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This paper presents the effects of various properties on nanofluid flows and heat transfer over a permeable stretching sheet of variable thickness in the presence of a transverse magnetic field. Mathematically, the leading coupled partial differential equations are transformed into a self-similar system of ordinary differential equations through similarity variables, which are solved thereafter using Keller-box and Haar’s wavelet methods. Moreover, the impacts of various flow parameters involved in the physical problem are discussed thoroughly via tables and graphs. As findings, the analysis discloses that the nanofluid flow is significantly influenced by the physical parameters. Dynamically, the nanofluid flow is accelerated prominently with the strengthening in the injection process and decelerated in other situations. Furthermore, the obtained results are compared successfully with the earlier published findings. [ABSTRACT FROM AUTHOR]

The present investigation is to analysis the solution of steady state boundary layer flow and heat transfer past an exponential shrinking surface. The governing equations describes physics of the problem and are transformed into system of nonlinear ordinary differential equations through suitable similarity transformations. The similarity solutions of these equations are obtained by using semi-numerical technique, viz. shifted Chebyshev collocation method. The occurrence of dual solution is observed for both velocity and temperature profiles. The analysis shows, for a particular range of mass suction parameter, boundary layer flow over an exponential shrinking sheet is exist and enhancement in mass suction parameter increases the skin friction coefficient for the upper branch solution and reverse behavior is observed for lower branch solution. Whereas, both the solutions of temperature profiles decrease with increasing values of the Prandtl number. The computed results are validated with the earlier finding and are comparable. [ABSTRACT FROM AUTHOR]

The paper presents, surface roughness effect for thermo-hydrodynamic analysis of journal bearings extended to couple stress lubricants with high polymer additives. A modified energy equation is simultaneously solved with heat transfer equation as well as modified Reynolds equation by using Multigrid method. The effects of couple stress and surface roughness on the performances of a finite journal bearing are presented in detail. Further, it is shown that lubricants with couple stress and surface roughness, not only increases the load capacity and decreases the friction coefficient, but also generates a lower bearing temperature field. Thus, the lubricant with couple stress improves the performance of journal bearings. The characteristics of bearing are compared with numerical results.

The boundary roughness effects on nonlinear saturation of Rayleigh-Taylor instability (RTI) in couple-stress fluid have been studied using numerical technique on the basis of stability of interface between two fluids of the system. The resulting fourth order ordinary nonlinear differential equation is solved using Adams-Bashforth predictor and Adams-Moulton corrector techniques numerically. The various surface roughness effects and surface tension effects on nonlinear saturation of RTI of two superposed couple-stress fluid and fluid saturated porous media are well investigated. At the interface, the surface tension acts and finally stability of the problem is discussed in detail.

This paper presents Dirichlet series and approximate analytical solutions of magnetohydrodynamic (MHD) flow due to a suction / blowing caused by boundary layer of an incompressible viscous flow. The governing nonlinear partial differential equations of momentum equations are reduced into a set of nonlinear ordinary differential equations (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use elegant fast converging Dirichlet series and approximate analytical solutions (method of stretching of variables) of these nonlinear differential equations. These methods have advantages over pure numerical methods for obtaining derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domains as compared with DTM-Padé and classical numerical schemes.

In this article, the lubrication of a long porous slider in which the fluid is injected into the porous bottom is considered. The similarity transformations reduce the governing problem of Navier-Stokes equations to coupled nonlinear ordinary differential equations which are solved by HAM. Solutions are obtained for much larger values of Reynolds number compared to analytical and numerical methods. The results comprise good agreement between approximate and numerical solutions. HAM gives rapid convergent series solutions which show that this method is efficient, accurate and has advantages over other methods. Further, homotopy-pade’ technique is used to accelerate the convergence of series solution.

The paper presents Elastohydrodynamic lubrication line contact problem with bio-based oil as lubricants for an isothermal case. The fast convergence method for the solution of Elastohydrodynamic lubrication line contact problem with seed oil as lubricant is analyzed using Multigrid, Multilevel Multi-Integration with the influence of different load and speed. The result shows that the use of these oils has the potential to substitute the function of common lubricant so as to reduce dependence on conventional oil lubricants. The results obtained are comparable and the pressure spikes are smooth as compared to the earlier findings which are shown in terms of graphs and tables.

The paper presents the numerical solution of line contact thermal elastohydrodynamic lubrication (EHL) with bio-based lubricant. The model comprises Reynolds equation, film thickness, load balance and energy equations with appropriate boundary conditions by incorporating viscosity–pressure–temperature and density–pressure–temperature relations. Second-order finite difference scheme is used for the discretised form and their equation. The multigrid method with full approximation scheme is used to solve the Reynolds equation along with multilevel multi-integration method for film thickness equation. The pressure, film thickness and temperature distributions for two rolling velocities and various loads with a bio-based lubricant are presented in detail. The present findings yield a reduction in the minimum film thickness for high speed. Details of pressure spike as a function of relevant parameters are given. The results are compared with earlier findings based on different methods. [ABSTRACT FROM AUTHOR]

The paper presents steady isothermal elastohydrodynamic lubrication (EHL) of elliptical contact with Roelands pressure–viscosity model over varying rotational speed. The governing Reynolds and film-thickness equation for elliptical contact in roller bearings are analysed by using multigrid method with full approximation scheme. The non-dimensional pressure distribution and film-thickness for elliptical contacts are obtained. The distinct friction models appropriate to lubricants in contact regions are predicted. The result shows that rolling contact weariness does not occur on the surfaces with longitudinal roughness and wear or scraping exists in circular EHL contacts with entrainment along major axis to that of minor axis. The computation predicts that minimum film thickness, central film thickness and elastic deformation increase as the rotational speed increases. The computed results are compared with earlier finding which are in good agreement. [ABSTRACT FROM AUTHOR]

The paper presents analysis of two-dimensional non-Newtonian incompressible viscous flow between parallel plates. The governing problem of momentum equations are reduced to nonlinear ordinary differential equation (NODE) using similarity transformations. The resulting equation is solved using computer extended series solution (CESS) and homotopy analysis method (HAM). These methods have advantages over pure numerical methods for obtaining the derived quantities accurately for various values of parameters and results are valid in much larger parameter domain compared with numerical schemes. [ABSTRACT FROM AUTHOR]

The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet caused by boundary layer of an incompressible viscous flow. The governing three partial differential equations of momentum equations are reduced into ordinary differential equation (ODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel mathematical tools for their analysis. We use fast converging Dirichlet series and Method of stretching of variables for the solution of these nonlinear differential equations. These methods have the advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and also they are valid in much larger parameter domain as compared with HAM, HPM, ADM and the classical numerical schemes. [ABSTRACT FROM AUTHOR]

The paper presents the semi-numerical solution for the magnetohydrodynamic (MHD) viscous ow due to a stretching sheet caused by boundary layer of an incompressible viscous ow. The governing partial differential equations of momentum equations are reduced into a nonlinear ordinary differential equation (NODE) by using a classical similarity transformation along with appropriate boundary conditions. Both nonlinearity and infinite interval demand novel the mathematical tools for their analysis. The solution of the resulting third order nonlinear boundary value problem with an infinite interval is obtained using fast converging Dirichlet series method and approximate analytical method viz. method of stretching of variables. These methods have the advantages over pure numerical methods for obtaining the derived quantities accurately for various values of the parameters involved at a stretch and they are valid in much larger parameter domain as compared with HAM, HPM, ADM and the classical numerical schemes. Also, these methods require less computer memory space as compared with pure numerical methods. [ABSTRACT FROM AUTHOR]