This study presents a mathematical model for the coupled growth of two interacting wax particles in a non-isothermal laminar flow. The formulation is based on a diffusion-controlled framework, in which the particle evolution is governed by a Stefan-type moving boundary condition with temperature-dependent interfacial concentration. An asymptotic analysis is developed in the limit where the particles’ size is small compared to their separation distance. This leads to a reduced system of nonlinear ordinary differential equations that captures the combined effects of particle interaction and thermal asymmetry. The analysis reveals that both mechanisms enter at leading order and jointly determine the growth dynamics. Numerical simulations are performed to investigate symmetric and asymmetric configurations. The results demonstrate that temperature differences induce a symmetry-breaking mechanism, leading to distinct growth rates even for initially identical particles. Furthermore, the interaction between particles amplifies this asymmetry through a competitive growth process. A key finding is the monotonic increase in the asymmetry ratio, reflecting progressive divergence driven by thermal effects. The proposed model extends the classical method of reflections for interacting Stefan problems to account for thermally induced asymmetry, incorporating non-identical boundary conditions governed by a prescribed temperature field.
Awatif Alhowaity (2026) studied this question.