Magnetohydrodynamic nanofluid technologies are emerging in several areas including pharmacology, medicine and lubrication (smart tribology). The present study discusses the heat transfer and entropy generation of magnetohydrodynamic (MHD) Ag-water nanofluid flow over a stretching sheet with the effect of nanoparticles shape. Three different geometries of nanoparticles—sphere, blade and lamina—are considered. The problem is modeled in the form of momentum, energy and entropy equations. The homotopy analysis method (HAM) is used to find the analytical solution of momentum, energy and entropy equations. The variations of velocity profile, temperature profile, Nusselt number and entropy generation with the influences of physical parameters are discussed in graphical form. The results show that the performance of lamina-shaped nanoparticles is better in temperature distribution, heat transfer and enhancement of the entropy generation.

The telegraph model describes that the current and voltage waves can be reflected on a wire, that symmetrical wave patterns can form along a line. A numerical study of these voltage and current waves on a transferral line has been proposed via a modified extended cubic B-spline (MECBS) method. The B-spline functions have the flexibility and high order accuracy to approximate the solutions. These functions also preserve the symmetrical property. The MECBS and Crank Nicolson technique are employed to find out the solution of the non-linear time fractional telegraph equation. The time direction is discretized in the Caputo sense while the space dimension is discretized by the modified extended cubic B-spline. The non-linearity in the equation is linearized by Taylor’s series. The proposed algorithm is unconditionally stable and convergent. The numerical examples are displayed to verify the authenticity and implementation of the method.

The focus of the present paper is to analyze the shape effect of gold (Au) nanoparticles on squeezing nanofluid flow and heat transfer between parallel plates. The different shapes of nanoparticles, namely, column, sphere, hexahedron, tetrahedron, and lamina, have been examined using water as base fluid. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable transformations. As a result, nonlinear boundary value ordinary differential equations are tackled analytically using the homotopy analysis method (HAM) and convergence of the series solution is ensured. The effects of various parameters such as solid volume fraction, thermal radiation, Reynolds number, magnetic field, Eckert number, suction parameter, and shape factor on velocity and temperature profiles are plotted in graphical form. For various values of involved parameters, Nusselt number is analyzed in graphical form. The obtained results demonstrate that the rate of heat transfer is maximum for lamina shape nanoparticles and the sphere shape of nanoparticles has performed a considerable role in temperature distribution as compared to other shapes of nanoparticles.

The time–fractional reaction–diffusion (TFRD) model has broad physical perspectives and theoretical interpretation, and its numerical techniques are of significant conceptual and applied importance. A numerical technique is constructed for the solution of the TFRD model with the non-singular kernel. The Caputo–Fabrizio operator is applied for the discretization of time levels while the extended cubic B-spline (ECBS) function is applied for the space direction. The ECBS function preserves geometrical invariability, convex hull and symmetry property. Unconditional stability and convergence analysis are also proved. The projected numerical method is tested on two numerical examples. The theoretical and numerical results demonstrate that the order of convergence of 2 in time and space directions.

Graphene nanofluids have attracted the attention of many researchers because of a variety of remarkable properties such as extraordinary electronic transport properties, high thermal conductivity, and large specific surface areas. This paper investigates the shape effects of nanoparticles on the Marangoni boundary layer of graphene–water nanofluid flow and heat transfer over a porous medium under the influences of the suction parameter. The graphene–water nanofluid flow was contained with various shapes of nanoparticles, namely sphere, column, platelet, and lamina. The problem is modeled in form of partial differential equations (PDES) with boundary conditions. The governing transport equations are converted into dimensionless form with the help of some suitable nondimensional variables. The solution of the problem was found numerically using the NDSolve technique of Mathematica 10.3 software. In addition, the numerical solutions were also compared with analytical results. The homotopy analysis method (HAM) is used to calculate the analytical results. The results show that lamina-shaped nanoparticles have better performance on temperature distribution while sphere-shaped nanoparticles are more efficient for heat transfer than other shapes of nanoparticles.