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Callaway's simplified heat flow model is often used to confirm experimentalrealizations of unconventional, hydrodynamic and Poiseuille phonon transport inultrahigh thermal conductivity ($\kappa$) materials, due to its simplicity andlow computational cost. Here, we show that the Callaway model worksexceptionally well for most ultrahigh-$\kappa$ materials like diamond and boronnitride, but fails dramatically for boron arsenide (BAs) and boron antimonide(BSb). This failure is driven by the inability of the Callaway model toeffectively describe the severely restricted phonon scattering in BAs and BSb,where many scattering selection rules are activated simultaneously. Our workhighlights the powerful predictive capability of the Callaway model, and givesinsights into the nature of phonon scattering in ultrahigh-$\kappa$ materialsand the suitability of the Callaway's description of heat flow through them.

Dramatic Failure of the Callaway Description of Heat Flow in Boron Arsenide and Boron Antimonide Driven by Phonon Scattering Selection Rules