Heat always flows from hot to cold
Heat is energy on the move because of a temperature difference. It never flows from cold to hot by itself. In winter a house loses heat to the outside, so we need a heater to replace it. In summer the heat comes in, so we need shade or a cooler. "Cold coming in" is really heat going out.
A building loses heat in three ways. Conduction passes heat through walls, roof, floor and glass. Convection carries heat when warm air leaks out through gaps and cracks and cold air comes in. Radiation carries heat as infrared waves, for example through windows, or from the sun onto the roof.
Conduction through a wall: q = ΔT ÷ R
The heat flowing through each square metre of wall is q = ΔT ÷ R, in watts per m². ΔT is the temperature difference between inside and outside. R is the thermal resistance of the wall. For one layer, R = L ÷ k, where L is the thickness in metres and k is the thermal conductivity (W/m·K), a number that tells how easily the material passes heat.
Typical k values: brick 0.8, glass 1.0, wood 0.15, still air 0.026, foam insulation 0.03. When layers are joined, their R values add: Rtotal = R₁ + R₂ + … The whole wall's heat loss is Q = q × area. Doubling the thickness doubles R and halves the loss. A layer with small k gives a large R even when thin.
Insulation, windows, roofs and draughts
Insulation such as foam, mineral wool, cork or even a closed air gap has a small k because it holds air still. Air itself is a poor conductor if it cannot move. Fit insulation in the walls and the roof, where most heat leaves.
Windows lose heat fast. Double glazing has two panes with trapped air or gas between them, which lowers conduction and convection. Draughts are convection through gaps, so seal doors and windows. Roofs in hot places can be painted white or reflective so that less sun radiation is absorbed (a "cool roof"). Thick walls with high heat capacity (mud, stone) store heat by day and release it at night, which smooths the temperature swings.
In a hot country the same maths applies the other way: insulation keeps the heat out, and an air conditioner has less work to do.
Try it: test your own room
Feel an outside wall and an inside wall on a cold or a hot day. Which one feels cooler or warmer? Put a thermometer or a hand near a window and then near a wall. Then in the 3D lab, first predict what happens when you add 5 cm of foam, then add it. Try to bring the loss under 10 W using only 10 cm of brick.
Key formulas and definitions
- q = ΔT ÷ R (heat flow per m², in W/m²)
- R = L ÷ k for one layer (L in m, k in W/m·K)
- R_total = R₁ + R₂ + … (layers in a row)
- U = 1 ÷ R_total (the "U-value", W/m²·K)
- Q = q × A (heat flow through area A, in watts)
- Energy = power × time (1 kWh = 1 kW for 1 hour)
Worked examples
1. A 20 cm brick wall (k = 0.8 W/m·K) has 22 °C inside and 2 °C outside. Find R and q.
R = L ÷ k = 0.20 ÷ 0.8 = 0.25 m²·K/W. ΔT = 20 °C. q = 20 ÷ 0.25 = 80 W/m².
2. The wall in the last question has an area of 10 m². How much heat flows out each second?
Q = q × A = 80 × 10 = 800 W, so 800 J every second.
3. Find R for a 5 cm layer of foam (k = 0.03 W/m·K).
R = 0.05 ÷ 0.03 = 1.67 m²·K/W. This is about 7 times the R of 20 cm of brick.
4. Add the 5 cm foam to the 20 cm brick wall. Find the new R and q for ΔT = 20 °C.
R_total = 0.25 + 1.67 = 1.92 m²·K/W. q = 20 ÷ 1.92 ≈ 10.4 W/m², much less than 80.
5. For the 10 m² insulated wall, how much energy is lost in 24 hours?
Q = 10.4 × 10 = 104 W. Energy = 104 W × 24 h = 2496 Wh ≈ 2.5 kWh.
6. Compare the daily cost of heat loss for the bare brick wall (800 W) and the insulated wall (104 W), at ₹8 per kWh.
Bare: 0.8 kW × 24 h = 19.2 kWh, cost ₹154. Insulated: 2.5 kWh, cost ₹20. Saving about ₹134 a day.
Common mistakes
- Saying "cold flows in". What really happens is that heat flows out. Cold is just a lack of heat.
- Adding k values or thicknesses instead of R values. For layers in a row, add R = L ÷ k, not k.
- Forgetting to change cm to metres in R = L ÷ k. 20 cm is 0.20 m.
- Thinking thicker always beats better material. 5 cm of foam can beat 40 cm of brick because its k is about 27 times smaller.