Generalized engineering equations of heat-transfer performance for twisted heat exchanger with slurries from biogas plants by using Machine learning driven by mechanism and data

• Effective shear-based generalized equations were established with machine learning. • Error of generalized engineering equations is within 17.3 % for different slurries. • Generalized engineering equations quantitatively reveal mechanism of enhancement. The development of generalized engineering equations of the heat-transfer performance in enhanced geometries for different slurries is crucial for practical applications but difficult owing to the complex rheological properties. In the present study, a method of computational-fluid-dynamics-data-driven machine learning was proposed to establish generalized engineering equations in a novel twisted geometry for multiple slurries with a single substrate. The applicability of the equations for a mixed slurry was determined by comparing the predictions and computational fluid dynamics simulations. It was found that the established equations considering the key parameter–effective shear rate show a high accuracy with an average relative deviation of 17.3 % for single-substrate slurries with the scope of viscosities and flow behavior index ranging from 0.057-93.96 Pa·s and 0.257–0.579, respectively. Moreover, the generalized engineering equations show an average relative deviation of 12.4 % in prediction for the mixed slurry possessing the temperature- and shearing-sensitive rheological behavior. The generalized engineering equations quantitatively reveal the positive effect of non-Newtonian behavior on the heat-transfer enhancement of THT for different slurries. Based on this mechanism, a mixed slurry is recommend with energy-conservation of 60.00 GW·h/year for a full-scale biogas plant.