Thermal Slip Effects Research Articles

An analysis of Maxwell fluid through a shrinking sheet with thermal slip effect: a Lie group approach

Two-dimensional magnetohydrodynamic (MHD) boundary layer flow of an upper-convected Maxwell (UCM) fluid passing through the shrinking sheet is considered. With the impact of thermal slip, thermal radiation and heat source-sink conditions, the UCM fluid model is integrated. The method of the Lie scaling group is used to transform the strongly nonlinear governing partial differential equations (PDEs) into the ordinary differential equations (ODEs). The transformed ODEs are numerically solved using NDSolve command of MATHEMATICA and graphically presented with their results. The Deborah number’s influence on the velocity profile $$f^{\prime } (\eta )$$ is studied for different values and different behavior observed. The Hartmann number M and the mass transfer parameter S have decreased the boundary layer thickness. The Prandtl number has increased the temperature profile $$\theta (\eta )$$ . In contrast, the thermal boundary layer thickness was decreased by the heat source-sink parameter Q , the radiation parameter R and the thermal slip parameter L. Table 1 shows the verification of the results.

Velocity and thermal slip effects on MHD nanofluid flow past a stretching cylinder with viscous dissipation and Joule heating

The motivation behind the current study is to investigate the flow and heat characteristics of magnetohydrodynamic (MHD) silver–water (Ag/H2O) nanofluid under the influence of Joule heating and viscous dissipation over a stretching cylinder in the presence of suction/injection and slip boundary conditions. Problem formulation is created considering low magnetic Reynolds number subjected to boundary layer theory. Two different models of thermal conductivity and dynamic viscosity based on unlike shapes of nanoparticles, namely spherical and cylindrical (nanotubes), are also considered. The associated PDEs related to conservation terms of hydroflow and hydrothermal are molded to system of non-dimensional ODEs with the help of appropriate similarity transformation. The obtained nonlinear equations are solved with the help of numerical approach Runge–Kutta–Fehlberg (RKF) fourth–fifth order via shooting algorithm. The convergence of its solution profiles has been demonstrated through graphs and numerical data. A detailed parametric study is performed to describe the influences of relevant physical parameters on velocity and temperature profiles. Nusselt number is also tabularized and examined for both models. Some of the results of the investigation are effects of magnetic parameter and thermal slip to decrease the velocity profiles, which in turn causes the increment in temperature profiles. Moreover, temperature fields show a similar behavior for dissipation and heat generation/absorption parameter, but the reverse trend is observed in the case of suction/blowing parameter. The computed results are validated with existing ones for limiting sense and provided excellent agreement.

Partial slip in Darcy-Forchheimer carbon nanotubes flow by rotating disk

This article intends to illustrate the velocity and thermal slip effects in Darcy-Forchheimer flow by a rotating disk. Viscous dissipation is considered. Carbon nanotubes of two types (recognized as SWCNTs and MWCNTs) are utilized. Suitable variables are introduced for conversion of partial differential expressions into a system of ordinary differential equations. Computation of nonlinear system is arranged by optimal homotopic analysis technique (OHAM). Behaviors of involved variables on quantities of interest are graphically examined. Skin friction coefficients are increasing functions of velocity slip parameters. Local heat transfer rate has similar response for thermal slip parameter and Eckert number.

Entropy Analysis of an MHD Synthetic Cilia Assisted Transport in a Microchannel Enclosure with Velocity and Thermal Slippage Effects

The magnitude of shear stress at the ciliated wall is considered as the measure of efficiency of cilia beatings as it describes the momentum transfer between the medium and the cilia. Under high shear rate, some non-Newtonian fluids behave as visco-inelastic fluids. We consider here a ciliated channel coated with Prandtl fluid, a visco-inelastic fluid, with Hartmann layer under momentum and thermal slip effects. The flow in the channel is produced due to beatings of cilia that obey an elliptic path of motion in the flow direction. An entropy analysis of the flow is also conducted in wave frame. After introducing lubrication approximations in the governing equation, the perturbation solutions are calculated. The data for pressure rise per metachronal wavelength and frictional force at the ciliated wall are obtained by numerical integration. The analysis reveals that the higher values of cilia length and velocity slip parameters support fluid flow near the channel wall surface. Fluid temperature is an increasing function of thermal slip but a decreasing function of cilia length and slip parameters. Entropy in the channel can be minimized with an increase in cilia length and slip effect at the boundary. The magnitude of the heat transfer coefficient decreases by taking the substantial slippage and tiny cilia in length at the microchannel wall.

Micropolar flow of EMHD nanofluid with nonlinear thermal radiation and slip effects

Magneto-micropolar electrically conducting nanofluid flow over a linearly stretching sheet for heat and mass transfer in the presence of convective boundary condition is considered. In the energy equation, non-linear thermal radiation and Joule heating effects are incorporated. Velocity slip condition at the solid liquid interface is also employed. In the current model viscous dissipation and mixed convection aspects are also taken into account. Non dimensional ordinary differential equations are acquired by implementing the similar transformations on the governed partial differential equations. The shooting technique is utilized along with Runga-Kutta integration scheme to tackled the differential equations numerically. All the numerical calculations are further verified with MATLAB bvp4c scheme. Graphical results are exploited to view the behavior of emerging parameters on velocity, temperature and concentration of nanofluid. In limiting case, MATLAB code is verified with a published article and a good agreement is noted. Numerical computations are performed for the local Sherwood and Nusselt number and skin friction coefficients. It is observed that the electric field is dominant over the magnetic field. The behavior of velocity profile is reserved in the absence of the electric field. Further, the nonlinear thermal radiation aggregates the temperature profile.

Numerical and perturbation solutions of third-grade fluid in a porous channel: Boundary and thermal slip effects

The steady flow of a third-grade fluid due to pressure gradient is considered between parallel plane walls which are kept at different temperatures. The space between the plane walls is assumed to be a porous medium of constant permeability. The viscosity of the fluid is taken as constant as well as a function of temperature. It is further assumed that the fluid may slip at the wall surfaces. The consequence of this assumption results in non-linear boundary conditions at the plane walls. The temperature field is also supposed to satisfy thermal slip condition at the walls. The governing equations are modelled under these assumptions and the approximate solution is obtained using the perturbation theory. The skin friction coefficient is a decreasing function of slip parameters in the case of temperature-dependent viscosity models while no variation is noted for the case of constant viscosity via boundary slip parameter. The heat transfer rate increases with the boundary slip parameter and decreases with the thermal slip parameter. The validity of the approximated solution is checked by calculating the numerical solution as well. The absolute error is calculated and listed in tabular form in the case of constant and temperature-dependent viscosity via boundary and thermal slip parameters. The influence of various emerging parameters on flow velocity and temperature profile is discussed through graphs.

Effect of Thermal Radiation, Temperature Jump and Inclined Magnetic Field on the Peristaltic Transport of Blood Flow in an Asymmetric Channel with Variable Viscosity and Heat Absorption/Generation

This article is aimed at describing the effect of thermal radiation, heat source/sink and thermal slip on the peristaltic flow of blood in an asymmetric channel. Mathematical analysis has been carried out in the presence of aligned magnetic field. The physical problem is first modeled, and then, the solutions of coupled nonlinear differential equations are obtained by means of regular perturbation method. Assumptions of long wavelength and low Reynolds number approximations were adopted. Physical characteristics of various embedded parameters such as Hartmann number, radiation parameter, aligned magnetic field parameter and heat source/sink parameter are illustrated and discussed graphically.

Effect of Brownian Diffusion on Squeezing Elastico-Viscous Nanofluid Flow with Cattaneo-Christov Heat Flux Model in a Channel with Double Slip Effect

The present study deals with the analysis of heat transfer of the unsteady Maxwell nanofluid flow in a squeezed rotating channel of a porous extensile surface subject to the velocity and thermal slip effects incorporating the theory of heat flow intensity of Cattaneo-Christov model for the expression of the energy distribution in preference to the classical Fourier’s law. A set of transformations is occupied to renovate the current model in a system of nonlinear ordinary differential equations that are numerically decoded with the help of MATLAB integrated function bvp4c. The effects of various flow control parameters are investigated for the momentum, temperature and diffusion profiles, as well as for the wall shearing stress and the heat and mass transfer. The results are finally described from the material point of view. A comparison of heat flux models of Cattaneo-Christov and Fourier is also performed. An important result from the present work is that the squeezing parameter is strong enough in the middle of the channel to retard the fluid flow.

Comment on the paper “Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: Modified Legendre wavelets approach, Feroz Ahmed Soomro, Muhammad Usman, Rizwan Ul Haq, W. Wang” [Phys. E Low-dimens. Syst. Nanostruct. 104 (2018) 130–137

Comment on the paper “Thermal and velocity slip effects on MHD mixed convection flow of Williamson nanofluid along a vertical surface: Modified Legendre wavelets approach, Feroz Ahmed Soomro, Muhammad Usman, Rizwan Ul Haq, W. Wang” [Phys. E Low-dimens. Syst. Nanostruct. 104 (2018) 130–137

Dual Solutions and Stability Analysis of Micropolar Nanofluid Flow with Slip Effect on Stretching/Shrinking Surfaces

The purpose of the present paper is to investigate the micropolar nanofluid flow on permeable stretching and shrinking surfaces with the velocity, thermal and concentration slip effects. Furthermore, the thermal radiation effect has also been considered. Boundary layer momentum, angular velocity, heat and mass transfer equations are converted to non-linear ordinary differential equations (ODEs). Then, the obtained ODEs are solved by applying the shooting method and in the results, the dual solutions are obtained in the certain ranges of pertinent parameters in both cases of shrinking and stretching surfaces. Due to the presence of the dual solutions, stability analysis is done and it was found that the first solution is stable and physically feasible. The results are also compared with previously published literature and found to be in excellent agreement. Moreover, the obtained results reveal the angular velocity increases in the first solution when the value of micropolar parameter increases. The velocity of nanofluid flow decreases in the first solution as the velocity slip parameter increases, whereas the temperature profiles increase in both solutions when thermal radiation, Brownian motion and the thermophoresis parameters are increased. Concentration profile increases by increasing N t and decreases by increasing N b .

Numerical analysis of water based CNTs flow of micropolar fluid through rotating frame

BackgroundIn this article, the nanomaterial flow of micropolar fluid in rotating frame is considered. The SWCNT and MWCNT with base fluid namely pure water is also taken into account to analyze the flow behavior over stretching surface. Mathematical model have been constructed under the nanomaterial of micropolar fluid. MethodThe governing equations have been developed in the form of system of partial differential equations. The partial differential equations are transformed into ordinary differential equations using similarity transformations. The transformed system has been solved through MAPLE software. ResultsThe physical parameters like as thermal slip effects, velocity slip effects and magnetic hydrodynamics on the micropolar nanofluid are presented by tables and graphs. Surprisingly in the rotating parameter, F′′(0) and − θ′(0) increases for higher values of the rotating parameter while opposite to be noted for G′′(0). The Nusselt number and skin friction increases for higher values of micropolar parameter but MWCNT achieves higher heat transfer as associated to SWCNT.

3D Bioconvective multiple slip flow of chemically reactive Casson nanofluid with gyrotactic micro‐organisms

AbstractIn the present study, we investigate the velocity, thermal, solutal, and motile micro‐organism (MM) slip effects on the flow of chemically reactive Casson nanofluid flowing over an exponentially stretched electromagnetic sheet in the presence of a chemical reaction. In addition, a mechanism of improving the motion of nanoparticles (Brownian motion and thermophoresis) is incorporated. The nondimensionalized ordinary differential equations are tackled by using symbolic computation software, MATLAB 2012b, with bvp4c function. Some significant and relevant characteristics of associated profiles are displayed graphically and discussed beautifully with the aid of tables through comprehensive numerical computations. The results of the study show that elevated Casson fluid parameter, gyrotactic micro‐organism, and electromagnetic strength belittle both axial as well as transverse velocities and the related momentum boundary layer thickness. Another important outcome is that low Prandtl fluids and enhancement in the strength of electromagnetic field fasten the diffusion of micro‐organisms, thereby augmenting the density of MM in the related boundary layer.

Peristalsis of carbon nanotubes with radiative heat flux

The purpose of this analysis is to highlight the CNTs characteristics in peristaltic flows through non-uniform channels. Viscosity is considered temperature in this analysis. Peristaltic walls comprise the momentum and thermal slip effects. Radiative heat flux is also taken into account to study the thermal radiation aspects. Physical properties for CNTS (i.e. single and multiple wall) are used which was suggested by Iijima. Flow equations are modeled in view of mass, momentum and energy conservation principles. Moreover, such equations are simplified through lubrication assumptions. Solution for flow quantities is carried out in the form of exact solution. Numerical integration technique is used for pressure rise per wavelength plotting. Bar charts are made for effective heat transfer rate analysis.

Multiple Slip Effects on Magnetohydrodynamic Axisymmetric Buoyant Nanofluid Flow above a Stretching Sheet with Radiation and Chemical Reaction

The present article investigates the effect of multiple slips on axisymmetric magnetohydrodynamics (MHD) buoyant nano-fluid flow over a stretching sheet with radiation and chemical effect. The non-linear partial differential equations were transformed to a non-linear control equation using an appropriate similarity transformation. The governing equations were solved through the finite element method. The influence of physical parameters such as multiple slips, magnetic, thermal radiation, Prandtl number, stretching, Brownian motion, thermophoresis, Schmidt number, Lewis number and chemical reaction on the radial velocity, temperature, solutal concentration and nano-fluid volume fraction profile were investigated. We noted that the boundary layers increases in the presence of multiple slip effects whereas, the effect of thermal slip on Nusselt number increases with the increasing values of magnetic and thermal radiation. To verify the convergence of the numerical solution, the computations were made by reducing the mesh size. Finally, our results are parallel to previous scholarly contributions.

Influence of variable viscosity and thermal conductivity, hydrodynamic, and thermal slips on magnetohydrodynamic micropolar flow: A numerical study

AbstractThermophysical and wall‐slip effects arise in many areas of nuclear technology. Motivated by such applications, in this article, the collective influence of variable‐viscosity, thermal conductivity, velocity and thermal slip effects on a steady two‐dimensional magnetohydrodynamic micropolar fluid over a stretching sheet is analyzed numerically. The governing nonlinear partial differential equations have been converted into a system of nonlinear ordinary differential equations using suitable coordinate transformations. The numerical solutions of the problem are expressed in the form of nondimensional velocity and temperature profiles and discussed from their graphical representations. The Nachtsheim‐Swigert shooting iteration technique together with the sixth‐order Runge‐Kutta integration scheme has been applied for the numerical solution. A comparison with the existing results has been done, and an excellent agreement is found. Further validation with the Adomian decomposition method is included for the general model. Interesting features in the heat and momentum characteristics are explored. It is found that a greater thermal slip and thermal conductivity elevate thermal boundary layer thickness. Increasing Prandtl number enhances the Nusselt number at the wall but reduces wall couple stress (microrotation gradient). Temperatures are enhanced with both the magnetic field and viscosity parameter. Increasing momentum (hydrodynamic) slip is found to accelerate the flow and elevate temperatures.

Magnetized and non-magnetized two layer liquids: A Lie symmetry analysis

It is well trusted that the physical believe subject to non-Newtonian fluid models in a magnetized frame always yield the complex mathematical equations and an exact solution in this direction seems impossible. Therefore, it remains challenging task for the researchers to report acceptable solutions. The current pagination contains a systemic remedy in this direction. To be more specific, the Carreau fluid flow towards flat surface is considered along with an externally applied magnetic field. The flow regime is manifested with pertinent physical believes namely, the heat source/sink and chemical reaction. The flow field is additionally supported with both the velocity and thermal slip effects. The Lie group of transformations is proposed for the present problem by means of group theoretic approach. The symmetry generator is constructed against developed Lie group of transformations. The characteristic equation subject to symmetry generator gives suitable set of variables. Such set of variables are used to step down the flow narrating differential equations in terms of an independent variables. Further, the reduced system is solved by numerical algorithm and the observations are offered by way of graphs. It is observed that the Carreau fluid velocity is suppressed for the case of magnetized flow field as compared to non-magnetized Carreau flow field. Further, the temperature of flow regime is higher in strength when the heat source is present. Finally, the results are validated by constructing comparison with an existing work.

On both MHD and slip effect in micropolar hybrid nanofluid past a circular cylinder under stagnation point region

The physical model of the micropolar hybrid nanofluid flow with magnetohydrodynamic and thermal slip effects is considered. The flow of three-dimensional stagnation point of micropolar hybrid nanofluid past a circular cylinder is also taken into account. The flow model is controlled through partial differential equations. These equations are highly nonlinear in character and reduce to ordinary differential equations through applying the suitable similarity transformation. The reduced system is solved numerically using the shooting technique. The mutual effects are presented using graphs while comparative numerical results are presented in the tables. The diverse physical parts of the issue have been talked about. This study aims to investigate the solid nano-sized particle on the surface of a circular cylinder having sinusoidal variation. These nanosized particles are used to analyze the heat transfer improvement of micropolar hybrid nanofluid as compared to micropolar nanofluid.

Thermal radiation and slip effects on magnetohydrodynamic (MHD) stagnation point flow of Casson fluid over a convective stretching sheet

Current study examines the combined effect of thermal radiation and velocity slip along a convective heated stretching sheet. magnetohydrodynamic (MHD) effect near the stagnation point is also under consideration. The main structure of partial differential equations attained in the form of momentum, energy and concentration equations. For a self-similar solution, the system of governing PDEs assimilated into the set of nonlinear ordinary differential equations by applying suitable similarity transformation. Resulting nonlinear ODEs are successfully solved via Runge-Kutta-Fehlberg method. All obtained unknown functions are discussed in detail after plotting the numerical results against different arising physical parameters. The validations of numerical results have been taken into account with two different numerical approaches and it is found to be in excellent agreement with the numerical results. The study reveals that concentration boundary layer thickness decreases by increasing the values of Schmidt number and increases by increasing the chemical reaction parameter.

Unsteady MHD Non-Newtonian Heat Transfer Nanofluids with Entropy Generation Analysis

AbstractA theoretical study of unsteady magnetohydrodynamic boundary layer stagnation point flow, heat and mass transfer of a second grade electrically-conducting nanofluid from a horizontal stretching sheet with thermal slip and second order slip velocity effects is presented. The Buongiorno formulation is employed for nanofluids and in addition the no-flux nanoparticle boundary condition is also considered. The appropriate similarity transformations are applied to convert the governing equations into the system of nonlinear partial differential equations, which is solved by using homotopy analysis method. Entropy generation and Bejan number have also been evaluated for the effects of magnetic parameter, Reynolds number and slip parameter in non-Newtonian (second-grade) time-dependent flow. The computations show that skin friction coefficient and entropy generation number increase with an increment in magnetic parameter whereas Bejan number decreases with it. Local Nusselt number decreases with an increase in the value of Eckert number (viscous dissipation) and thermal slip whereas the converse behaviour is captured for velocity parameter. The work is relevant to magnetohydrodynamic nanomaterials processing.

A numerical investigation of Newtonian fluid flow with buoyancy, thermal slip of order two and entropy generation

In the present article, the Newtonian fluid flow problem with buoyancy and thermal radiation in non-linear form is investigated by considering the entropy generation. The boundary is mathematically modeled with slip conditions (velocity and thermal) of order two. The parameters for the slip conditions of order two are calculated from the slip parameters of order one. The governing PDE's and the corresponding BC's are derived and transformed into ODE's by suitable transformation. Fourth order RK with shooting method is utilized to solve the transformed non-dimensional governing equations along with the boundary conditions. The efficiency of the present type of thermal fluidic system can be increased by reducing the generation of entropy. In view of these, the influences of slip conditions of order two on the entropy generation number are discussed. It is found that the increase of second order velocity and thermal slip effects reduces the entropy generation. Furthermore, the significant results are discussed with buoyancy effects. The present research work suggests to increase the second order slip factors in order to achieve the higher efficiency in the present type of thermal fluidic system.