**5. Results and Discussion**

The role of *β* on velocity profile is detected in Figure 2. The ferromagnetic parameter emphasizes the effect of the magnetic dipole's external magnetic field on fluid dynamics. As the magnetic field acts as a deforming force, the axial velocity decreases. Figure 3 depicts the important properties of the *Fr* on the dimensionless velocity. Obviously, increasing *Fr* causes the velocity of fluid layers to decrease. From a physical standpoint, the local inertia parameter generates resistance forces against the motion of fluid particles. Moreover, as the local inertia parameter increases, so does the velocity. Figure 4 depicts the impact of increasing *P*<sup>1</sup> on the velocity. The porosity parameter is defined as the kinematic viscosity to permeability strength of porous space ratio. As the porosity parameter increases, the velocity curves definitely decrease. Figure 5 depicts the effect of the *Rab* on the velocity profile. It was discovered that when the values of *Rab* rise, the velocity accelerates. As a result of the buoyancy forces caused by bioconvection, the fluid velocity increases by increasing the bioconvection Raleigh number. Figure 6 shows that the temperature on the boundary layers enhances as a result of increasing the values of *β*. This is due to an interaction of the fluid's movement and the interference of the ferromagnetic particles. The interplay reduces the velocity while frictional heating increases between the fluid layers, resulting in an increase in the thermal boundary layer thickness. The effect of *λ* on the temperature profile is depicted in Figure 7. In this case, temperature is displayed as an increasing function of *λ*. Usually, as the values of *λ* increase, so does the thermal conductivity, and thus the temperature. Figure 8 displays the role of *Fr* on temperature profile. A rise in *Fr* results in a rise in temperature and the thermal boundary layer thickness. Figure 9 reveals that as *Bi* increases, so does the thickness of the thermal boundary layer, and the temperature also enhances. A higher Biot number contributes to more convection, which leads to the enhancement of the temperature and thermal boundary layer thickness. Figure 10 shows the effect of *S* < 0 on the dimensionless temperature. This figure reveals that when increasing *S* < 0, the temperature and the thickness of the thermal boundary layers both decrease. As an outcome, suction is removed from the warm fluid in the boundary layer region to a large extent. Moreover, the opposite trend is observed in the temperature profile, as shown in Figure 11 with *S* > 0. This is attributable to the fact that the temperature of the fluid is raised by injecting warm fluid into the boundary layer region. Figure 12 depicts the effects of *Rd* on the temperature profile for various *Rd* values. An increase in the *Rd* causes a rise in the temperature, and the effect of thermal radiation improves the medium's thermal diffusive. Besides that, for higher *Nt* values, temperatures rise in the boundary layer region (Figure 13). The thermophoretic force developed in the boundary layer regime is an outcome of the temperature gradient; such forces entail the diffusion of nanoparticles out of the higher temperature area to a lower temperature area, leading to a thermal boundary layer thickness enhancement. Figure 14 depicts the *Nb* characteristics on a temperature profile. Usually, a rise in *Nb* improves the motion of fluid particles randomly, resulting in more heat generation. As a result, the temperature rises. Figure 15 depicts the temperature distribution by raising *Ec* values. The *Ec* defines the connection among the flow of kinetic energy and heat enthalpy variation. As a consequence, raising *Ec* also raises the kinetic energy. Moreover, temperature is well understood to be defined as average kinetic energy. As a result, the fluid's temperature rises. This graph shows that as *Ec* increases, so does the temperature. Figure 16 shows the role of *Pr* on the temperature profile. It has been discovered that raising the *Pr* lowers the temperature of the fluid flow. Large *Pr* values clearly result in the thinning of thermal boundary layers. As *δ* increases, so does the concentration profile. The concentration becomes less effective as the delta values increase, as shown in Figure 17. The physical effect of *Nb* on a concentration profile is depicted in Figure 18. Brownian motion does play a role in determining the efficiency of heat transfer during nanofluid flow. The nanoparticles collide with one another and transfer energy due to the random motion of a nanofluid. As a result, as *Nb* levels rise, the concentration profile falls. The effect of *Nt* on nanoparticle concentration is depicted in Figure 19. The concentration field rises in this case due to an increase in *Nt*. Larger *Nt* causes an increase in thermophoresis forces, which further frequently carries nanomaterials from higher to lower temperature regions. As a result, the concentration decreases. The effect of *Sc* on concentration is depicted in Figure 20. Sc denotes the momentum-to-mass diffusivity ratio, which measures the relative efficacy of momentum and mass transport through diffusion within concentration boundary layers. Figures 21 and 22 show the effects of *Pe* and *Lb* on the microorganism profile. According to these figures, the microorganism field decreases with increase of both numbers. According to Table 3, as *Pr* estimates increase, so does the Nusselt number. Table 4 shows that as *δ* and *Sc* increase, so does the Sherwood number. The results of motile microorganism density are increased by increasing *Lb* and *Rab*, as shown in Table 5.

**Figure 2.** Influence of *β* on *f* (*ζ*).

**Figure 3.** Influence of *Fr* on *f* (*ζ*).

**Figure 4.** Influence of *P*<sup>1</sup> on *f* (*ζ*).

**Figure 5.** Influence of *Rab* on *f* (*ζ*).

**Figure 6.** Influence of *β* on *θ*(*ζ*).

**Figure 7.** Influence of *λ* on *θ*(*ζ*).

**Figure 8.** Influence of *Fr* on *θ*(*ζ*).

**Figure 9.** Influence of *Bi* on *θ*(*ζ*).

**Figure 10.** Influence of *S* < 0 on *θ*(*ζ*).

**Figure 11.** Influence of *S* > 0 on *θ*(*ζ*).

**Figure 12.** Influence of *Rd* on *θ*(*ζ*).

**Figure 13.** Influence of *Nt* on *θ*(*ζ*).

**Figure 14.** Influence of *Nb* on *θ*(*ζ*).

**Figure 15.** Influence of *Ec* on *θ*(*ζ*).

**Figure 16.** Influence of *Pr* on *θ*(*ζ*).

**Figure 17.** Influence of *δ* on *φ*(*ζ*).

**Figure 18.** Influence of *Nb* on *φ*(*ζ*).

**Figure 19.** Influence of *Nt* on *φ*(*ζ*).

**Figure 20.** Influence of *Sc* on *φ*(*ζ*).

**Figure 21.** Influence of *Pe* on *χ*(*ζ*).

**Figure 22.** Influence of *Lb* on *χ*(*ζ*).


**Table 3.** Influence of *β*, *ε*, *λ*, *S*, *Rd*, *Fr*, *Ec*, and *Pr* on *θ* (0).

**Table 4.** Influence of *δ*, *Sc*, *Nb* on *φ* (0).


**Table 5.** Influence of *Nδ*, *Pe*, *Lb*, *Rab* on *χ* (0).

