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The aim and significance of paper presents, the semi-numerical investigation of magnetohydrodynamic flow of micropolar nanofluid with stagnation point is carried out under the influence of viscous dissipation and heat generation. The micropolar nanofluids are electrically conducting non-Newtonian fluids. The important applications of these fluids are observed in many research areas viz. bioengineering, biofuels and biomedical sectors etc. The appropriate similarity transformations are used to transform the governing equations into system of coupled nonlinear ordinary differential equations and are solved by using shifted Chebyshev collocation method and Haar wavelet collocation method. The variations in velocity, angular velocity, temperature and concentration profiles under the impact of various physical parameters, characterizing the flow field are discussed and are presented via graphs and tables. Temperature enhancement occurs with increment in each parameter except for Prandtl number. The concentration near the surface decreases with increment in the values of parameters and gradually it increases, except for Prandtl number and Schmidt number. The reverse trend of heat transfer occurs​ near a surface, when the dominance of stream velocity over stretching velocity is observed. [ABSTRACT FROM AUTHOR]

The paper presents the boundary layer flow of mass transfer on a continuous flat plate moving in parallel or reversely to a free stream with a chemical reaction. By using suitable similarity transformations, the boundary-layer equations are transformed into coupled nonlinear ordinary differential equations (NODEs) over semi-infinite interval. These equations have been analysed using a novel semi-numerical method, viz. spectral method. The dual solutions for velocity and concentration distributions are determined using Chebyshev collocation method (CCM) and the results are presented in the form of tables and graphs. The obtained spectral solutions are compared with previously published results and are comparable. Many interesting physical properties of the problem are observed and verified through both theoretical as well as semi-numerical approach. The derived quantities show that the mass transfer rate is established to be increased as the Schmidt number increases for the solution of the upper branch and reduces for the solution of lower branch.

ABSTRACTThe 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.

ABSTRACTThe 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.

In this article, the investigation is made to shed a light on the influence of convective boundary conditions on the boundary layer flow over a linearly stretching flat surface. The equations (partial differential equations) describing the model are transformed into system of nonlinear ordinary differential equations using similarity transformations. Equations contain various non-dimensional flow characterizing numbers viz. Prandtl number Pr,Lewis number Le,Biot number Bi, Brownian motion parameter Nband thermophoresis parameter Nt. The influence of these parameters on thermal boundary layer, concentration distribution and temperature are analyzed in detail, by solving the equations using novel Shifted Chebyshev collocation method. The computed results, reduced Nusselt number, reduced Sherwood number, surface temperature and concentration profiles as functions of dimensionless numbers are validated by comparing the predicted results with available earlier findings (using other methods). To assert the convergence and stability of the scheme used (for much larger, but moderate, parameters values), predicted results are presented in various tabular forms. For presenting finer details of the computed values some results are also given graphically. The innovative semi-numerical scheme is robust and efficient compared with other conventional methods, used in previous studies and enables the analysis of the complex problem adequately.

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.

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.