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Recent advancement in nanotechnology brings the idea of hybrid nanomaterials which offer distinguish applications in thermal reservoirs, cooling systems, energy applications, chemical engineering, vehicle engines etc. The understating of shape features for hybrid nanomaterials is quite essential as such consequences highly influenced various thermal properties like viscosity, thermal conductivity, optical properties, stability etc. The objective of current work is to examine heat transfer analysis due to thin film unsteady flow of hybrid nanofluid. The properties of hybrid nanofluid are justified for entertaining the copper (Cu), aluminium oxide (Al2O3) nanoparticles with water (H2O) base fluid. Additionally, applications of viscous dissipation, heat source and nonlinear radiated effects are attributed to current flow problem. The thermal properties of nanoparticles are examined in presence of five shape features consisting of blades, platelets, cylinders, bricks and spheres. Numerical simulations of problem are performed via Runge-Kutta-Fehlberg method. Comparative heat transfer is performed for mono nanofluid (Cu/H2O) and hybrid nanofluid (Cu−Al2O3)//H2O. It has been observed that heat transfer enhancement is more stable for cylindrical particles as compared to spherical nanoparticles. The skin friction enhances due to Hartmann number for both mono nanofluid (MNF) and hybrid nanofluid (HNF). Current results claim applications in coating thin films, lubrication systems, improving the thermal efficiency in thermal and industrial systems, heat exchangers, cooling systems etc.

An attempt has been made to examine the two dimensional free stream squeezed flow through a horizontal sensor surface of an electrically conducting Carreau-Yasuda fluid subject to transverse magnetic field. The governing nonlinear partial differential equations are modeled and then simplified with the aid of suitable similarity transformations. Well known numerical scheme Runge–Kutta–Fehlberg method is utilized to solve the system. Concrete graphical analysis is carried out to investigate the behavior of different pertinent parameters on velocity profile with inclusive discussion. Numerical influence of friction factor is also discussed.

The two-dimensional unsteady laminar free convective heat and mass transfer fluid flow of a non-Newtonian fluid adjacent to a vertical plate has been analyzed numerically. The two parameters Lie group transformation method that transforms the three independent variables into a single variable is used to transform the continuity, the momentum, the energy and the concentration equations into a set of coupled similarity equations. The transformed equations have been solved by the Runge–Kutta–Fehlberg fourth-fifth order numerical method with shooting technique. Numerical calculations were carried out for the various parameters entering into the problem. The dimensionless velocity, temperature and concentration profiles were shown graphically and the skin friction, heat and mass transfer rates were given in tables. It is found that friction factor and heat transfer (mass transfer rate) for methanol are higher (lower) than those of hydrogen and water vapor. Friction factor decreases while heat and mass transfer rate increase as the Prandtl number increases. Friction (heat and mass transfer rate) factor of Newtonian fluid is higher (lower) than the dilatant fluid.

This paper reflects some research outcome denoting as to how Lotka–Volterra prey predator model has been solved by using the Runge–Kutta–Fehlberg method (RKF). A comparison between Runge–Kutta–Fehlberg method (RKF) and the Laplace Adomian Decomposition method (LADM) is carried out and exact solution is found out to verify the applicability, efficiency and accuracy of the method. The obtained approximate solution shows that the Runge–Kutta–Fehlberg method (RKF) is a more powerful numerical technique for solving a system of nonlinear differential equations.

The present problem is the steady boundary layer flow and heat transfer of a hyperbolic tangent fluid flowing over a vertical exponentially stretching cylinder in its axial direction. After applying usual boundary layer with a suitable similarity transformation to the given partial differential equations and the boundary conditions, a system of coupled nonlinear ordinary differential equations is obtained. This system of ordinary differential equations subject to the boundary conditions is solved with the help of Runge–Kutta–Fehlberg method. The effects of the involved parameters such as Reynolds numbers, Prandtl numbers, Weissenberg numbers and the natural convection parameter are presented through the graphs. The associated physical properties on the flow and heat transfer characteristics that is the skin friction coefficient and Nusselt numbers are presented for different parameters.