U-Values & Thermal Resistance

Start with a single material layer. Its resistance to conductive heat flow - its R-value - is simply its thickness divided by its thermal conductivity: R = thickness / k, in m2K/W. A thick layer of a poor conductor has a high R (good); a thin layer of a good conductor has a low R (poor). Take 50mm of mineral-wool insulation with k around 0.036: R = 0.05 / 0.036 = 1.39 m2K/W. Take 230mm of dense brick with k around 0.81: R = 0.23 / 0.81 = 0.28 m2K/W. The 50mm of insulation out-resists the 230mm of brick roughly five to one - the entire argument for insulation in one comparison.

R-value is the quantity insulation products are sold on (a 'higher R' board resists more heat for the same thickness), and it is additive for layers stacked in series, which is what makes the whole calculation tractable. One caution on units: the SI R-value used here (m2K/W) is not the same number as the imperial 'R-value' printed on North American products; always check which system you are in before comparing figures.

Notice what the formula tells you to reach for when you want a better wall. You can raise R three ways: make a layer thicker, choose a lower-conductivity material, or add a new resisting layer. Thickening brick barely helps because its k is high; adding even a thin layer of low-k insulation helps enormously. This is the quiet lesson every energy modeller internalises early - resistance is bought cheaply with conductivity, expensively with bulk - and it is why the insulation line, not the structural one, is where the performance of a modern wall is decided.

Heat crossing a wall passes through every layer in turn, like current through resistors in series - so the resistances simply add. To the material layers you must add two more: the thin, still films of air clinging to each face, called the surface resistances Rsi (inside) and Rso (outside). These are the convection-and-surface-radiation effects from lesson 3.1, tabulated as standard values - typically Rsi around 0.13 and Rso around 0.04 m2K/W for a wall (the outside film is smaller because wind scrubs it thinner). Any unventilated air cavity adds its own resistance too.

Sum them all to get R total. Then the U-value is simply its reciprocal: U = 1 / R total. That inversion trips beginners: resistances add, but you invert the total to get the transmittance. High resistance means low U means a good wall. Once you have U, the heat loss through that element is just U x area x temperature-difference watts - the term a model evaluates for every surface, every hour. Everything downstream, from an EnergyPlus run to an ECBC compliance check, is built on this one chain.

Take a real insulated cavity wall, outside to inside: outer surface film (Rso 0.04), 20mm external plaster (0.02), 230mm brick (0.29), 50mm insulation (1.39), 100mm concrete block (0.20), 20mm internal plaster (0.02), inner surface film (Rsi 0.13). Add them: 0.04 + 0.02 + 0.29 + 1.39 + 0.20 + 0.02 + 0.13 = 2.09 m2K/W. Invert: U = 1 / 2.09 = 0.48 W/m2K.

Read what the numbers tell you. The 50mm of insulation alone contributes 1.39 of the 2.09 - two-thirds of the wall's entire resistance from one-twentieth of its thickness. Strip the insulation out and R falls to 0.70, so U jumps to about 1.4 W/m2K - the same wall performs roughly three times worse. This is why, in a simulation, the insulation layer is the variable worth studying first: a five-minute change to that one line moves the result far more than fussing over plaster thicknesses. It is also why 'thermal' and 'structural' thickness are different things - the wall got most of its performance from a thin, light layer, not from mass.

Two habits make this calculation trustworthy in practice. First, always sanity-check the magnitude: an insulated wall should land somewhere around 0.3-0.5 W/m2K, a solid uninsulated masonry wall nearer 1.5-2.5, and a single-glazed window up near 5-6. If your arithmetic produces a wall U of 0.05 or 8, you have slipped a unit or forgotten to invert. Second, remember that this clean sum is the 'middle of wall' figure; the real element is a little worse once repeating bridges (mortar joints, wall ties, timber studs) and junctions are counted - which is the subject of the next section, and the reason a software U-value rarely matches the hand figure exactly.

The layer-by-layer sum assumes heat flows straight through in neat parallel layers. Real buildings break that assumption at thermal bridges - places where a more-conductive element bypasses the insulation: a concrete floor slab poking through to a balcony, a steel or concrete column, a window reveal, a wall-roof junction, mortar joints around lightweight blocks. Heat takes the easy path, so the real wall loses more than the ideal U-value predicts, and the inside surface at the bridge runs colder - a prime site for condensation and mould (the subject of lesson 3.4).

Simulation and codes handle this two ways. A repeating bridge (mortar, wall ties, studs) is folded into a corrected U-value. A linear bridge along a junction gets a separate psi-value (W/mK, heat lost per metre of junction), and a whole-building model can add these up. The practical lesson: an envelope's real performance is set as much by its junctions as by its middle-of-wall build-up, and a slab that punches through the insulation can quietly undo much of it. Detailed 2-D heat-flow tools (for example THERM) exist precisely to quantify bridges the simple sum cannot.

U-values are not just design feedback; they are how energy codes regulate the envelope. India has two BEE codes. For commercial buildings, the Energy Conservation Building Code (ECBC) sets maximum U-values for roofs, walls and glazing (and limits on window-to-wall ratio and solar heat gain), tightening by climate zone. For homes, the Eco Niwas Samhita (ENS) - the residential code - sets a limit on the overall envelope through a single 'thermal transmittance of the envelope' figure (RETV, roughly a whole-envelope U weighted across walls and windows) plus a separate roof U-value cap. In both, a lower U is what you demonstrate to comply.

So the same arithmetic you just did is what a compliance model reports. A word of honesty the whole course insists on: statutory compliance and certification are the job of the relevant authority and an accredited professional - your simulation is decision-support that helps you design to the limit, not the certificate itself. But knowing that a roof in a hot Indian zone must beat a set U-value tells you, before any software, roughly how much insulation the design will need - and lets you spend the simulation on the choices that are genuinely open.

It also pays to notice which element the code leans on hardest. In India's cooling-dominated zones the roof is the priority - it takes the most sun and the codes set its U-value tightest - so an under-insulated roof is usually the first thing a compliance model flags. Walls come next, and glazing is regulated on two fronts at once: its U-value and its solar heat gain, because a window leaks heat by conduction and admits it by radiation. That pairing is a reminder that a low U-value is necessary but not sufficient in a hot climate: you can pass on conduction and still overheat on solar gain, which is why Modules 6 and 9 return to glazing with shading and solar control in hand.