**4. Results and Discussion**

The MATLAB software is used herein, through the so-called BVP4C routine, to solve the coupled set of nonlinear ODEs given by Equations (10)*–*(14) and their accompanying boundary conditions. To achieve mathematical results, we have utilized the following values for various non-dimensional parameters: *M* = 0.5, *A* = 0.5, *β*<sup>1</sup> = 1.0, *Pr* = 4.0, *Nt* = 0.2, *Nb* = 0.3, *Sc* = 6.0, *Sb* = 6.0, *Pb* = 0.1, *τ*<sup>0</sup> = 1. With the exception of the modified parameters displayed in the figures, these are maintained as constant. We have discussed the influence of various parameters, such as magnetic parameter (*M*), curvature parameter (*A*), slip parameter (*β*1), thermophoresis parameter (*Nt*), Prandtl number (*Pr*), Brownian motion parameter (*Nb*), bio-convection Schmidt number (*Sb*), Schmidt number (*Sc*), bio-convection Peclet number (*Pb*). Some of these were examined based on the local motile micro-organisms' number. Table 3 summarizes the values for the physical quantities of interest given in Equations (20)*–*(23).

**Table 3.** Numerical values of *Cf Re* <sup>1</sup> 2 *<sup>s</sup>* , *NusRe*<sup>−</sup> <sup>1</sup> <sup>2</sup> *<sup>s</sup>* , *ShsRe*<sup>−</sup> <sup>1</sup> <sup>2</sup> *<sup>s</sup>* , and *MnsRe*<sup>−</sup> <sup>1</sup> <sup>2</sup> *<sup>s</sup>* .



**Table 3.** *Cont.*
