Developing thermal systems’ heat and mass transfer characteristics is critical for achieving optimal results across various applications. Comprehending the system’s functions is crucial for optimizing the system’s performance in industrial applications, including cooling systems and heat exchangers. Hence, the primary goal of this study is to investigate the Casson-Sutterby mixed convection nanofluid flow over wedge in presence of sinusoidal magnetic field. The relevant nonsimilar transformations are applied to the nonlinear partial differential equations governing the flow, heat, mass, nanoparticle volume fraction, and microbe density fields to attain a nondimensional expression. In addition, the quasilinearization technique and an implicit finite difference scheme are used to solve a final set of coupled nonlinear partial differential equations. Furthermore, multiple linear regression is employed to analyse the influence of relevant variables on the skin friction coefficient and microbial density number. The values of the physical parameters are specified within the following ranges: Richardson number \(Ri\left( { - 1 \le {\text{Ri}} \le 10} \right)\) , the Deborah number \({\text{De}}\left( {0 \le {\text{De}} \le 2} \right)\) , the Casson parameter \(\beta \left( {1 \le De \le 10} \right)\) , the magnetic parameter \(M\left( {0 \le M \le 3} \right)\) , the bioconvection Rayleigh number \({\text{Rb}}\left( {0.1 \le {\text{Rb}} \le 0.3} \right)\) , nanoparticle buoyancy ratio \(Nr\left( {0.1 \le Nr \le 0.3} \right)\) , thermophoresis \(Nt\left( {0.1 \le Nt \le 1} \right)\) , Brownian diffusion \(Nb\left( {0.1 \le Nb \le 1} \right)\) , Eckert number \({\text{Ec}}\left( { - 0.05 \le {\text{Ec}} \le 0.05} \right)\) , the Peclet number \({\text{Pe}}\left( {0.1 \le {\text{Pe}} \le 0.8} \right)\) , the ratio of consumption of oxygen on the diffusion rate of species concentration \(\Delta_{1} \left( {5 \le \Delta_{1} \le 50} \right)\) , the microbial density difference ratio \(\Delta_{2} \left( {5 \le \Delta_{2} \le 30} \right)\) , the ratio of consumption of oxygen to the diffusion rate of nanoparticles \(\Delta_{3} \left( {1 \le \Delta_{3} \le 8} \right)\) , bioconvection Lewis number \({\text{Lb}}\left( {1 \le {\text{Lb}} \le 5} \right)\) , and the Lewis number \({\text{Le}}\left( {1 \le {\text{Le}} \le 5} \right)\) . The skin friction coefficient is reduced considerably due to bioconvection ( \(Rb\) and \(Nr\) ). Noticed that, an increase of heat transfer rate \({\text{Re}}^{ - 1/2} Nu\) , approximately 436% at Ec = 0.05, and a decrease of \({\text{Re}}^{ - 1/2} Nu\) , approximately 699% at Ec = − 0.05 when M rises from 0.1 to 0.5 for \(\xi\) = 1.8. The nanoparticles mass transfer rate \({\text{Re}}^{ - 1/2} NSh\) increases approximately about 306% and 367% by augmenting \(\Delta_{3}\) from 1 to 8 at \(\xi = 1.75\) for \(\Delta_{2} = 5\) and \(\Delta_{2} = 10\) , respectively. The microbial density number \({\text{Re}}^{ - 1/2} Nn\) enhances significantly by about 396% for \(Pe = 0.1\) when \(\Delta_{2}\) increased from 1 to 8, and it is about 384% for \({\text{Pe}} = 0.8\) at \(\xi = 1.75\) .The regression analysis shows the parameters \(Pe\) and \(Lb\) have negative impact on \({\text{Re}}^{ - 1/2} Nn\) , while the parameter \(\Delta_{2}\) positively impacts \({\text{Re}}^{ - 1/2} Nn\) . By comparing the findings from this study to those of earlier studies, we can see that they are entirely consistent with the literature.
