Enrichment · STEM Explorations

Where the heat goes,
in watts.

Build a wall layer by layer and see how much heat it lets through, where the temperature drops, and how a window compares. Then work out convection and radiation, and run a cooling-curve experiment with two mugs.

Open the estimator What you get

The estimator

Four tools, one worked example each: a house wall, a warm panel in still air, a person in a cool room and two mugs of hot water.

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The materials table

Thermal conductivity near room temperature. Real materials vary with density, moisture and temperature, so treat these as typical values, not specifications.

Material	k, W/(m·K)	R per inch (US)	Source
Copper (pure)	401	0.00036	Incropera et al.
Aluminum (pure)	237	0.00061	Incropera et al.
Carbon steel (plain)	60.5	0.0024	Incropera et al.
Stainless steel (AISI 304)	14.9	0.0097	Incropera et al.
Ice (0 °C)	2.2	0.066	ASHRAE, typical
Concrete (stone mix)	1.4	0.10	Incropera et al.
Brick (face)	1.3	0.11	Incropera et al.
Brick (common)	0.72	0.20	Incropera et al.
Window glass (soda-lime)	1.0	0.14	ASHRAE, typical
Water (still, 27 °C)	0.613	0.24	Incropera et al.
Gypsum board (drywall)	0.17	0.85	Incropera et al.
Hardwood (oak, maple)	0.16	0.90	Incropera et al.
Plywood	0.12	1.20	Incropera et al.
Softwood (fir, pine)	0.12	1.20	Incropera et al.
Fiberglass batt (about R-3.7 per inch)	0.039	3.70	U.S. DOE, typical R per inch
Expanded polystyrene board (about R-4 per inch)	0.036	4.01	U.S. DOE, typical R per inch
Extruded polystyrene board (about R-5 per inch)	0.029	4.97	U.S. DOE, typical R per inch
Polyisocyanurate board (about R-6 per inch)	0.024	6.01	U.S. DOE, typical R per inch
Still air (27 °C)	0.0263	5.48	Incropera et al.

Glazing, center of glass

Glazing	U, W/(m²·K)	U, Btu/(h·ft²·°F)
Single pane, clear	5.9	1.04
Double pane, air gap	2.7	0.48
Double pane, low-e coating, argon	1.7	0.30
Triple pane, low-e, argon	1.0	0.17

Typical values for the glass alone. A whole window, frame included, usually does worse; use the rated U-factor on the window's label for a real window.

What you get

Enrichment · STEM ExplorationsFree

What you finish with: Heat-flow estimates you can explain: R and U for a wall you build, the temperature at every layer, watts and kilowatt-hours, a wall-against-window comparison, convection and radiation answers with the arithmetic shown, and a fitted cooling curve with a printable lab sheet.
Who it is for: Middle and high school students in physical science, physics, engineering and environmental science classes; science fair projects; teachers who want a ready experiment; families checking why a room is cold.
Format: Browser tool. Works on a phone or computer. Print any tool's results, save the cooling readings as a .csv, and move work between devices by file.
Access: Free. No account and no sign-in. Numbers stay in this browser; nothing is sent to Caveat.
Where it lives: The STEM Explorations space in Caveat Enrichment.
Support: Questions, a correction or a request: team@caveatacademic.com.

How to use it

Start with Wall or window. Change the insulation layer and watch the heat flow and the temperature profile.
Swap in a window to see why windows matter so much for heating bills.
On Convection and Radiation, try the typical values and compare the two for the same surface.
For the experiment, follow the plan on the Cooling curve tab, type your readings and compare the two runs' cooling constants.
Print the results for a lab notebook or a science fair board.

Open the estimator

The physics, in four lines

Every formula on this page, with the assumptions that come with it.

Conduction

One slab: Q = k A ΔT ÷ d, where k is the conductivity, A the area, ΔT the temperature difference and d the thickness. Heat flows from hot to cold.
Layers in a row add like resistors: each has R = d ÷ k, the total is the sum, and U = 1 ÷ R_total, so Q = U A ΔT. A thin layer of still air on each face adds resistance; the standard values are 0.13 inside and 0.04 outside (m²·K/W).
The temperature drop across each layer is proportional to its R, which is why the insulation layer carries most of the drop.
US R-values are in h·ft²·°F/Btu: multiply an SI R-value by 5.678 to get one. Real walls have studs and gaps that let more heat through than this layered estimate.

Convection, radiation and cooling

Convection: q = h A (T_s − T_∞). The coefficient h is measured, and ranges over five orders of magnitude from still air to boiling water.
Radiation: q = εσA(T_s⁴ − T_sur⁴), with temperatures in kelvin, for a surface much smaller than its surroundings. σ = 5.670374419 × 10⁻⁸ W/(m²·K⁴).
Newton's law of cooling: when a well-mixed object loses heat at a rate proportional to its temperature difference, T(t) = T_air + (T₀ − T_air) e^−kt. Taking ln(T − T_air) turns the curve into a straight line of slope −k, which is how the tool fits it.
An open cup also loses heat by evaporation, faster when hot, so its points bend away from a single exponential. A lid is the easiest variable to test.

The worked wall, checked with python3 when the page is built: 13 mm drywall, an 89 mm fiberglass batt, 12 mm plywood and 90 mm brick, with both air films, give R = 2.75 m²·K/W (about R-16 in US units) and U = 0.363 W/(m²·K). A 3.0 by 2.5 m wall with 20 °C inside and −5 °C outside loses 68 W, 1.63 kWh a day. The same 1.5 m² as a double-pane window would lose 101 W against 14 W through wall. A person's skin at 34 °C in a 20 °C room radiates about 150 W net over 1.8 m². The mug readings are made up to behave the way real ones do; the no-lid mug's cooling constant is 0.0329 per minute and the lidded mug's 0.0207.

Sources

Bergman, T. L., Lavine, A. S., Incropera, F. P., and DeWitt, D. P. (2011). Fundamentals of Heat and Mass Transfer (7th ed.). Wiley. Rate equations for conduction, convection and radiation; the typical ranges of h (Table 1.1); thermal conductivities at 300 K (Appendix A).
ISO 6946:2017, Building components and building elements: Thermal resistance and thermal transmittance, Calculation methods. Surface resistances of 0.13 (inside) and 0.04 (outside) m²·K/W for horizontal heat flow.
ASHRAE (2021). ASHRAE Handbook: Fundamentals, chapter 15 (fenestration: center-of-glass U-factors) and chapter 26 (thermal properties of building materials).
U.S. Department of Energy, Energy Saver, "Types of Insulation": typical R-values per inch for fiberglass batts and foam boards, converted here to conductivity.
CODATA 2018 recommended values (NIST): the Stefan-Boltzmann constant, which the build recomputes from the exact SI defining constants. Unit conversions use the International Table Btu (1055.05585262 J) and the international foot (0.3048 m).

An estimator for learning and rough planning, not a building energy model or an engineering design tool. Material values are typical; a real wall, window or cup will differ. Use hot water, not boiling water, and an adult's help for younger students. Support: team@caveatacademic.com.

Where the heat goes,in watts.