🌡️ Temperature Distribution

Visualise how temperature distributes along rods, fins, and slabs under various boundary conditions. Compare numerical (FDM) solutions with exact analytical answers, and observe transient temperature evolution over time.

Mode

Boundary & Properties

T_left 100 °C T_right 0 °C Source Q 0 W/m³ Diffusivity α 0.1

Statistics

T mean—

T max—

T min—

Fourier # Fo—

Numerical

Analytical

Heat Transfer Theory

Steady-state (no heat source): T(x) = T_L + (T_R−T_L)·x/L — linear profile. With uniform volumetric heat source Q: T(x) = T_L + (T_R−T_L)·x/L + Q/(2k)·x(L−x) — parabolic. Transient: ∂T/∂t = α·∂²T/∂x² solved by explicit FDM. The Fourier number Fo = α·t/L² measures dimensionless time; at Fo ≈ 0.2 the solution approaches steady-state. Extended surface (fin): d²θ/dx² − m²θ = 0, m² = hP/(kA), θ = T−T_∞, giving an exponential solution θ(x) = θ_b·cosh[m(L−x)]/cosh(mL).