This study investigates the coupled effects of hydrostatic pressure and crystal size on the lattice thermal conductivity (LTC) of diamond using a unified thermodynamic–transport framework that combines the Clapeyron relation with a modified Debye–Callaway model. We use the pressure-dependent melting temperature as a thermodynamic scaling parameter to determine how the Debye temperature

phonon group velocities

Grüneisen parameter

and phonon-scattering mechanisms evolve under compression. The calculated melting curve reproduces diamond’s characteristic non-monotonic melting behaviour

providing a consistent thermodynamic basis for pressure-dependent phonon transport. Hydrostatic compression enhances lattice stiffness

increases the Debye temperature and phonon group velocities

and reduces lattice anharmonicity

thereby suppressing Umklapp phonon scattering and improving intrinsic phonon transport. In contrast

boundary scattering is governed primarily by crystal size and becomes the dominant thermal resistance mechanism in nanoscale diamond. Consequently

lattice thermal conductivity increases continuously with pressure for all investigated crystal sizes

with the largest enhancement in bulk diamond and progressively smaller improvements as crystal size decreases because of stronger phonon confinement. The predicted pressure dependence differs from that reported for many conventional semiconductors

highlighting diamond’s distinctive phonon-transport behaviour under hydrostatic compression. The proposed thermodynamic–transport framework provides a computationally efficient and physically transparent approach for investigating coupled pressure and size effects over broad thermodynamic conditions and complements more computationally intensive first-principles methods.