Exploring the effect of axial wall conduction on the heat transfer mechanism of hourglass microchannels: Design guidelines for maintaining a constant wall temperature

Abstract

To accurately estimate the heat transfer mechanisms of microscale thermal devices, it is essential to quantify the effects of axial wall conduction, which can significantly alter the thermal boundary conditions. This study focuses on exploring the effect of axial wall conduction on the thermal mechanism of hourglass microchannels, a topology that has proven useful in several engineering applications. However, there is a lack of research on the impact of axial wall conduction on the heat transfer mechanism of hourglass microchannels, and their potential for maintaining constant temperatures in biological applications has not been explored. To address this issue, a three-dimensional numerical analysis is conducted to investigate the impact of various design variables on the thermal mechanics of hourglass microchannels. An experiment has also been performed to validate the numerical approach employed in the study. The results show that the axial wall conduction effect is insignificant for modified Maranzana number below 0.01. It is further noted that the Nusselt number attains a maximum at an intermediate thermal conductivity ratio. This ratio ranges from 27 to 246 and is moderately dependent on the convergence-divergence angle, width ratio, and thickness ratio. Interestingly, an hourglass shape can maintain a near-isothermal boundary condition with a temperature difference of 1.4K at a lower width ratio. This work also establishes the design criteria for achieving a nearly isothermal condition within prescribed limits for important parameters, such as convergence-divergence angle (8°-16°), width ratio (1–2), thermal conductivity ratio (>646), thickness ratio (>10), and Reynolds number (>300). The established design criteria will pave the way for developing lab-on-chip devices for biological applications, such as PCR, that require the maintenance of constant wall temperature.