Explain conjugate heat transfer analysis and when it becomes necessary in thermal design.

Conjugate heat transfer (CHT) simultaneously solves heat conduction in solids and convection in adjacent fluids with coupled boundary conditions at interfaces. It becomes necessary when: temperature distribution in solid significantly affects fluid behavior (thermal developing flows), solid thermal resistance is comparable to convective resistance (Bi≈1), detailed local heat flux distribution is needed (electronic cooling), or when simplified boundary conditions are inadequate (turbine blade cooling). CHT requires matching temperature and heat flux at interfaces: T_solid = T_fluid and k_s(∂T/∂n)_s = k_f(∂T/∂n)_f. Computational cost is higher than decoupled analysis but essential for accurate hot-spot prediction in gas turbines, electronic packages, and compact heat exchangers.