Explain how to use Heisler charts for transient conduction analysis and their limitations.

Heisler charts provide solutions for 1D transient conduction in plane walls, cylinders, and spheres with convective boundary conditions. They plot dimensionless temperature θ = (T-T∞)/(Ti-T∞) versus Fourier number Fo = αt/L² for various Biot numbers. Usage: calculate Bi = hL/k and Fo, read centerline θ₀ from first chart, use second chart for temperature at other positions θ/θ₀ vs x/L. For multidimensional bodies (short cylinder, rectangular block): apply product solution θ_total = θ_plane × θ_cylinder. Limitations: constant thermal properties assumption (problematic for large ΔT), uniform initial temperature required, constant boundary conditions, applicable only after initial transient (Fo>0.2), chart reading errors (±5%), and single-term series approximation. For complex geometries, variable properties, or time-varying boundaries, numerical methods (FDM, FEM) with smaller time steps provide better accuracy.