All Labs

Heat Transfer Lab

Simulate how heat flows through materials via conduction, convection, and radiation. Adjust temperatures, materials, and thermal properties to observe temperature heatmaps and discover Fourier's law, Newton's cooling, and the Stefan-Boltzmann equation.

Guided Experiment: Comparing Conductors and Insulators

If you replace a copper rod with a glass rod (much lower thermal conductivity), what do you predict will happen to the heat flux?

Write your hypothesis in the Lab Report panel, then click Next.

Controls

Left Temperature (hot side)600.0 K
Right Temperature (cold side)300.0 K
Rod Length1.0 m
Thermal Conductivity385.0 W/m·K

Results

q=kΔTL=385.0000×3001.0=115500.0 W/m2q = k \frac{\Delta T}{L} = 385.0000 \times \frac{300}{1.0} = 115500.0 \text{ W/m}^2
Heat Flux
115500.0 W/m²
Temperature Gradient
300.0 K/m
Left Temperature
600 K
Right Temperature
300 K

Temperature Profile (Linear)

Data Table

(0 rows)
#TrialModePosition(m)Temperature(K)Heat Flux(W/m²)
0 / 500
0 / 500
0 / 500

Reference Guide

Conduction (Fourier's Law)

Heat conduction is the transfer of energy through a material due to a temperature gradient, without bulk motion of matter.

q=−kdTdxq = -k \frac{dT}{dx}

Where q is the heat flux (W/m²), k is the thermal conductivity (W/m·K), and dT/dx is the temperature gradient. A negative sign means heat flows from hot to cold.

For a uniform rod in steady state, the temperature profile is linear: the midpoint temperature is the average of the two ends.

Convection (Newton's Cooling)

Convection transfers heat through the bulk movement of fluid (liquid or gas). Newton's cooling law describes how a hot surface loses heat to a cooler fluid environment.

dTdt=−h(T−Tenv)\frac{dT}{dt} = -h(T - T_{\text{env}})

Where h is the heat transfer coefficient (W/m²·K) and T_env is the ambient fluid temperature. Higher h means faster cooling — typical values range from 2-5 for natural convection to 100-600 for forced convection in water.

Radiation (Stefan-Boltzmann)

Thermal radiation is energy emitted by any object above absolute zero, in the form of electromagnetic waves. No medium is required — radiation travels through vacuum.

P=εσAT4P = \varepsilon \sigma A T^4

Where P is radiated power (W), ε is emissivity (0–1), σ = 5.67 × 10⁻⁸ W/(m²·K⁴) is the Stefan-Boltzmann constant, A is surface area, and T is absolute temperature. Power scales with T⁴, so doubling temperature increases emission by 16×.

Thermal Conductivity

Thermal conductivity (k) measures how readily a material conducts heat. Metals are excellent conductors because free electrons carry thermal energy efficiently.

Material k (W/m·K)
Copper385
Aluminum205
Steel50
Glass1.0
Wood0.15

Copper conducts heat about 2500× better than wood, which is why metal cookware heats up quickly and wooden handles stay cool.