Effects of nonlinear velocity slip and temperature jump onpseudo-plastic power-law fluid over moving permeable surface in presence of magnetic field

Flow and heat transfer of a pseudo-plastic power-law fluid over a stretching permeable surface with the magnetic effect is investigated. In the boundary conditions,the nonlinear temperature jump and the velocity slip are considered. Semi-similarity equations are obtained and solved by bvp4c with MATLAB. The problem can be considered as an extension of the previous work done by Mahmoud(Mahmoud, M. A. A. Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation. Mathematical and Computer Modelling, 54, 1228–1237(2011)). Efforts are made to discuss the effects of the power-law number, slip velocity, and temperature jump on the dimensionless velocity and temperature distribution.

Lattice Boltzmann Method for Simulating the Temperature Jump and Velocity Slip in Microchannels

The velocity slip and temperature jump in micro-Couette flow are investigated with the lattice Boltzmann method(LBM).A new slip boundary condition with the non-equilibrium extrapolation scheme is used in a thermal lattice Boltzmann model(TLBM)where double distribution functions are used to simulate the velocity and the temperature fields in order to capture the velocity slip and the temperature jump of the wall boundary.The simulated velocity and temperature profiles are in good agreement with the analytic results,which shows the suitability of the present model and the new boundary treatment for describing thermal microflows with viscous heat dissipation.

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Slip boundary conditions for rough surfaces

The velocity slip and temperature jump for a two-dimensional rough plate under hypersonic conditions were analyzed using the Direct Simulation Monte Carlo(DSMC)method.Surface roughness was explicitly modeled by introducing various structures on the flat plate.The influences of relative roughness height,which involves the roughness height,roughness spacing,incoming velocity,and the degree of rarefaction,were analyzed and discussed.It is found that with the increase of the relative roughness height,the jump temperature increases,while the slip velocity decreases gradually.The effects of surface roughness on the slip coefficients can be attributed to the change of accommodation coefficients.A new slip model for rough surfaces was established in this paper,which accounts for the coupling effects of gas rarefaction and surface roughness,without the effort to model the surface roughness explicitly.The nitrogen flows in the microchannel,and flows over a blunt cone and an axisymmetric bi-conic body,were simulated under the modified and conventional slip boundary conditions,respectively.The numerical solutions were validated with experimental data.It can be safely concluded that compared with the traditional first-order slip boundary conditions,the modified slip model improves the accuracy of macroscopic properties,especially the heat transfer coefficient.

Interplay of non-conducting and conducting walls on magnetohydrodynamic(MHD)natural convection flow in vertical micro-channel in the presence of induced magnetic field

In this research paper,exact solution for fully developed magnetohydrodynamic(MHD)natural convection flow of viscous,incompressible,electrically conducting fluid in parallel walls in the presence of velocity slip and temperature jump at the micro-channel walls electrically conducting fluid in the presence of transverse magnetic field is taken into equations are coupled.The exact solutions in dimensionless form have been obtained under temperature field,induced current density and skin friction have been obtained.The effects of interaction,Hartmann number and the magnetic Prandtl number are demonstrated through number causes a pronounced reduction in volume flow rate.

Impact of induced magnetic field on magnetohydrodynamic(MHD)natural convection flow in a vertical annular microchannel in the presence of radial magnetic field

This study is devoted to investigate the effect of induced magnetic field on fully developed magnetohydrodynamic(MHD)natural convection flow of electrically conducting fluid in a vertical annular micro-channel formed by two concentric cylinders in the presence of imposed radial magnetic field.The velocity slip and temperature jump at the annular micro-channel surfaces are taken into account.The influence of induced magnetic field arising due to the motion of an electrically conducting fluid is taken into consideration.The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained under relevant boundary conditions.The expressions for velocity field,the induced magnetic field,temperature field,induced current density and skin friction have been obtained.A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity field,the induced magnetic field,temperature,induced current density,volume flow rate and skin friction are illustrated graphically to show interesting features of the radius ratio,rarefaction,fluid wall interaction,Hartmann number and the magnetic Prandtl number.During the course of investigation,it is found that for fixed value of Hartmann number,the skin friction profiles in the presence of induced magnetic field are higher compared to the case when the induced magnetic field is neglected.

Axisymmetric stagnation-point flow over a stretching/shrinking plate with second-order velocity slip

The axisymmetric stagnation point flow over a stretching/shrinking surface with second-order slip and temperature jump is studied numerically.The governing partial differential equations are transformed into ordinary(similarity)differential equations.These equations along with the corresponding boundary conditions are solved numerically using a boundary value problem solver bvp4c in Matlab software.It is observed that dual(first and second)solutions exist for the similarity equations.The effects of different parameters on the velocity and the temperature distributions as well as the skin friction coefficient and the Nusselt number are analyzed and discussed.

Interplay of conducting and non-conducting walls on hydromagnetic natural convection flow in a vertical micro-channel with Hall current

Theoretical investigation on the interaction between conducting and nonconducting walls on hydromagnetic natural convection flow of viscous incompressible and electrically conducting fluid through a vertical micro-channel taking into account the effects of induced magnetic field in presence of Hall current is presented.Governing coupled equations responsible for the flow are obtained when either the micro-channel walls are electrically conducting or are electrically non-conducting.Using the method of undetermined coefficients,exact solution are obtained and presented in dimensionless form subject to relevant boundary conditions.Expressions for fluid velocity,induced magnetic field,skin friction,volume flow rate and induced current density in both primary and secondary flow directions are also obtained.Effects of some governing parameters like Hall current parameter,rarefaction parameter and Hartmann number on the different flow situations are given using the aid of line graphs and Tables.The main conclusion of the present analysis is that,in the existence of rarefaction parameter,primary fluid velocity could be enhanced with the increase in Hall parameter when the micro-channel walls are either insulated or when the left micro-channel wall is electrically conducting.Results obtained in this work are relevant in many magnetically controlled devices and could also be used as a benchmark in checking the accuracies of result obtained in some empirical experiments.