Most of the fluid used in industrial application (i.e. Oils and gas industry, food manufacturing, lubrication and biomedical) do not conform to the Newtonian postulate. In contrast to the Newtonian fluid, the viscosity of the fluid can change when under force to either more liquid or more solid and dependent on shear rate history. This behaviour of fluids is commonly known as non-Newtonian fluid. The non-Newtonian fluid is so widespread in nature and technology resulting in very high interest of investigating among scientist. The Reiner-Philippoff fluid is one of the types of non-Newtonian fluid models that exhibiting the dilatant, pseudoplastic and Newtonian behaviors. Hence, this study is devoted to analyze the flow and heat transfer of Reiner-Philippoff fluid with the presence of first and second order velocity slip together with the temperature jump effects over a stretching sheet. Partial differential equations of continuity, momentum and energy equations were transformed into the similarity equations. The obtained equations were then solved via bvp4c function in MATLAB software. For the validation purpose, the present model and its numerical solution were compared with previous established solutions under limiting case where the present model is condensed to be identical with the reported model and turn to be in very strong agreement. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form.

Non-Newtonian fluid model was created against the Newton’s Law of viscosity where the viscosity is no more constant and dependent on the shear rate. The existing such fluid can be found in many industrial claims especially in food manufacturing, lubrication, biomedical flows and oil and gas. Besides, the used of non-Newtonian fluid occurs in mining industry where the slurries and muds are often handled. There are many models on non-Newtonian fluid available in literature where some of them capture the specific properties. The Reiner–Philippoff (RP) fluid model is considered in this endeavour due to the capabilities of the model which can be acted in three different family of fluid which are viscous, shear thickening and the shear-thinning. Mathematical model is constructed using continuity, momentum and energy equations where in form of partial differential equations (PDEs). The complexity of the proposed model is abridged by deduced the equations into ordinary differential equations (ODEs) by adopting similarity variables before the computation is done by bvp4c function drive in MATLAB software. To ratify the validity of the proposed model as well as numerical outputs, the comparative study is performed and it found to be in very strong agreement under limiting case where the present model is condensed to be identical with the reported model previously. The consequences of pertinent parameters on fluid’s characteristics are analyzed in details through the plotted graphic visuals and tabular form.

The nonlinear density variation with temperature happens in many thermal applications like solar collectors, energy production, heat exchangers, and combustions, and it gives a significant impact on heat transfer and fluid flows. Thus, a nonlinear convective of an unsteady stagnation point flow under the influence of gravity modulation in the presence of water-based nanoparticles alumina (Al2O3) is studied here. Suitable variables are utilized to reduce the highly coupled nonlinear governing equations into a system of dimensionless simple partial differential equations. The Keller-box method is then applied to solve the consequent governing equations. Velocity and temperature profiles for various values of pertinent parameters are displayed graphically and discussed. The results indicate that the quadratic convection has enhanced the fluid flow and heat transport. Furthermore, the nonlinear convection parameter and the nanoparticles volume fractions have delivered a positive effect on the skin friction and the rate of heat transfer.

The effectiveness of the heat transfer fluid in the cooling or heating process determines the optimal performance of the nuclear reactor, microelectronic devices, and chip production. Since thermal conductivity improved in hybrid nanofluids, the current study sought to investigate the unsteady free convection hybrid nanofluid flow near a stagnation point as influenced by g-jitter. A hybrid nanofluid consisted of copper (Cu) and alumina (Al2O3) nanoparticles, which were added into water to form Cu-Al2O3/water was considered. Next, relevant variables transformed the governing equation into dimensionless equations before being solved numerically using a centered implicit finite difference method. The fluid field and heat transfer were discussed concerning the stagnation point curvature ratio. The results showed that the g-jitter effect caused fluctuation in all profiles and physical quantities. The frequency and amplitude of the g-jitter reduced the velocity profile while improving the temperature distribution. The heat transfer rate increased by 10.77% when the hybrid nanoparticles volume fractions rose from 0.1 to 0.2. However, the presence of hybrid nanoparticles had reduced the thickness of the momentum boundary layer due to an increase in the local skin friction.

The study of mass transfer in the non-Newtonian fluid is essential in understanding the engine lubrication, the cooling system of electronic devices, and the manufacturing process of the chemical industry. Optimal performance of the practical applications requires the appropriate conditions. The unsteady transient free convective flow of second-grade fluid with mass transfer and wall transpiration is concerned in the present communication. The behavior of the second-grade fluid under the influence of injection or suction is discussed. Suitable non-dimensional variables are utilized to transform the governing equations into non-dimensional governing equations. A Maple solver “pdsolve” that is using the centered implicit scheme of a finite difference method is utilized to solve the dimensionless governing equations numerically. The effects of wall injection or suction parameter, second-grade fluid viscoelastic parameter, Schmidt number, and modified Grashof number on the velocity and concentration profiles are graphically displayed and analyzed. The results show that with increasing wall suction, viscoelastic parameter, and Schmidt number, the velocity and concentration profiles decrease. Whereas, the velocity profiles show an opposite tendency in situations of wall injection. The wall suction has increased the skin friction and also the rate of mass diffusion in the second-grade fluid.

This study emphasis on the analysis of boundary layer flow of viscoelastic fluid with microrotation moving over a porous horizontal circular cylinder. The model of the problem is based on Navier Stokes equations which involved continuity, momentum and micro inertia equations. The mentioned equations are first undergo Boussinesq and boundary layer approximation before transforming to non-dimensional form which in partial differential equations system. Since the boundary layer equations of viscoelastic fluid are an order higher than Newtonian (viscous) fluid, the adherence boundary conditions are insufficient to govern the solutions entirely. Hence, the augmentation of an extra boundary conditions is necessary to perform the computation. The computation is done by adopting the established procedures called Keller box method. The results are computed for velocity and microrotation distribution as well as skin friction coefficient. It is worth to mentioned at the special case, the present model can be deduced to the established model where the porosity, microinertia and magnetic term excluded. The output computed will be served as a reference to study the complex fluid especially when the fluid exhibit both viscous and elastic characteristics with microrotation effect.