Trombe Wall Heat Storage Calculator

Introduction: what a Trombe wall does

A Trombe wall is a passive solar heating system that places a high-thermal-mass wall (masonry, concrete, adobe, stone, or similar) behind exterior glazing on a sun-facing facade. Shortwave solar radiation passes through the glazing and is absorbed by the wall surface. That heat then moves through the wall by conduction and is released to the interior later, often when outdoor temperatures drop. In practice, a Trombe wall is a way to trade time for comfort: it reduces daytime temperature spikes and shifts useful heat into the evening.

Designers typically ask three early-stage questions: (1) How much energy can the wall store? (2) How much solar energy might it absorb in a day? and (3) How long is the delay between peak sun and indoor heat delivery? This page answers those questions with a simplified model. It is intended for comparison and rough sizing, not for final engineering. If you are comparing two materials or wondering whether a thicker wall will help or hurt evening comfort, these are exactly the kinds of trade-offs this calculator is meant to surface quickly.

How to use the calculator

Start with the wall geometry. Width and height determine the solar collection area, while thickness determines how much mass is available to store heat and how long that heat will take to travel through the wall. After that, enter the material properties: density, specific heat, and thermal diffusivity. Density and specific heat tell the calculator how much energy the wall can hold per degree of temperature rise. Diffusivity controls timing: it governs how rapidly a temperature wave moves through the slab.

The last two inputs describe the solar resource. Insolation is the daily solar energy hitting the wall area, and absorptivity is the fraction of that energy the wall actually absorbs. A dark, matte surface usually absorbs more than a light one. When you click Calculate, the result panel summarizes the wall's 10°C storage capacity, the absorbed daily solar gain, and the simplified lag estimate. The Copy Summary button is useful if you want to drop the result into a memo, spreadsheet note, or concept report.

1. Enter wall width, height, and thickness in meters.
2. Enter density (kg/m³) and specific heat (kJ/kg·K) for the wall material.
3. Enter thermal diffusivity α in m²/s.
4. Enter solar insolation in kWh/m²/day and absorptivity as a percent.
5. Review the result as a quick sizing estimate, not as a final performance guarantee.

Units matter. Keep every input in the units shown on the form. If you work in imperial units, convert first. Insolation should be based on the wall's orientation and the season you care about, often winter or shoulder-season performance for passive solar heating. Cloudiness, overhangs, neighboring buildings, and glazing details can all change real-world behavior.

Formulas and assumptions

The calculator uses a simple energy storage equation and a one-dimensional conduction lag approximation. It assumes a fixed temperature rise of ΔT = 10°C for the storage calculation. This does not mean the wall will only warm by 10°C; it means the reported storage is the energy associated with a 10°C swing. If your design allows a larger swing, the usable stored energy could be proportionally higher.

1) Wall thermal storage capacity (kWh for a 10°C rise)

Storage is computed from: Energy equals mass times specific heat times temperature change. $E=mc\Delta T$ where mass is: $m=\rho V$ and volume is: $V=AL$ with A = width × height and L = thickness.

Because the input specific heat is in kJ/kg·K, the computed energy is in kJ and is converted to kWh by dividing by 3600. The result is a convenient comparison number for early design decisions. It helps answer a practical question: if the wall temperature rises by about 10°C, how much heat does that represent in useful stored energy?

2) Absorbed daily solar gain (kWh/day)

Absorbed solar energy is estimated as: $Q=I\times A\times \beta$ where I is insolation (kWh/m²/day), A is wall area (m²), and β is absorptivity (0-1). This is a simplified absorbed-gain estimate; it does not subtract glazing transmittance losses, frame shading, angle-of-incidence effects, or night-time losses.

That simplicity is intentional. At concept stage, you often want to know whether one option is in the right ballpark before modeling every glazing layer or vent detail. If the absorbed gain looks tiny relative to the storage capacity, the wall may not be using much of its mass. If the absorbed gain looks very large, you may need to think harder about overheating, vent management, and seasonal shading.

3) Thermal lag (hours)

Thermal lag is approximated using a slab conduction relation: $t=\frac{L^2}{{\pi }^2\alpha }$ where L is thickness (m) and α is thermal diffusivity (m²/s). The result is converted from seconds to hours.

If you only have conductivity k (W/m·K), density ρ (kg/m³), and specific heat c (J/kg·K), diffusivity can be estimated by: $\alpha =\frac{k}{\rho c}$ (Be careful with units: this formula expects c in J/kg·K, not kJ/kg·K.)

A useful design intuition falls straight out of that formula: lag increases with the square of thickness. A modest thickness change can therefore shift release time quite a bit. That sensitivity is why Trombe wall design is never only about storage. A thicker wall may hold more heat, but it can also release that heat later than you want. Many articles describe whole-system response times that feel longer than the bare slab value shown here because real performance also includes glazing behavior, room-side convection, vent operation, and daily cycling. The number reported by this calculator is the simplified conduction term only, which makes it best for comparison rather than final comfort prediction.

Worked example

Suppose you have a wall that is 3.0 m wide, 2.5 m tall, and 0.30 m thick. Material properties: density 2200 kg/m³, specific heat 0.84 kJ/kg·K, diffusivity 8×10⁻⁷ m²/s. Site conditions: insolation 5 kWh/m²/day and absorptivity 90%.

• Area = 3.0 × 2.5 = 7.5 m²
• Volume = 7.5 × 0.30 = 2.25 m³
• Mass = 2.25 × 2200 = 4950 kg
• Storage (ΔT = 10°C) = 4950 × 0.84 × 10 = 41,580 kJ ≈ 11.55 kWh
• Absorbed solar gain = 5 × 7.5 × 0.90 = 33.75 kWh/day
• Lag ≈ 0.30²/(π²×8×10⁻⁷) ≈ 1.14×10⁴ s ≈ 3.17 hours

Interpretation: the absorbed daily solar energy can exceed the wall's 10°C storage increment. That does not automatically mean the design will overheat, because real walls lose heat to outdoors, glazing transmits less than 100%, and the wall may not absorb the full daily insolation. It does mean the wall could move through a 10°C temperature rise relatively quickly on a clear day unless losses, shading, or a larger working temperature swing absorb part of that energy. If you were aiming for a later evening release than this example suggests, you would look at greater thickness, lower diffusivity, or the broader wall-plus-room system rather than the slab alone.

Material guidance

If you are unsure what to enter, the ranges below can help you spot typos. They are not substitutes for manufacturer data, but they are useful as a reality check. A common error is entering specific heat in J/kg·K when the calculator expects kJ/kg·K. Another is confusing conductivity and diffusivity, which are related but not interchangeable.

• Density: adobe or earth blocks often about 1700-1900 kg/m³; brick about 1600-1900; concrete about 2200-2400; stone varies widely.
• Specific heat: many masonry materials fall around 0.75-1.0 kJ/kg·K.
• Thermal diffusivity: common masonry is often around 5×10⁻⁷ to 1.2×10⁻⁶ m²/s.
• Absorptivity: dark matte finishes can often be 80-95%; lighter finishes can be much lower.

If you are modeling a wall with an interior finish, a selective exterior coating, or a layered construction, remember that the calculator treats the wall as one uniform slab. Surface coatings mainly change how much sun the wall absorbs, while the internal layers influence effective density, heat capacity, and diffusivity.

Limitations and design notes

This tool is intentionally simplified. Use it for early-stage sizing and comparison, not as a final HVAC or code-compliance model. The goal is clarity, not exhaustive physics. That makes the result fast and interpretable, but it also means you should read the output with the right level of caution.

• Fixed ΔT assumption: storage is computed for a 10°C rise. Real walls may operate at different temperature swings.
• No glazing or air-gap loss model: absorbed gain is not reduced by glazing transmittance, convection in the air gap, wind, or night losses.
• One-dimensional lag approximation: the lag formula is a slab approximation and does not capture vents, internal convection, or multi-layer assemblies.
• Insolation variability: daily insolation changes with season, weather, shading, and orientation; use local data for the relevant months.
• Comfort and overheating: high gains can cause overheating without shading, vent control, or night insulation.

Practical rule of thumb: lag increases roughly with thickness squared. Doubling thickness can increase lag by about four times if diffusivity stays the same. That can be helpful for evening heat, but it also increases weight and can make the wall less responsive on partly cloudy days. In other words, there is no universally ideal thickness. The right answer depends on when the room needs heat, how consistent the solar resource is, and how much buffering you want between afternoon sun and evening occupancy.

For many homes, the best performance comes from treating the Trombe wall as part of a whole passive-solar strategy: good airtightness, controlled ventilation, a well-insulated envelope, and sensible seasonal shading. If you plan operable vents, think about preventing reverse thermosiphoning at night. If you plan a fixed, unvented wall, consider night insulation or low-emissivity glazing to reduce losses.

Thickness vs. lag

The table below illustrates how the simplified slab lag changes with thickness for a representative diffusivity of 8×10⁻⁷ m²/s. Your own result will change immediately if you enter a different diffusivity. The point of the table is not to prescribe one perfect value, but to show how strongly timing shifts as the wall gets thicker.

FAQ

Why does the calculator use a 10°C temperature rise?

It is a convenient reference increment for comparing designs. If your wall typically swings 5°C, the stored energy would be about half of the reported value. If it swings 20°C, it would be about double. The real swing depends on glazing, losses, venting, and how much sun you get.

What if my absorbed solar gain is much larger than storage?

That can happen easily on clear days. It suggests that without losses or control, the wall could warm more than 10°C, or that some energy will be lost back outdoors. In practice, designers manage this with shading, vent timing, selective coatings, and sometimes night insulation.

Does a longer lag always mean better performance?

Not always. Longer lag can align heat delivery with evening demand, but it can also delay heat too much or reduce responsiveness after changing weather. The best lag depends on climate, occupancy, and whether you want earlier daytime buffering, evening comfort, or late-night release.

Related calculators

Keep iterating with related planners to design complementary systems that smooth interior temperatures: passive solar glazing ratio calculator, phase-change storage estimator, and greenhouse thermal mass calculator.