# Mathematical Modeling and Microparticle Size Control for Enhancing Heat Transfer Efficiency in High-Viscosity Food Suspensions

## TL;DR

This study shows how adjusting microparticle size can improve heat transfer in thick food mixtures, depending on the temperature difference.

## Contribution

The novel contribution is demonstrating how microparticle size optimization enhances convective heat transfer in high-viscosity suspensions.

## Key findings

- Smaller particles increased shear-thinning behavior and improved heat transfer under large temperature gradients.
- Larger particles showed better heat transfer under smaller temperature differences.
- Nusselt numbers reached up to 100 at a 9 °C temperature difference with smaller particles.

## Abstract

This study investigated how microparticle size affects natural convective heat transfer in high-viscosity suspensions. Suspensions were formulated using 0.5% xanthan gum and 3% stearic acid, with particle sizes ranging from 120 to 750 nm. Key thermal properties, including thermal conductivity (0.598–0.679 W/m·K), specific heat, and the volumetric thermal expansion coefficient (0.990–1.000/°C), were measured. Rheological analysis based on the Herschel–Bulkley model revealed that reducing the particle size increased the consistency index from 0.56 to 0.75 Pa·s, while reducing the flow index from 0.63 to 0.50. This indicates enhanced shear-thinning behavior. A Rayleigh–Bénard convection system revealed that suspensions containing smaller particles exhibited higher Rayleigh and Nusselt numbers under large temperature gradients. Nusselt numbers reached values of up to 100 at a temperature difference of 9 °C. Conversely, suspensions containing larger particles exhibited relatively higher Rayleigh and Nusselt numbers under smaller temperature differences. These results demonstrate that optimizing microparticle size can enhance the efficiency of heat transfer in high-viscosity suspensions depending on the applied thermal gradient. This has practical implications for improving heat transfer in food and other viscous systems where convection is limited.