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 nondimensional and non-similarity transformation variables are utilized to reduce the dimensional governing equations into three non-dimensional partial differential equations (PDEs). Subsequently, the obtained PDEs 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.

Non-Newtonian is a type of fluid that does not comply with the viscosity under the Law of Newton and is being widely used in industrial applications. These include those related to chemical industries, cosmetics manufacturing, pharmaceutical field, food processing, as well as oil and gas activities. The inability of the conventional equations of Navier-Stokes to accurately depict rheological behavior for certain fluids led to an emergence study for non-Newtonian fluids' models. In line with this, a mathematical model of forced convective flow on non-Newtonian Eyring Powell fluid under temperature-dependent viscosity (TDV) circumstance is formulated. The fluid model is embedded with the Newtonian heating (NH) boundary condition as a heating circumstance and is assumed to move over a stretching sheet acting vertically. Using appropriate similarity variables, the respective model was converted into ordinary differential equations (ODE), which was later solved utilizing the Keller box approach. The present model is validated by comparing the existing output in literature at certain special limiting cases, where the validation results display a firm agreement. The current outputs for the proposed model are shown in tabular and graphical form for variation of skin friction plus Nusselt number, velocity and temperature distribution, respectively.

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 non-dimensional 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 the velocity and temperature profiles are both augmented with rising values of nanoparticles volume fraction. 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.

Convection refers to the heat transfer that occurs between moving fluid and surface at a different temperature. Nowadays, there has been a great deal of interest in the convective boundary layer fluid flow problems. Despite its popularity, the review paper discussing the mathematical model for various fluid types regarding various geometry and boundary conditions has been observed to fall short. This review paper adopts a thematic review based on the mathematical model captured in published fluid flow problems from 2015 until 2020. The articles were analysed using thematic analysis ATLAS.ti 8 software. Using keyword search and filtering criteria from Scopus and Web of Science (WOS) databases, 198 peer-reviewed journal articles were identified. However, after the exclusion and inclusion processes, only 50 articles were reviewed as final articles. The thematic review of these articles has further identified 120 initial codes characterising the mathematical model, grouped into 7 clusters: Viscoelastic, Williamson, Casson, Brinkman, Jeffrey, Nanofluid and hybrid Nanofluid. The report from the code-to-document in ATLAS.ti 8 found that the boundary condition, geometry and method were highlighted in the literature. The outcomes of this study will benefit the future research direction to identify the gap for future studies, specifically in extending the mathematical model for fluid flow problems as well as choosing the suitable geometry and boundary condition.

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.