Steady-State Energy Balance for a Sealed Electronics Enclosure

Hello! In the previous lesson, you traced several heat-flow paths from components on a PCB to the surroundings of a sealed enclosure. This lesson puts a steady-state energy balance around those paths. The balance will tell you how much heat the enclosure must reject, help you estimate an enclosure surface temperature, and give you a check on a future Fluent result.

Choose the boundary before writing the equation

An energy balance is meaningful only after you specify what is inside it. Imagine a control volume that contains the PCB, components, trapped air, and enclosure wall. Its boundary lies just outside the enclosure’s exterior surface.

Recall the diagram from the previous lesson: air circulates inside the box, while convection and radiation occur outside it. Internal circulation can change where the wall becomes hot, but it does not carry air across the sealed boundary. Likewise, radiation from a component to the inner wall transfers energy within our chosen control volume.

Watch the control-volume portion of Heat Transfer (02): Introductory examples, energy balance on a control volume and control surface, from CPPMechEngTutorials. Focus on the distinction between a rate entering the boundary, a rate generated within it, and a rate stored within it.

For thermal accounting, write the balance as

Here every term is a rate, measured in watts. Steady state means temperatures and stored thermal energy are no longer changing with time, so the right-hand side is zero. It does not mean that heat stops moving. A component can continuously generate heat while the enclosure continuously rejects the same amount.

Be consistent about electrical power. If you already converted component electrical data into heat-dissipation rates in the first lesson, treat those rates as your heat inputs. Do not add the equipment’s full electrical input again: that would count some energy twice. Alternatively, you could begin with all electrical energy entering and subtract electrical or other useful energy leaving, but that is a different accounting convention.

Apply the balance to the whole enclosure

Suppose your component inventory contains an IC dissipating $3\mathrm{W}$, an inductor dissipating $2\mathrm{W}$, and another component dissipating $1\mathrm{W}$. The total heat load is

Assume for now that there is no solar heating, no cooling device, and no appreciable heat flow through mounting hardware or cables. At steady state, the enclosure must reject $6\mathrm{W}$ through its exterior:

The two terms describe external convection to air and radiation to surrounding surfaces. They are not the internal component-to-air and component-to-wall transfers drawn last lesson. Those internal transfers redistribute the $6\mathrm{W}$; adding them to the exterior losses would double-count it.

A real installation may have other boundary crossings. For instance, an enclosure mounted on a larger metal structure may conduct heat into that structure. An externally illuminated enclosure may absorb radiation. With outgoing rates taken as positive, a more general balance is

Include a term only when its physical path exists. A sealed wall prevents bulk airflow between inside and outside; it does not rule out heat conduction through a mount or cable. Also, heat-flow direction depends on temperatures: an exterior surface colder than its surroundings may gain heat rather than lose it.

Relate exterior heat loss to temperature

The balance tells you the required heat-rejection rate, but not the temperature needed to achieve it. To make a first estimate, suppose the exterior has one approximately uniform surface temperature $T_s$. For area $A_{\mathrm{conv}}$ exposed to external air at $T_{\mathrm{air}}$,

The coefficient $h_{\mathrm{ext}}$ represents external convection for the chosen geometry and airflow conditions. It is not a fixed property of the enclosure material.

For a gray exterior surface exchanging radiation with much larger surroundings at an approximately uniform temperature $T_{\mathrm{sur}}$, an introductory estimate is

where $\epsilon$ is surface emissivity and $\sigma =5.67\times 10^{-8}W/({\mathrm{m}}^2{\mathrm{K}}^4)$. Both temperatures in the fourth-power expression must be in kelvin. External air temperature and surrounding-surface temperature are distinct quantities, even when an initial estimate assigns them the same value. We will examine the limitations of radiation estimates more closely in a later module.

The video’s earlier review is useful here because it distinguishes a convective temperature difference from the absolute temperatures required for radiation.

Now consider a deliberately simple estimate for the $6\mathrm{W}$ enclosure. Let its exposed exterior area be $0.060{\mathrm{m}}^2$, use $h_{\mathrm{ext}}=5W/({\mathrm{m}}^2\mathrm{K})$ and $\epsilon =0.80$, and set both external air and surrounding surfaces to $25^{\circ }\mathrm{C}$. Assuming the full area participates in both mechanisms, the steady balance becomes

with $T_s$ expressed in degrees Celsius in this particular equation. At approximately $T_s=35^{\circ }\mathrm{C}$, exterior convection removes $3.0\mathrm{W}$ and exterior radiation removes about $3.0\mathrm{W}$. Their sum is approximately the required $6\mathrm{W}$.

This is an illustrative wall-temperature estimate, not a prediction of junction temperature. The junction, package, PCB, internal air, inner wall, and exterior wall can all have different temperatures. A single $T_s$ also hides variations among the top, sides, and bottom of the enclosure. Those distinctions matter when checking a component limit, but they do not change the whole-enclosure conservation requirement.

The estimate exposes a useful modeling error. If you omit radiation while retaining the assumed $h_{\mathrm{ext}}$, the same $6\mathrm{W}$ load requires a $20^{\circ }\mathrm{C}$ convective temperature difference, giving $T_s=45^{\circ }\mathrm{C}$ rather than roughly $35^{\circ }\mathrm{C}$. Whether radiation actually contributes as estimated depends on the surface and what it faces; the energy balance shows the consequence of the assumption without proving that assumption is accurate.

Move the boundary to diagnose a thermal model

A whole-enclosure balance cannot tell you which component is hottest. Moving the control-volume boundary helps distinguish that question from the total heat-rejection question.

Imagine drawing a boundary around the components, PCB, and internal air, but inside the enclosure wall. At steady state, the heat generated by the components must reach the wall through some combination of air-mediated transfer, interior radiation, and solid contacts. Draw a second boundary around the wall. The heat arriving at its inner side must be accounted for by heat leaving its exterior and any genuine conductive connection to an external support.

When you combine those two balances, the transfers between the interior and wall cancel: what leaves one region enters the other. This is why a whole-enclosure report must not sum “heat transferred to the inner wall” and “heat lost from the outer wall” as though they were separate exits.

This boundary choice becomes a practical numerical check in Fluent. Once you have a converged steady model, you can compare the sum of specified component heat sources with the net heat transfer across the model’s external boundaries. If the inputs total $6\mathrm{W}$ but reported exterior losses total only $5.94\mathrm{W}$, the difference is $0.06\mathrm{W}$, or $1\%$ of the input. That number is a balance discrepancy to investigate against your study’s accuracy needs—not, by itself, proof that every predicted temperature is correct.

In particular, check which quantity a report contains. If a reported total wall heat-transfer rate already includes convection and radiation, adding separately reported convective and radiative rates to that total counts them twice. Conversely, a model with positive heat generation and every exterior boundary specified as perfectly insulated has no steady heat exit. It cannot represent the stated steady operating condition.

Closing perspective

A steady-state balance starts with a clearly drawn boundary. For the whole sealed enclosure, component dissipation and any genuine external heat gains must equal heat rejected through its exterior and other real connections. Internal air circulation and interior radiation determine how heat reaches the wall; they are not additional losses from the whole enclosure. Exterior convection and radiation can both contribute to the final rejection rate.

Keep the distinction between a conservation check and a temperature prediction: balancing watts is necessary, but it cannot establish that a junction stays below its limit. Next, you will use a series thermal-resistance network to estimate the temperature rises along a particular junction-to-ambient path.