Treat Rods in Series and in Parallel Like Resistors
Steady heat conduction behaves exactly like current in a resistor network. The heat current plays the part of current, the temperature difference plays the part of voltage, and the thermal resistance of a slab combines in series and in parallel just as electrical resistance does.
Electricity questions depend on identifying charge, a conducting path and the condition that controls current or magnetic effect.
Rate of conduction and thermal resistance
Thermal conductivity K sets how well a material conducts. Two rods of different material with equal thermal resistance conduct equally for the same ΔT, so when the conductivity ratio is 4 : 9 the geometry (length over area) must have the opposite ratio. For the same temperature difference the rod with the largest K A / L conducts the most heat.
Series, parallel and junction temperatures
Rods in series carry the same heat current and their resistances add, R = R1 + R2, with the temperature drop across each rod proportional to its resistance. Rods in parallel share the same temperature difference and their conductances add.
for two rods of equal area side by side it is (K1 + K2)/2. At a junction where several rods meet, the heat current flowing in equals the heat current flowing out, which gives the junction temperature: for rods of conductivities 3K, 2K and K with ends at 100 °C, 50 °C and 0 °C, set the sum of K A ΔT / L into the junction to zero and solve for T. For a composite slab in steady state, find the layer resistances first, then the temperatures at the interfaces.
Convection and why metal feels cold
In natural convection a heated portion of fluid moves because it expands, its density becomes less than that of the surrounding fluid, and buoyancy lifts it. This is why it is hotter directly above a fire than beside it: convection carries most of the heat upward. A metal surface feels colder than wood on a cold morning because metal has high thermal conductivity, so it carries heat away from your hand faster; the two surfaces are at the same temperature.
OlympIQ exam lens
- ✓H = K A ΔT / L and thermal resistance R = L / (K A)
- ✓Series: same heat current, resistances add; parallel: same ΔT, conductances add
- ✓At a junction, total heat current in equals total heat current out
- ✓Natural convection happens because heated fluid is less dense and is pushed up by buoyancy
- ✓Metal feels colder than wood at the same temperature because of higher thermal conductivity
Do not assume the temperature falls equally across each layer of a composite slab. The temperature drop across a layer is proportional to its thermal resistance, so a low-conductivity layer takes most of the temperature difference.
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