<p>This paper investigates heat and mass diffusion in a spherical domain with a moving boundary arising from convective drying with shrinkage. The governing equations are formulated in spherical coordinates subject to Robin boundary conditions, where the domain evolution is governed by a moisture-dependent radius, leading to a time-dependent spatial diffusion operator. The problem is reformulated within a parameter-dependent Sturm–Liouville framework, resulting in instantaneous eigenvalue problems whose spectra evolve with the geometry. Analytical representations of the temperature and moisture fields are derived via eigenfunction expansions associated with the evolving operator under a quasi-static instantaneous eigenfunction approximation, yielding a non-autonomous spectral system. A spectral convergence and truncation error analysis is presented in a weighted Hilbert space, demonstrating completeness of the eigenfunctions, exponential decay of higher modes, and convergence of the series solutions within the adopted approximation framework. Explicit truncation error estimates are obtained, providing quantitative bounds for finite-mode approximations and indicating that geometric contraction accelerates spectral decay. The influence of boundary evolution on the eigenvalue spectrum is further characterized through time-dependent spectral shifts and enhanced modal damping. Numerical simulations validated against experimental data demonstrate excellent agreement and show that incorporating shrinkage significantly improves predictive accuracy, particularly in diffusion-dominated regimes. The results indicate that geometric contraction enhances modal damping and accelerates spectral convergence compared with the fixed-domain case.</p>