This simulator cools or heats a lumped aluminum sphere inside an airflow chamber. Adjust the convective heat-transfer coefficient, surface area and internal heater power, then compare the sphere's temperature history, instantaneous heat flow and thermal time constant against Newton's law of cooling.
• A real-time 3D workbench (a temperature-colored aluminum sphere, an airflow chamber with adjustable flow, an internal heater cartridge and thermocouple probes) with home view, focus-selected-part, auto-rotate, expand and hide-labels scene tools. • Experiment controls: convective heat-transfer coefficient, sphere surface area, ambient air temperature, internal heater power and initial sphere temperature sliders, plus pause/resume, single-step and 60 s-step buttons, six playback speeds, and restart/start/stop actions. • A Curves & measurements analysis tab with two live charts (heat transfer to air; energy accounting), the underlying Newton's-law-of-cooling and thermal-time-constant equations, and snapshot readouts (instantaneous heat rate, sphere temperature, thermal time constant, and stored/input/output energy). • An Experiments tab with four guided fixtures (measuring the cooling time constant, strengthening convection, reaching heater equilibrium, and warm air heating a cool sphere) 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 convection reference.
The sphere's temperature approaches ambient exponentially, following Newton's law of cooling: the instantaneous heat rate is proportional to the convective coefficient, the surface area and the temperature difference from ambient air. Because temperature is assumed uniform throughout the sphere (a 'lumped' model), the entire object cools or heats along a single exponential curve rather than developing internal gradients.
Surface area and heat capacity compete directly: a larger sphere has more area to exchange heat but also more thermal mass to change temperature, so the thermal time constant reflects the ratio of heat capacity to hA. The cooling-time-constant experiment isolates this behavior directly, while the stronger-convection experiment shows how increasing the coefficient h shortens the time constant.
The lumped-capacitance approximation is only valid when the Biot number — the ratio of internal conduction resistance to external convection resistance — is small, meaning the sphere's internal conductivity is high enough that internal temperature gradients are negligible compared to the surface-to-air temperature difference. This simulator assumes that condition holds throughout.
The model uses a lumped uniform-temperature aluminum sphere, constant properties and convection coefficient, and a fixed ambient air temperature with an ideal internal heater. Radiation, support conduction, sensor lag and empirical flow correlations are omitted. Setting h = 0 is an idealized adiabatic comparison, not a realistic still-air coefficient. Temperature evolution is computed analytically. A 200 °C boundary pauses the trial before further extrapolation — this is a model limit, not a thermostat or a material failure prediction. Runs pause at one simulated hour, and parameter edits reset the experiment.
It states that the rate of heat loss from an object is proportional to the temperature difference between the object and its surroundings, given a constant heat-transfer coefficient and surface area. This produces an exponential approach to ambient temperature rather than a linear one.
Heat rate is proportional to h × A × ΔT. Raising h directly increases the heat rate at any given temperature difference, which shortens the thermal time constant — demonstrated in the simulator's stronger-convection experiment.
No. It uses a lumped-capacitance model that assumes uniform temperature throughout the sphere, which is valid only when the Biot number is small (high internal conductivity relative to external convection). Objects with poor internal conductivity or very high convection coefficients would develop gradients this model does not capture.
The sphere approaches a heater-equilibrium temperature where convective heat loss to the air matches the heater's input power — explored directly in the heater-equilibrium experiment. The simulator pauses the trial at a 200 °C boundary rather than extrapolating further, which is a model limit rather than a thermostat.