Regression-Based Numerical Analysis of Heat and Mass Transfer in Bioconvective Blood-Based Tetra-Hybrid Nanofluid Flow

Abstract

The present study investigates the regression-based prediction of surface drag force, local heat transfer, mass transfer, and motile microorganism density transfer rates in the bioconvective flow of a blood-based tetra-hybrid nanofluid(HNF) over a stretchable sheet. The cross-fluid model is employed to characterize the non-Newtonian behavior of the tetra-HNF. The bioconvective tetra-HNF is synthesized by using titanium dioxide (TiO 2 ), aluminum oxide (Al 2 O 3 ), silver (Ag), and gold (Au) nanoparticles suspended in blood in the presence of gyrotactic microorganisms. The Cattaneo–Christov model is incorporated for heat and mass transport instead of the conventional Fourier and Fick laws. The stretching surface is assumed to be permeable, and the effects of an applied magnetic field are considered, while inertial effects are neglected. Temperature-dependent thermal conductivity is also incorporated. The mathematical formulation further accounts for viscous dissipation, chemical reaction, thermal radiation, activation energy, and internal heat generation. Appropriate transformations are employed to transform the flow governing dimensional equations into a system of nonlinear ordinary differential equations(ODEs), which is solved numerically using the built-in NDSolve function of Mathematica 11.3. The effects of the governing parameters on the velocity, temperature, nanoparticle concentration, and motile microorganism density distributions are examined for both tetra- and ternary-HNFs. Subsequently, regression models are developed to establish predictive relationships between the governing physical parameters and the engineering response quantities. The regression results demonstrate high coefficients of determination, indicating strong agreement between the predicted and computed response values. The results further reveal that variations in thermal conductivity substantially alter the temperature gradients and consequently influence the heat transfer characteristics of both tetra- and ternary-HNFs. Moreover, the obtained p-values are below the significance level of 0.05 for the considered response quantities, confirming statistically significant relationships between the governing parameters and the corresponding physical responses. The proposed regression framework provides an effective predictive tool for quantifying the transport characteristics of blood-based tetra/ternary-HNF and supports the design and optimization of thermal and biomedical flow systems.