HEAT CONDUCTION

"Heat flows from hot to cold objects at a rate proportional to the temperature difference."

- Fourier's Law of Heat Conduction

Model Assumptions

Only Conduction: Models direct heat conduction between two bodies in perfect thermal contact and does not account for enviromental loss.

Variable Contact Area: Set to the smaller of the two bodies' face areas assuming cubic shapes, in m².

Contact Thickness: Heat transfer occurs across 1cm thickness (L = 0.01 m) in Fourier's equation.

Uniform Temperature: Each body has the same temperature throughout.

Temperature Units: Input temperatures in °C, but ΔT in equation uses Kelvin (K) for dimensional consistency with k values.

Body A

Initial Temperature
80 °C
Volume
5 cm³
Material

Body B

Initial Temperature
20 °C
Volume
5 cm³
Material
TIME: 0.0 s

Current State

Temp A 80.0 °C
Temp B 20.0 °C
Difference 60.0 °C

Heat Transfer

Heat Flow Rate 415.0 W
Effective k 237.0 W/m·K
A B
Time (s) Temp (°C) Body A Body B
Time (s) Heat Flow Rate (W) Heat Flow Rate
Fourier's Law of Heat Conduction
q = keff · A · ΔTL
q
Heat Flow Rate
415.0 W
keff
Effective Conductivity
237 W/m·K
A
Contact Area
0.0003 m²
ΔT
Temp Difference
60.0 K
L
Thickness
0.01 m
Effective Thermal Conductivity
keff = 2 kA kBkA + kB
kA
Conductivity A
237 W/m·K
kB
Conductivity B
237 W/m·K
Thermal Capacity
C = ρ cp V
CA
Capacity Body A
12.1 J/K
CB
Capacity Body B
12.1 J/K
ρA cp,A
Vol Heat Cap A
2420000 J/m³·K
ρB cp,B
Vol Heat Cap B
2420000 J/m³·K
VA, VB
Volumes
5 cm³ each (different V/materials yield different C)
Lumped Capacitance Model (Time Evolution)
dTdt = ± qC
dTAdt
Rate Change A
-34.3 °C/s
dTBdt
Rate Change B
+34.3 °C/s
q
Heat Flow Rate
415.0 W (from Fourier's)
CA, CB
Thermal Capacities
12.1 J/K each (sign: - for hot, + for cold)