Transient Conduction
Quenching, cooling, baking: the calculator checks Bi = h·Lc/k, uses lumped capacitance when Bi < 0.1, and the one-term approximation (λ₁, A₁) beyond that. Solve T(t) — or invert for the time to reach a target.
Body
Fluids
Solve
Frequently asked
- When can I use lumped capacitance?
- When Bi = h·Lc/k < 0.1 the body's internal resistance is negligible and its temperature is uniform: T(t) = T∞ + (Tᵢ − T∞)·e^(−bt) with b = h/(ρ·cₚ·Lc). The calculator checks Bi and switches between lumped and one-term automatically.
- What is the one-term approximation?
- For Bi ≥ 0.1 the first term of the exact series is accurate for Fourier τ > 0.2: θ₀ = A₁·e^(−λ₁²τ), with λ₁ and A₁ from the transcendental eigenvalue equation for your geometry (wall, cylinder, sphere). Center and surface temperatures both come from it.
- Can it solve for time?
- Yes — leave t blank and give a target center temperature; the solver inverts the lumped exponent or the one-term ratio for t.