Laminar cross-flow convective heat transfer of a finned cylindrical tube in the presence of particle deposition and deposit erosion

Cross-flow finned tube heat exchangers are extensively used in a variety of industrial and commercial applications. Although the fins increase surface area and hence enhance heat transfer rate, the fouling potential also increases due to the more complex geometry leading to performance deterioration. This paper presents an integrated numerical model to study the effect of fouling on convective heat transfer of a finned cylindrical tube. In this model, fluid flow, particle transport, particle deposition, deposit erosion and heat transfer are all accounted for in a fully coupled manner. Moreover, the fluid-deposit interface is captured using a level-set method and the interfacial velocity is derived from the net effect of combined particle deposition and deposit erosion. In such a way, the evolution of deposit layer is implicitly tracked in a fixed mesh, and its influences on fluid flow and heat transfer are considered by updating the thermophysical properties of the deposit region. Based on this integrated model, comprehensive parametric studies are conducted to investigate the effects of tube orientation angle (β), Reynolds number (Re), Damkholer number (Da), erosion number (Er), particle Peclet number (Pe_C) and thermal Peclet number (Pe_T) and dimensionless critical shear stress (τ*_crit). It is found that the amount of deposits accumulated increases for a lower β within the range of 0°-45°, a higher β in the range of 45°-90°, a higher Re, a higher Da, a lower Er, a lower Pe_C and a lower τ*_crit. Heat transfer deteriorates as the insulating deposit layer grows thicker and at a higher Pe_T. This study demonstrates the capabilities of the developed model, and provides fundamental insights on the coupled fouling and heat transfer processes of cross-flow finned tube heat exchangers in the trend towards miniaturization.