A rigorous analysis of coupled nonlinear equations for third-grade viscoelastic power-law non-Newtonian fluid is presented. Initially, the governing partial differential equations for conservation of energy and momentum are transformed to nonlinear coupled ordinary differential equations using exact similarity transformations which are known as Cattaneo–Christov heat flux model for third-grade power-law fluid. The homotopy analysis method (HAM) is utilized to approximate the systematic solutions more precisely with shear-thickening, moderately shear-thinning, and most shear-thinning fluids. The solution depends on various parameters including Prandtl number, power index, and temperature variation coefficient. A systematic analysis of boundary-layer flow demonstrates the impact of these parameters on the velocity and temperature profiles.

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In the this paper, a new modified method is proposed for solving linear and nonlinear Lane-Emden type equations using first kind Chebyshev operational matrix of differentiation. The properties of first kind Chebyshev polynomial and their shifted polynomial are first presented. These properties together with the operation matrix of differentiation of first kind Chebyshev polynomial are utilized to obtain numerical solutions of a class of linear and nonlinear LaneEmden type singular initial value problems (IVPs). The absolute error of this method is graphically presented. The proposed framework is different from other numerical methods and can be used in differential equations of the same type. Several examples are illuminated to reveal the accuracy and validity of the proposed method.

Purpose The development of a new class of engineering materials is the current demand for aircraft and automobile companies. In this context metal, composite materials have a widespread application in different areas of manufacturing sectors. Design/methodology/approach In this paper, an attempt is made to develop the aluminium-based nano metal matrix composite reinforced with graphene nanoparticles (GNP) by using the stir casting method. Different weight percentage (0.4%, 0.8% and 1.2% by weight) of GNPs are used to fabricate metal matrix composites (MMCs). The developed nanocomposites were further validated by density calculation and optical microstructures to discuss the distribution of GNPs. The tensile test was conducted to determine the strength of the developed MMCs and also supported by fractographic analysis. In addition to it, the Rockwell hardness test and impact test (toughness) with fracture analysis were also conducted to strengthen the present work. Findings The results reveal the uniform distribution of GNPs into the matrix material. The yield strength and ultimate tensile strength obtained a maximum value of 155.67 MPa and 170.28 MPa, respectively. The hardness value (HRB) is significantly increased and 84 HRB was obtained for the sample with AA1100/0.4% GNP, while maximum hardness value (94 HRB) was obtained for the sample AA1100/1.2% GNP. The maximum value of toughness 14.3 Jules/cm2 is recorded for base alloy AA1100 while increasing the reinforcement percentage, it decreases up to 9.7 Jules/cm2 for AA1100/1.2% GNP. Originality/value Graphene nanoparticles are used to develop nanocomposites, which is one of the suitable alternatives for heavy engineering materials such as steels and cast irons. It has improved microstructural and mechanical properties which makes it preferable for many engineering and structural applications.

A rigorous analysis of unsteady electrically conducting nanofluid with MHD effect is presented. First, the governing partial differential equations for momentum and energy conservation are converted to couple nonlinear ordinary differential equations by means of exact similarity transformation. The Tiwari-Das nanofluid model is employed to obtain the analytical approximations for flow velocity and temperature distributions of alumina-sodium alginate nanofluid using HAM. The solution is found to be dependent on some parameters including the nanoparticle volume fraction, unsteadiness parameter, magnetic parameter, mixed convection parameter and the generalized Prandtl number. A systematic study is carried out to illustrate the effects of these parameters on the velocity and temperature distributions. Also, the value of skin friction coefficient and local Nusselt number are evaluated with variation of Prandtl number and compared with different nanoparticles.