Lumped capacitance and Heisler charts model temperature change over time.
When conduction inside is fast relative to convection (Biot number Bi=hL_c/k<0.1), temperature is uniform: T(t)-T_∞=(T_i-T_∞)e^{-t/τ}, τ=ρVc/(hA). For Bi>0.1 solve the heat equation (Heisler charts, semi-infinite solid erf solutions).
A thermocouple bead cools to 63% of the way within one time constant.
Transient conduction predicts how fast a body heats or cools, which controls process times, safety waiting periods and thermal stresses.
Lumped capacitance and Heisler charts model temperature change over time.
Transient conduction predicts how fast a body heats or cools, which controls process times, safety waiting periods and thermal stresses.
An approximation that treats a body as uniform in temperature, which is valid when the Biot number is small, typically below 0.1.
The ratio of convective resistance at the surface to conductive resistance inside the body, which decides whether the lumped approach is accurate.
Typical applications include estimating the time for a steel billet to cool to handling temperature, predicting how fast a sensor responds to a temperature step and checking whether a thin part cools quickly enough for a production cycle.
Study "Fins" first (topic 91 of 105 in Thermodynamics & Fluids). It covers the groundwork this topic builds on.
Lumped capacitance. Fourier number Fo=αt/L². Thermal time constant.
A thermocouple bead cools to 63% of the way within one time constant.
The next topic is "Heat exchangers", which builds directly on this one.
It is classed as Advanced in Thermodynamics & Fluids (topic 92 of 105). It is an advanced topic. It assumes you are comfortable with the intermediate topics in Thermodynamics & Fluids.
Want to practise? Open the interactive course for quick checks, quizzes, simulations and progress tracking.