Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects

Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.

Two-component modeling for non-Newtonian nanofluid slip flow and heat transfer over sheet: Lie group approach

The present paper deals with the multiple solutions and their stability analy- sis of non-Newtonian micropolar nanofluid slip flow past a shrinking sheet in the presence of a passively controlled nanoparticle boundary condition. The Lie group transformation is used to find the similarity transformations which transform the governing transport equations to a system of coupled ordinary differential equations with boundary condi- tions. These coupled set of ordinary differential equation is then solved using the Runge- Kutta-Fehlberg fourth-fifth order （RKF45） method and the ode15s solver in MATLAB. For stability analysis, the eigenvalue problem is solved to check the physically realizable solution. The upper branch is found to be stable, whereas the lower branch is unsta- ble. The critical values （turning points） for suction （0 〈 sc 〈 s） and the shrinking parameter （Xc 〈 X 〈 0） are also shown graphically for both no-slip and multiple-slip conditions. Multiple regression analysis for the stable solution is carried out to inves- tigate the impact of various pertinent parameters on heat transfer rates, The Nusselt number is found to be a decreasing function of the thermophoresis and Brownian motion parameters.

Numerical solution of thermo-solutal mixed convective slip flow from a radiative plate with convective boundary condition

A mathematical model for mixed convective slip flow with heat and mass transfer in the presence of thermal radiation is presented. A convective boundary condition is included and slip is simulated via the hydrodynamic slip parameter. Heat generation and absorption effects are also incorporated. The Rosseland diffusion flux model is employed. The governing partial differential conservation equations are reduced to a system of coupled, ordinary differential equations via Lie group theory method. The resulting coupled equations are solved using shooting method. The influences of the emerging parameters on dimensionless velocity, tempera- ture and concentration distributions are investigated. Increasing radiative-conductive parameter accelerates the boundary layer flow and increases temperature whereas it depresses concentration. An elevation in convection-conduction parameter also accelerates the flow and temperatures whereas it reduces concentrations. Velocity near the wall is considerably boosted with increasing momentum slip parameter although both temperature and concentration boundary layer thicknesses are decreased. The presence of a heat source is found to increase momentum and thermal boundary layer thicknesses but reduces concentration boundary layer thickness. Excelle- nt correlation of the numerical solutions with previous non-slip studies is demonstrated. The current study has applications in bio- reactor diffusion flows and high-temperature chemical materials processing systems.

Stefan blowing effect on bioconvective flow of nanofluid over a solid rotating stretchable disk

A mathematical model for the unsteady forced convection over rotating stretchable disk in nanofluid containing microorganisms and taking into account Stefan blowing effect is presented theoretically and numerically.Appropriate transfonnations are used to transform the governing boundary layer equations into non-linear ordinary differential equations,before being solved numerically using the Runge-Kutta-Fehlberg method.The effect of the governing parameters on the dimensionless velocities,temperature,nanoparticle volume fraction(concen­tration),density of motile microorganisms as well as on the local skin friction,local Nusselt,Sherwood number and motile microorganisms numbers are thoroughly examined via graphs.It is observed that the Stefan blowing increases the local skin friction and reduces the heat transfer,mass transfer and microorganism transfer rates.The numerical results are in good agreement with those obtained from previous literature.Physical quantities results from this investigation show that the effects of higher disk stretching strength and suction case provides a good medium to enhance the heat,mass and microorganisms transfer compared to blowing case.

Natural convective heat transfer in a square enclosure utilizing magnetic nanoparticles

In the present paper,unsteady natural convective heat transfer flow inside a square enclosure filled with nanofluids containing magnetic nanoparticles using nonhomogeneous dynamic model is investigated numerically.The horizontal top wall of the enclosure is considered a colder wall and the bottom wall is maintained at uniform temperature whereas two other vertical walls of the cavity are thermally insulated.The Galerkin weighted residual finite element method has been used to solve the governing non-dimensional partial differential equations.In numerical simulations,four types of nanoparticles such as magnetite(Fe_(3)O_(4)),cobalt ferrite(CoFe_(2)O_(4)),Mn-Zn ferrite(Mn-ZnFe_(2)O_(4)),and silicon dioxide(SiO2),and three types of base fluids such as water(H_(2)O),engine oil(EO)and kerosene(Ke)have been considered.Comparisons with previously published work are performed and excellent agreement is obtained.The effects of various model parameters such as thermal Rayleigh number,nanoparticles volume fraction and nanoparticles shape factor are studied.The results show that the average Nusselt number increases as the thermal Rayleigh number and nanoparticles volume fraction intensify.The results indicate that the average Nusselt numbers are higher for the blade shape of nanoparticles.

Electrostatic Nonplanar Positron-Acoustic Shock Waves in Superthermal Electron-Positron-Ion Plasmas

The basic properties of the nonlinear propagation of the nonplanar （cylindrical and spherical） positronacoustic （PA） shock waves （SHWs） in an unmagnetized electron-positron-ion （e-p-i） plasma containing immobile positive ions, mobile cold positrons, and superthermal （kappa distributed） hot positrons and electrons are investigated both analytically and numerically. The modified Burgers equation （roBE） is derived by using the reductive perturbation method. The basic features of PA SHWs are significantly modified by the cold positron kinematic viscosity （U）, superthermal parameter of electrons （ke）, superthermal parameter of hot positrons （kp）, the ratio of the electron temperature to hot positron temperature （or）, the ratio of the electron number density to cold positron number density （μe）, and the ratio of the hot positron number density to cold positron number density （μph）. This study could be useful to identify the basic properties of nonlinear electrostatic disturbances in dissipative space and laboratory plasmas.

Melting and second order slip effect on convective flow of nanofluid past a radiating stretching/shrinking sheet

A mathematical model is presented for forced convective slip flow of a nanofluid past a radiating stretching/shrinking sheet.Melting boundary condition is taken into account.The nanofluid model involves the Brownian motion and thermophoresis effects.Lie group transformation is used to the transport equations as well as the boundary conditions to develop the similarity equations,before being solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order numerical method.To show the effects of the controlling parameters on the dimensionless velocity,temperature,nanoparticle volume fraction,skin friction factor,local Nusselt,and local Sherwood numbers,numerical results are presented both in graphical and tabular forms.It is found that the friction factor decreases with slip and melting parameters for both stretching/shrinking sheets.It is also found that the Nusselt number decreases with the first order slip while it increases with melting and radiation parameters in both cases.Also,the Sherwood number decreases with the melting parameter both for radiating and non-radiating stretching/shrinking sheets.An excellent agreement is found between the present numerical results and published results.