# Fluid Dynamics Thesis, UPM, Malaysia Many scholars have suggested theories about micropolar fluids. Although the literature includes a wide range of such theories

 University Universiti Putra Malaysia (UPM) Subject Fluid Dynamics

Many scholars have suggested theories about micropolar fluids. Although the literature includes a wide range of such theories, this analysis will concentrate on five significant themes that appear periodically throughout the review.

These themes are Micropolar fluid, stretching/shrinking surface, and geometry surface. Although the literature depicts this issue in a variety of circumstances, this research will primarily examine their findings.

Micropolar Fluid

The study of micropolar fluids has expanded in various ways to include several physical effects, such as Nazar, Amin, Filip, and Pop (2004), who studied the stagnation point flow of micropolar fluid toward a stretching sheet using the Keller-box method for solving partial differential equations. The results demonstrate that increasing the material parameter decreases the skin friction coefficient for shrinking and expanding the skin friction coefficient for stretching the surface.

Attia investigated the constant laminar flow of an incompressible non-Newtonian micropolar fluid impinging on a permeable flat plate with heat transfer. The article demonstrated that increasing the micropolar parameter increases both the velocity and the thickness of the thermal boundary layer. The influence of suction velocity on shear stress and blowing velocity on heat transfer rate at the wall was then determined by the non-Newtonian parameter.

Ishak, Lok, and Pop investigated the similarity solutions for the steady stagnation-point flow toward a shrinking sheet submerged in an incompressible micropolar fluid. It is assumed that the shrinking velocity and ambient fluid velocity vary linearly with distance from the stagnation point. To solve the converted nonlinear ordinary differential equations by using the Keller-box method.

The system of equations was also numerically solved using the Runge-Kutta method with a shooting technique for specific parameter values to assess the accuracy of the numerical results obtained. This study also considers the second solution. The results confirmed the findings of Nazar et al. (2004) in that the material parameter decreases the skin friction coefficient on a shrinking surface.

The steady three-dimensional stagnation-point flow of an incompressible, homogeneous, electrically conducting micropolar fluid over a flat plate is computed by Borrelli, Giantesio, and Patria. The BVP4c in MATLAB is used to solve the three non-linear ordinary boundary value problems. As a result, the magnetic field alters the thickness of the boundary layer, which decreases with increasing magnetic parameters.

Mishra et al. (2018) investigated the free convective micropolar fluid over a shrinking sheet in the presence of a heat source/sink. The solution approach includes similarity transformation. Using the Runge-Kutta method and the shooting technique, the coupled non-linear partial differential equations were reduced to a set of non-linear ordinary differential equations. It was discovered that the heat source influences the velocity profile and causes the boundary layer to drop.

As the value of the material parameter grows, so does the angular velocity profile. The material parameter reduces skin friction, couple stress, and Nusselt number, while the opposite tendency is seen when the buoyancy parameter increased. The skin and couple stress, as well as the Nusselt number, are increased by the wall suction parameter. These findings differ from Attia (2008) because the micropolar parameter is set at 0.5, whereas Attia investigated a range of micropolar parameters.

The problem of MHD stagnation-point flow over a stretching/shrinking sheet in a micropolar fluid with a slip boundary have done by Solid, Ishak, and Pop (2018). The governing partial differential equations are transformed into a system of ordinary differential equations using similarity. The BVP4c in MATLAB is used to solve ordinary boundary value problems. The three partial differential equations continuity, momentum, and angular momentum equations with magnetohydrodynamic and slip boundary are taken into account.

It also investigated dual solution and stability analysis. The stability study revealed that the first solution has an early decrease of disturbance, but the second solution has an initial rise of disturbance, indicating that the first solution is stable and hence physically trustworthy, whereas the second solution does not. As a result of the first solution, increasing the micropolar parameter resulted in a drop in the skin friction coefficient and couple stress. The slip effects at the border on the skin friction coefficient and the couple stress exhibited similar behavior.

Siddiqa et al., discovered a different result when they investigated the influence of heat radiation on the conjugate natural convection flow of a micropolar fluid over a vertical surface. When the micropolar parameter is increased, the skin friction stress, couple stress, and rate of heat transfer all rise.

This might be owing to the vertical plate used in the study, whereas Solid et al., (2018) used a flat plate. Aside from that, the buoyancy effect has an impact on the outcome. Using an implicit finite difference Keller-box approach, the simplified system of partial differential equations was numerically integrated along the vertical plate.

Siddiqa et al., (2020) were similar to those obtained by Piyu Li et al., (2022) in their study of hybrid nanomaterial micropolar fluid flow over an exponentially stretched sheet stretching and shrinking surface with the increase of nanoparticle concentration.

The same findings are obtained even though there are differences in nanoparticle concentration and exponentially flat plate surface. The governing partial differential equations are solved using similarity and numerically solve using BVP4c in MATLAB.

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