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Investigations on the characteristics of fluid flow in manufacturing processes are essential since it will determine the quality of the end products. The flow might be involved whether the Newtonian (viscous) or non-Newtonian fluid moving over the different body depending on the process activities. Since the experimental works sometimes costly and hazardous, the study via mathematical approach is necessary to counter the limitations. Hence, this paper aims to investigate the flow at lower stagnation point over a horizontal circular cylinder on Brinkman Viscoelastic fluid embedded in porous medium. Mathematical model is constructed in terms of partial differential equations with some physical conditions to represent the condition of the problem. An appropriate non-dimensional variable is introduced to transform the model into the solvable system which is in less complexity, and then the system is solved using the Runge-Kutta-Fehlberg method. The numerical solutions for the temperature and velocity profiles as well as skin friction and heat transfer coefficient are computed and presented in graphical and tabular form. The feature of the flow and heat transfer characteristics for various values of mixed convection, Brinkman and viscoelastic parameter are analysed and discussed. This study has found that the incremented Brinkman and viscoelastic parameter have declined the fluid velocity while opposite trend is observed for temperature distribution. The theoretical results produced are relevance to researchers and engineers. It can be used for comparative purposes in data validation or experimentation study.

Numerical investigation of the boundary layer flow of Williamson fluid with the presence of dust particles over a stretching sheet is carried out by taking into account the variable viscosity effect and Newtonian heating boundary condition. The genuinely two-phase flow model which has been proved to be compatible to present the mutual relationship between non-Newtonian fluid and solid particles is considered in this present study. To be precise, the governing equations are initially transformed into ordinary differential equations through formulation process before proceeding further with the numerical computation by using Keller-box method. The resulting equations are then programmed in Matlab software. The obtained numerical results are validated with existing study found in open literature and a good agreement is achieved. The influence of pertinent parameters on velocity and temperature profiles, skin friction coefficient together with Nusselt number is presented in graphical and tabular forms. Results revealed that the increasing Williamson parameter decreases the fluid velocity of both fluid and dust phases. It is expected that the present numerical results could conceivably help in predicting the boundary layer problem arising in two-phase flow in the future.

Lower stagnation point flow of Jeffrey nanofluid from a horizontal circular cylinder is addressed under the influences of suction/injection, mixed convection and convective boundary conditions. Copper (Cu) is taken as the nanoparticles while Carboxymethyl cellulose (CMC) water is taken as the base fluid. The transformed boundary layer equations through the nondimensional variables and non-similarity transformation variables are subsequently tackled by means of the Runge-Kutta Fehlberg method (RKF 45). The impact of dimensionless parameters such as the suction/injection, nanoparticles volume fraction and Deborah number are graphically presented and discussed in detail. The outcomes reveal that both the velocity and temperature profiles are augmented with upsurge volume fraction values of nanoparticles. Velocity profile escalates as suction/injection parameter rises but declines as Deborah number upsurges. Temperature profile reduces when suction/injection parameter enlarges and augments when Deborah number increases.

The non-Newtonian Jeffrey fluid model describes the viscoelastic property that elucidates the dual components of relaxation and retardation times. Nonetheless, there has been considerable attention on its unsatisfactory thermal performance. The model of nanofluid is contemporarily in the limelight due to its superior thermal performance compared to the conventional fluid. The proposed study herein aims to examine the Jeffrey nanofluid model over a horizontal circular cylinder with mixed convection flow. The flow analysis is performed based on the Buongiorno model with the integration of Brownian motion and thermophoresis diffusion parameters. The influence of frictional heat is also accounted. The non-dimensional and non-similarity transformation variables are utilized to reduce the dimensional governing equations into three non-dimensional PDE. Subsequently, the obtained PDE are tackled numerically through the Keller-box method. Certain continent parameters are investigated with regards to the identified distributions. A comparative study is executed based on previous studies, which indicates good agreement with results of the current study. The findings specify that the transition of boundary-layer from laminar to turbulent flows happens for dissimilar values of mixed convection parameter, Deborah number, Brownian motion and Eckert number. In particular, the boundary-layer separates from cylinder for positive (heated cylinder) and negative (cooled cylinder) values of mixed convection parameter. Heating the cylinder defers the separation of boundary-layer, while cooling the cylinder carries the separation point close to the lower stagnation point.