This simulator places two material layers between two ideal temperature-controlled plates. Change each layer's material, thickness and cross-sectional area, add an areal contact resistance at the interface, and watch heat rate, interface temperatures and stored energy respond as the system warms toward steady state.
• A real-time 3D cutaway workbench (left and right temperature-controlled plates, a ten-cell first material layer, a resistive contact plane, a ten-cell second material layer, thermocouple probes and animated heat-flow indicators) with home view, focus-selected-part, auto-rotate, expand and hide-labels scene tools. • Experiment controls: layer 1 material (stainless steel, aluminum or copper), layer 2 material (foam, wood, brick or copper), left and right plate temperature, layer 1 and layer 2 thickness, cross-sectional area and areal contact resistance sliders, plus pause/resume, single-step and 60 s-step buttons, six playback speeds, and an 'Initialize steady state' action alongside restart/start/stop. • A Curves & measurements analysis tab with two live charts (boundary heat rates entering and leaving; energy accounting), the underlying Fourier's-law and thermal-resistance equations, and snapshot readouts (heat rate in/out, analytical steady heat rate, total thermal resistance, both interface temperatures, contact temperature jump, and stored/input/output energy). • An Experiments tab with four guided fixtures (a steady layered wall initialized directly at equilibrium, a copper-copper joint dominated by contact resistance, transient storage restarted from a uniform temperature, and a reversed gradient with the right plate hotter) and a Model verification bench with a timestamped event log and copyable trial report. • A Learn & assess tab with four guided lessons, a knowledge-check quiz with reset, and a written model-scope statement linking to a conduction reference.
Heat flows down a temperature gradient. For a uniform layer at steady state, heat rate follows Q̇ = kAΔT/L: increasing cross-sectional area increases heat transfer, while increasing thickness reduces it. When two layers and a resistive contact interface sit in series, their resistances add — Rtotal = (L1/k1 + Rc″ + L2/k2)/A — and the material with the largest L/k ratio typically dominates the total. The simulator's steady-state experiments (metal/foam wall, copper-copper joint) demonstrate this directly: swap in a highly resistive foam layer or an added contact resistance and see it absorb nearly the entire temperature difference.
During warm-up, the heat rate entering the left face need not equal the rate leaving the right face — their difference is the rate at which thermal energy accumulates in the layers, ΔU = Ein − Eout. Only once the system reaches steady state do the two boundary heat rates converge.
A finite areal contact resistance at the interface between the two layers supports a temperature discontinuity — heat cannot cross without a temperature difference, even though the contact plane itself stores no energy in this model. Each layer is discretized into ten finite-volume cells advanced with backward-Euler time steps of five seconds or less, and material properties (thermal conductivity and volumetric heat capacity) are representative constants rather than grade-specific data.
This is a one-dimensional model with insulated sides, two ideal fixed-temperature reservoirs, and no radiation, side convection, phase change, or finite heater power. A normal reset begins at the right-plate temperature; the 'Initialize steady state' action instead creates an analytical profile with a fresh energy reference and makes no claim about elapsed warm-up time. Runs pause automatically at one simulated hour, and any parameter edit resets the trial.
Only at steady state. During warm-up or cool-down, the difference between the heat rate entering the left face and leaving the right face is exactly the rate at which thermal energy is being stored in the layers — shown directly in the simulator's transient-storage experiment.
Series thermal resistances add, and resistance for a uniform layer is L/(kA). Foam's thermal conductivity (about 0.035 W/m·K) is roughly two orders of magnitude lower than steel's (about 15 W/m·K), so even a modest foam thickness contributes far more resistance than the metal layer, which is why nearly the full temperature difference appears across it.
A finite areal contact resistance. Real interfaces are never perfectly bonded — microscopic gaps and imperfect contact create a resistance that requires a temperature difference to pass a given heat rate. A perfectly bonded, zero-resistance interface would show no jump at all.
No. Thermal conductivities and volumetric heat capacities are representative constants for generic material classes (steel, aluminum, copper, foam, wood, brick), used for teaching the governing equations rather than reproducing a specific grade or supplier's certified data.