Periodic Boundary Condition Implementation and Computational Validation for Fully Developed Conjugate Heat Transfer in Packed Bed Microchannels

Modeling fully developed transport in particle-filled channels often requires extended computational domains to eliminate entrance effects. This study presents a pressure-gradient-based periodic approach that reproduces stabilized hydrodynamic and thermal behavior using a single representative unit. A constant pressure difference is imposed across periodic boundaries to sustain incompressible laminar flow while maintaining Reynolds number control. Thermal periodicity is enforced through an axial gradient decomposition, allowing cross-sectional temperature fields to repeat spatially. Finite element simulations were performed under steady conjugate heat transfer conditions. Results from a 25 mm extended channel were compared with those from a reduced periodic domain. Once flow stabilization occurred in the long channel, velocity and temperature distributions matched the periodic solution within numerical tolerance. The reduced model decreased degrees of freedom and computational time by approximately 80% while preserving physical consistency. The formulation provides an efficient framework for repeated parametric studies of packed-bed microsystems.