Casson-Sutterby nanofluid flow across a wedge: influence of oxytactic microorganisms and a sinusoidal magnetic field

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-1≤Ri≤10, the Deborah number De0≤De≤2, the Casson parameter β1≤De≤10, the magnetic parameter M0≤M≤3, the bioconvection Rayleigh number Rb0.1≤Rb≤0.3, nanoparticle buoyancy ratio Nr0.1≤Nr≤0.3, thermophoresis Nt0.1≤Nt≤1, Brownian diffusion Nb0.1≤Nb≤1, Eckert number Ec-0.05≤Ec≤0.05, the Peclet number Pe0.1≤Pe≤0.8, the ratio of consumption of oxygen on the diffusion rate of species concentration Δ15≤Δ1≤50, the microbial density difference ratio Δ25≤Δ2≤30, the ratio of consumption of oxygen to the diffusion rate of nanoparticles Δ31≤Δ3≤8, bioconvection Lewis number Lb1≤Lb≤5, and the Lewis number Le1≤Le≤5. The skin friction coefficient is reduced considerably due to bioconvection (Rb and Nr). Noticed that, an increase of heat transfer rate Re-1/2Nu, approximately 436% at Ec = 0.05, and a decrease of Re-1/2Nu, approximately 699% at Ec = − 0.05 when M rises from 0.1 to 0.5 for ξ = 1.8. The nanoparticles mass transfer rate Re-1/2NSh increases approximately about 306% and 367% by augmenting Δ3 from 1 to 8 at ξ=1.75 for Δ2=5 and Δ2=10, respectively. The microbial density number Re-1/2Nn enhances significantly by about 396% for Pe=0.1 when Δ2 increased from 1 to 8, and it is about 384% for Pe=0.8 at ξ=1.75.The regression analysis shows the parameters Pe and Lb have negative impact on Re-1/2Nn, while the parameter Δ2 positively impacts Re-1/2Nn. By comparing the findings from this study to those of earlier studies, we can see that they are entirely consistent with the literature.