Dirichlet series and approximate analytical method for the solution of mhd boundary layer flow of casson fluid over a stretching/shrinking sheet

The paper presents analytical and semi-numerical solution for magnetohydrodynamic (MHD) boundary layer flow of Casson fluid over a exponentially permeable shrinking sheet. The governing partial differential equations of momentum equations are reduced to ordinary differential equations 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 approximate analytical solution by the Method of stretching of variables for the solution of the nonlinear differential equation. 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.Publisher's Versio

A multigrid method for EHL line contact problem with Grease as lubricant

The paper presents an isothermal Elastohydrodynamic lubrication (EHL) of line contact problem with grease as a lubricant, described by Herschel-Bulkley model. The simulation of the governing problem is analyzed using Multigrid method with full approximation scheme (FAS) for varying load, speed and rheological index n Herschel-Bulkley model. The EHL problem considered comprises of Reynolds equation and film thickness understudy for different parameters of interest. The minimum film thickness and pressure spike decrease with a decrease in rheological index n. The present paper traces out the comparison of minimum film thickness with the standard results of Dowson and Higginson. The results obtained are comparable and are presented in terms of graphs and tables

Surface roughness effect on thermohydrodynamic analysis of journal bearings lubricated with couple stress fluids

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

Series analysis for the flow between two stretchable disks

In this paper, we present the semi-analytical/semi-numerical solution of an axis-symmetric flow between two coaxial infinite stretching disks. The governing momentum equations in cylindrical co-ordinates are reduced to fourth order nonlinear ordinary differential equation (NODE) with the relevant boundary conditions. The resulting nonlinear boundary value problem is solved by using Computer Extended Series Solution (CESS) and Homotopy Analysis Method (HAM). The effects of Reynolds number R and disk stretching parameter γ are discussed in detail. The resulting solutions are compared with the earlier numerical findings. The above methods admit a desired accuracy and the results are presented in the form of graphs. The validity of the series solution is extended to a much larger values of R up to infinity. Further, the variations of shear stress and pressure parameter as a functions of R and γ are analyzed. For very large R, the governing equation reduces to third order NODE with infinite boundary is solved by using Dirichlet series and the solution is compared with the numerical findings

Effect of boundary roughness on nonlinear saturation of Rayleigh-Taylor instability in couple-stress fluid

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

Numerical Solution for Thermal Elastohydrodynamic Lubrication of Line Contact with Couple Stress Fluid as Lubricant

In this paper, the detail analysis of the influence of thermal and non-Newtonian aspects of lubricant (couple stress fluid) on EHL line contact as a function of slide-roll ratio is presented. The novel low complexity FAS(Full approximation scheme), of  Multigrid scheme, with Jacobi dipole and Gauss Seidel relaxationis used for the solution of coupled equations viz.modified Reynolds equation, film thickness equation and energy equation satisfying  appropriate boundary conditions. The analysis reveals the combined influence of non-Newtonian, thermal and slide-roll ratio (of bearing movingwith different speeds) on pressure, film thickness and pressure spike covering wide range of physical parameters of interest. Results show that pressure spike is strongly influenced by thermal, slide-roll ratio and non-Newtonian character of lubricant with negligible effect on overall pressure distribution. Also, minimum film thickness is slightly altered and it increases with increase in couple stress parameter. These findings confirm the importance of non-Newtonian and thermal effects in the study of EHL

Convective heating and mass transfer in Buongiorno model of nanofluid using spectral collocation method of shifted Chebyshev polynomial

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 Nb and 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