In this paper, a three-stage fifth-order Runge-Kutta method for the integration of a special third-order ordinary differential equation (ODE) is constructed. The zero stability of the method is proven. The numerical study of a third-order ODE arising in thin film flow of viscous fluid in physics is discussed. The mathematical model of thin film flow has been solved using a new method and numerical comparisons are made when the same problem is reduced to a first-order system of equations which are solved using the existing Runge-Kutta methods. Numerical results have clearly shown the advantage and the efficiency of the new method.

An interesting quadratic fractional integral equation is investigated in this work via a generalized Mittag-Leffler (ML) function. The generalized ML–Hyers–Ulam stability is established in this investigation. We study both of the Hyers–Ulam stability (HUS) and ML–Hyers–Ulam–Rassias stability (ML-HURS) in detail for our proposed differential equation (DEq). Our proposed technique unifies various differential equations’ classes. Therefore, this technique can be further applied in future research works with applications to science and engineering.

No abstract

The aim of the present study is to examine the convective heat transfer of nanofluid past a wedge subject to first-order chemical reaction, heat generation/absorption and suction effects. The influence of wedge angle parameter, thermophoresis, Dufour and Soret type diffusivity are included. The local similarity transformation is applied to convert the governing nonlinear partial differential equations into ordinary differential equations. Shooting method integrated with fourth-order Runge-Kutta method is used to solve the ordinary differential equations. The skin friction, heat and mass transfer rates as well as the effects of various parameters on velocity, temperature and solutal concentration profiles are analyzed. The results indicate that when the chemical reaction parameter increases, the heat transfer coefficient increases while the mass transfer coefficient decreases. The effect of chemical reaction parameter is very important in solutal concentration field compared to velocity and temperature profiles since it decreases the solutal concentration of the nanoparticle.

No abstract

No abstract

No abstract

The present article describes a mathematical model for incompressible free convection flow with convective heat transport from an inclined stationary/moving flat plate under impact of induced magnetic field (IMF). The current flow model is formulated to consider different water-based nanofluids with metallic nanoparticles (Copper and Silver). Effectively a nanoscale formulation with the Tiwari-Das model deployed to study material properties for specific nanoparticles and base fluid. A similarity solution is obtained for non-dimensional form via similarity transformation rendered from basic flow equations for which numerical simulations utilizing the Spectral Relaxation Method (SRM). SRM is a simple iteration scheme that does not require any evaluation of derivatives, perturbation and linearization for solving non-linear system of equations. Graphical results for linear velocity, IMF, temperature, skin friction and Nusselt number distributions are presented for the different metallic-aqueous nanofluid cases as well as stationary/moving flat plate. The results are verified for limiting cases by comparing with various investigators for the case of stationary as well as moving flat plate and found to be in excellent agreement. Furthermore, computed numerical results for skin friction and Nusselt number for different emerging parameters in case Cu and Ag nanofluids for moving plate which are tabulated and discussed in detail.Nomenclature: Bi, biot number; 𝑐, constant; C f , skin friction coefficient; 𝐷, differentiation matrix in spectral algorithm; 𝑓, dimensionless stream function; f ′ , dimensionless velocity; g, dimensionless magnetic induction stream function; g ′ , dimensionless induced magnetic field stream function gradient; F r+1 (𝜂), current iteration level of dimensionless velocity; G r+1 (𝜂)), current iteration level of dimensionless magnetic stream function; Gr , grashof number; H 1 , H 2 , dimensional magnetic stream function components; h f , heat transfer coefficient (𝑊∕𝑚 2 𝐾); 𝐾, thermal conductivity (𝑊∕𝑚𝑘); 𝑀, magnetic body force number; 𝑁, collocation points deployed in spectral method; Nu x , local Nusselt number; Pr, Prandtl number; 𝑃𝑟 𝑚 , magnetic Prandtl number; Re x , local Reynolds number; 𝑇, magnetic nanofluid temperature (K); 𝑇 𝑓 , hot fluid temperature (K); T ∞ , temperature in the free stream (K); 𝑈, velocity of the free stream (at boundary layer edge); U w , velocity of moving wall (sheet); 𝑢, 𝑣, dimensional velocity components along the x-axis and y-axis, respectively (m/s) Greek: 𝛼, angle of inclination; 𝛼 1 , magnetic diffusivity (𝑚 2 ∕𝑠); 𝛽, thermal expansion coefficient; 𝜆, moving wall velocity parameter; 𝜂, dimensionless similarity variable (transverse coordinate),; 𝜂 ∞ , infinity value (to edge of boundary layer domain); 𝜌, density (𝑘𝑔∕𝑚 3 ); 𝜎, electrical conductivity (𝑆𝑚 −1 ); 𝜌𝐶 𝑝 , heat capacity (𝐽∕𝐾); 𝜌𝛽, thermal diffusivity (𝑚 2 ∕𝑠); θ