is the electrical power dissipated, but the local heat generation density determines the local temperature.
Battery Heating
Batteries generate heat during charging and discharging — from internal resistance (I²R losses) and from chemical reactions. The heat generation may be non-uniform across the battery pack (different cells at different states), and it may vary with time (higher during fast charge, lower during discharge). Battery thermal management is critical because battery performance, life and safety depend on temperature — overheating degrades the battery and can cause thermal runaway. The thermal model must represent the battery heat generation accurately — magnitude, distribution and temporal profile.
Frictional Heat Generation
Friction generates heat at sliding contacts — bearings, brakes, seals, gears. The heat generation equals the friction force times the sliding velocity: q = F·v. The heat is generated at the interface and partitions into the two contacting bodies. The partition depends on the thermal properties and the contact conditions — more heat flows into the body with higher thermal conductivity and larger heat capacity. The heat generation may be transient (braking event, start-up) and spatially localised (contact patch). Modelling frictional heating requires representing the contact, the friction and the heat partition.
Heat-Source Efficiency and Partition
In some cases, not all of the input energy becomes heat. An electric motor converts electrical energy to mechanical work and heat — the heat is the loss, not the total input. A laser deposits energy into a material — some is absorbed (heat) and some is reflected. The heat-source efficiency — the fraction of input energy that becomes heat — must be correctly specified. Similarly, when heat is generated at an interface between two materials, the partition — how much heat goes into each material — must be represented. An incorrect efficiency or partition produces an incorrect heat load and an incorrect temperature.
Key Takeaways
- Internal heat generation is heat produced within a material — electrical, chemical, frictional, aerodynamic
- Volumetric heat generation q''' (W/m³) is the source term in the heat conduction equation
- The same total heat can produce very different temperatures depending on where it is generated
- Spatial distribution determines the temperature field; temporal profile determines the transient response
- Heat-source efficiency and partition must be correctly specified — incorrect heat load means incorrect temperature