Evaluation of Thermal Transfer Efficiency and Nonlinear Shear Effects on Flow Modulation in a Flexible Microfluidic Heat Transfer System

This study examines the thermal transfer performance of a microfluidic heat transfer system, with a focus on the interplay between flow orientation, flexibility, and nonlinear shear dilution/enhancement effects. A mathematical model was developed to describe the heat transfer dynamics within a flexible microchannel subjected to Robin boundary conditions, accounting for complex flow behaviors. The governing partial differential equations (PDEs) were transformed into a system of coupled ordinary differential equations (ODEs) using appropriate similarity quantities, the fourth-order Runge-Kutta-Fehlberg method, and shooting techniques to facilitate efficient computation of thermal, mass, and flow distributions. Subsequently, Maplesoft 16 was used to simulate the resulting system of equations. The analysis explores how flow orientation influences shear-induced dilution or enhancement, impacting effective thermal conductivity and heat transfer efficiency. The flexibility of the microchannel walls introduces nonlinear effects, modulating the flow profile and heat dissipation rates. Results indicate that optimal flow orientation and controlled flexibility significantly enhance thermal performance, with nonlinear shear effects amplifying or mitigating heat transfer depending on the flow regime. These findings provide valuable insights for designing advanced microfluidic systems for applications requiring precise thermal management, such as microelectronics cooling and lab-on-chip devices. Additionally, the Nusselt number decreases as the Prandtl number increases, while the Sherwood number rises due to an enhanced Schmidt number.