Heat transfer and nanofluid flow over a porous plate with radiation and slip boundary conditions

Presence of different terms with various values can alter the thermal behavior of the nanofluids flow over porous surfaces.The aim of this research is to study the influence of nanoparticles volume fraction,nanoparticles type,suction or injection,the heat generation or absorption,the Eckert number,thermal and velocity slip parameters,and radiation on the velocity and temperature fields on the flow and heat transfer over a porous flat plate.Four different types of nanoparticles including metal nanoparticles (Cu),metal oxide nanoparticles (Al2O3) and carbon-based nanomaterials (MWCNTs and SWCNTs) which were dispersed in the water (as based fluid) are studied.The governing equations are converted into the ordinary differential equations using similarity solution and solved numerically by the RKF45 algorithm.The results of the simulations showed a contradiction with the results of other researchers who expressed that using nanoparticles with higher thermal conductivity and volume fraction led to increasing heat transfer rate in nanofluids;this study proves that,in some cases,boosting the volume fraction of nanoparticles has a potential to decrease the heat transfer rate due to significant changes in values of some parameters including radiation,heat generation,and viscous dissipation.

Transient flows of Maxwell fluid with slip conditions

Two fundamental flows, namely, the Stokes and Couette flows in a Maxwell fluid are considered. The exact analytic solutions are derived in the presence of the slip condition. The Laplace transform method is employed for the development of such solutions. Limiting cases of no-slip and viscous fluids can be easily recovered from the present analysis. The behaviors of embedded flow parameters are discussed through graphs.

Heat and Mass Transfer in MHD Micropolar Fluid Flow over a Stretching Sheet with Velocity and Thermal Slip Conditions

This study presents the problem of a steady, two-dimensional, heat and mass transfer of an incompressible, electrically conducting micropolar fluid flow past a stretching surface with velocity and thermal slip conditions. Also, the influences of temperature dependent viscosity, thermal radiation and non-uniform heat generation/absorption and chemical reaction of a general order are examined on the fluid flow. The governing system of partial differential equations of the fluid flow are transformed into non-linear ordinary differential equations by an appropriate similarity variables and the resulting equations are solved by shooting method coupled with fourth order Runge-Kutta integration scheme. The effects of the controlling parameters on the velocity, temperature, microrotation and concentration profiles as well as on the skin friction, Nusselt number, Sherwood and wall couple stress are investigated through tables and graphs. Comparison of the present results with the existing results in the literature in some limiting cases shows an excellent agreement.

Unsteady MHD Mixed Convection Flow with Slip of a Nanofluid in the Stagnation Region of an Impulsively Rotating Sphere with Effects of Thermal Radiation and Convective Boundary Conditions

Unsteady magnetohydrodynamic mixed convection flow of an electrically conducting nanofluid in a stagnation region of a rotating sphere is studied numerically in the present article. Slip and convective boundary conditions are imposed to surface of the sphere and the thermal radiation effects are taken into account. The nanofluid is simulated using Buongiorno’s nanofluid model and the nanofluid particle fraction on the boundary is considered to be passively rather than actively controlled. Non-similar solutions are applied on the governing equations and the MATLAB function bvp4c is used to solve the resulting system. Effects of the key-parameters such as slip parameter, Biot number, radiation parameter, rotation parameter, Lewis number and Brownian motion parameter on the fluid flow, temperature and nanoparticle volume fraction characteristics are examined. Details of the numerical solution and a comprehensive discussion with the physical meaning for the obtained results are performed. The results indicated that the increase in slip parameter enhances the velocity profiles, while it decreases the temperature distributions. Also, the increase in either slip parameter or Biot number causes an improvement in the rate of heat transfer.

Temporal Stability Analysis of Magnetized Hybrid Nanofluid Propagating through an Unsteady Shrinking Sheet: Partial Slip Conditions

The unsteady magnetohydrodynamic(MHD)flow on a horizontal preamble surface with hybrid nanoparticles in the presence of the first order velocity and thermal slip conditions are investigated.Alumina(Al_(2)O_(3))and copper(Cu)are considered as hybrid nanoparticles that have been dispersed in water in order to make hybrid nanofluid(Cu-Al_(2)O_(3)/water).The system of similarity equations is derived from the system of partial differential equations(PDEs)by using variables of similarity,and their solutions are gotten with shooting method in the Maple software.In certain ranges of unsteadiness and magnetic parameters,the presence of dual solutions can be found.Further,it is examined that layer separation is deferred due to the effect of the hybrid nanoparticles.Moreover,the capacity of the thermal enhancement of Cu-Al_(2)O_(3)/water hybrid nanofluid is higher as compared to Al_(2)O_(3)/water based nanofluid and enhancements inCu are caused to rise the fluid temperature in both solutions.In the last,solutions stability analyzes were also carried out and the first solution was found to be stable.

Unsteady MHD flow over exponentially stretching sheet with slip conditions

The present paper examines the hydromagnetic three-dimensional flow in- duced by a stretched surface. An incompressible material saturates the porous medium. Velocity and thermal slip boundary conditions are considered. Suitable transformations are used to obtain the nonlinear ordinary differential equations. Series solutions of the resulting systems are constructed. The effects of various pertinent parameters on the axial velocity and temperature distributions are analyzed graphically. The skin friction and the Nusselt number are computed numerically and graphically.

Stability Scrutinization of Agrawal Axisymmetric Flow of Nanofluid through a Permeable Moving Disk Due to Renewable Solar Radiation with Smoluchowski Temperature and Maxwell Velocity Slip Boundary Conditions

The utilization of solar energy is essential to all living things since the beginning of time.In addition to being a constant source of energy,solar energy(SE)can also be used to generate heat and electricity.Recent technology enables to convert the solar energy into electricity by using thermal solar heat.Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy.Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly.The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy.Moreover,the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer.The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically.The current numerical approach can produce double solutions by providing suitable initial guesses.In addition,the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction.The suction parameter delays the boundary layer separation.Moreover,stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable.

Numerical Modeling of Non-Similar Mixed Convection Heat Transfer over a Stretching Surface with Slip Conditions

In this paper, the heat transfer effect on the steady boundary layer flow of a Casson fluid past a stretching surface in the presence of slip conditions was analyzed. The stretching surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. The resulting equations are solved numerically by using the Kellerbox finite-difference method, and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for non-Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that both velocity and temperature decrease with an increase of the Casson fluid parameter.

Stokes flow before plane boundary with mixed stick-slip boundary conditions

A general theorem for the Stokes flow over a plane boundary with mixed stick-slip boundary conditions is established. This is done by using a representation for the velocity and pressure fields in the three-dimensional Stokes flow in terms of a biharmonic function and a harmonic function. The earlier theorem for the Stokes flow due to fundamental singularities before a no-slip plane boundary is shown to be a special case of the present theorem. Furthermore, in terms of the Stokes stream function, a corollary of the theorem is also derived, providing a solution to the problem of the axisymmetric Stokes flow along a rigid plane with stick-slip boundary conditions. The formulae for the drag and torque exerted by the fluid on the boundary are established. An illustrative example is given.

ON SOLUTION TO THE NAVIER-STOKES EQUATIONS WITH NAVIER SLIP BOUNDARY CONDITION FOR THREE DIMENSIONAL INCOMPRESSIBLE FLUID

In this article, we prove the existence and uniqueness of solutions of the NavierStokes equations with Navier slip boundary condition for incompressible fluid in a bounded domain of R^3. The results are established by the Galerkin approximation method and improved the existing results.

Dual solutions of MHD stagnation point flow and heat transfer over a stretching/shrinking sheet with generalized slip condition

An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITY BOUNDARY CONDITIONS ON NON-FLAT BOUNDARIES

We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary conditions, the pressure p can be still recovered by solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady Stokes equations and employ the solution to reduce our initial-boundary value problem into an initial-boundary value problem with absolute boundary conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary conditions and the initial condition （without the incompressibility condition）, which establishes a velocity mapping. Then we develop apriori estimates for the velocity mapping, especially involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary value problem. Finally, we establish that, when the viscosity coefficient tends zero, the strong solutions of the initial-boundary value problem in R^n（n ≥ 3） with nonhomogeneous vorticity boundary condition converge in L^2 to the corresponding Euler equations satisfying the kinematic condition.

An Analytical Solution to Neumann-Type Mixed Boundary Poiseuille Microfluidic Flow in Rectangular Channel Cross-Sections (Slip/No-Slip) including a Numerical Technique to Derive It

In most microfluidic applications, pressure-driven Poiseuille flow in a contained cross-section with no-slip boundary conditions is the underlying fluid-mechanical model. Solutions for this problem exist for many known cross-sections. We have recently demonstrated a simple method to solve the relevant Poisson equation using a finite difference scheme in a spreadsheet analysis tool such as Microsoft Excel. The numerical solutions obtained from such a spreadsheet are close-to-exact to the analytical solutions with errors on the order of only a few percent. However, there are numerous applications in microfluidics for which the no-slip boundary condition is not valid. Examples include drag-reducing air-retaining surfaces as well as open-channel flow. For these scenarios few to no analytical models exist. In this paper, we derive an analytical model for mixed boundary conditions (slip/no-slip) in two dimensions in a rectangular channel cross-section. We also demonstrate that the equivalent numerical solution can be derived conveniently by adaption of the spreadsheet. In general, mixed boundary-type flow scenarios are especially difficult to solve analytically whereas numerical solutions can be derived using Microsoft Excel within seconds.

Stokes flow of micro-polar fluids by peristaltic pumping through tube with slip boundary condition

This paper studies the Stokes flow of micro-polar fluids by peristaltic pumping through the cylindrical tube under the effect of the slip boundary condition. The motion of the wall is governed by the sinusoidal wave equation. The analytical and numerical solutions for the axial velocity, the micro-polar vector, the stream function, the pressure gradient, the friction force, and the mechanical efficiency are obtained by using the lu- brication theory under the low Reynolds number and long wavelength approximations. The impacts of the emerging parameters, such as the coupling number, the micro-polar parameter, the slip parameter on pumping characteristics, the friction force, the velocity profile, the mechanical efficiency, and the trapping phenomenon are depicted graphically. The numerical results infer that large pressure is required for peristaltic pumping when the coupling number is large, while opposite behaviors are found for the micro-polar parameter and the slip parameter. The size of the trapped bolus reduces with the increase in the coupling number and the micro-polar parameter, whereas it blows up with the increase in the slip parameter.

Navier’s slip condition on time dependent Darcy-Forchheimer nanofluid using spectral relaxation method

In industrial applications involving metal and polymer sheets, the flow situation is strongly unsteady and the sheet temperature is a mixture of prescribed surface temperature and heat flux. Further, a proper choice of cooling liquid is also an important component of the analysis to achieve better outputs. In this paper, we numerically investigate Darcy-Forchheimer nanoliquid flows past an unsteady stretching surface by incorporating various effects, such as the Brownian and thermophoresis effects, Navier’s slip condition and convective thermal boundary conditions. To solve the governing equations, using suitable similarity transformations, the nonlinear ordinary differential equations are derived and the resulting coupled momentum and energy equations are numerically solved using the spectral relaxation method. Through the systematically numerical investigation, the important physical parameters of the present model are analyzed. We find that the presence of unsteadiness parameter has significant effects on velocity, temperature, concentration fields, the associated heat and mass transport rates. Also, an increase in inertia coefficient and porosity parameter causes an increase in the velocity at the boundary.

Numerical study of homogeneous–heterogeneous reactions on stagnation point flow of ferrofluid with non-linear slip condition

This study deals with the stagnation point flow of ferrofluid over a flat plate with non-linear slip boundary condition in the presence of homogeneous-heterogeneous reactions.Three kinds of ferroparticles,namely,magnetite(Fe_3O_4),cobalt ferrite(CoFe_2O_4) and manganese zinc ferrite(Mn-ZnFe_2O_4) are taken into account with water and kerosene as conventional base fluids.The developed model of homogeneous-heterogeneous reactions in boundary layer flow with equal and unequal diffusivities for reactant and autocatalysis is considered.The governing partial differential equations are converted into system of non-linear ordinary differential equations by mean of similarity transformations.These ordinary differential equations are integrated numerically using shooting method.The effects of pertinent parameters on velocity and concentration profiles are presented graphically and discussed.We found that in the presence of Fe_3O_4-kerosene and CoFe_2O_4-kerosene,velocity profiles increase for large values of α and β whereas there is a decrement in concentration profiles with increasing values of if and K_s.Furthermore,the comparison between non-magnetic(A1_2O_3) and magnetic Fe_3O_4 nanoparticles is given in tabular form.

Effect of boundary slip on electroosmotic flow in a curved rectangular microchannel

The aim of this study is to numerically investigate the impact of boundary slip on electroosmotic flow(EOF) in curved rectangular microchannels. Navier slip boundary conditions were employed at the curved microchannel walls. The electric potential distribution was governed by the Poisson–Boltzmann equation, whereas the velocity distribution was determined by the Navier–Stokes equation. The finite-difference method was employed to solve these two equations. The detailed discussion focuses on the impact of the curvature ratio, electrokinetic width, aspect ratio and slip length on the velocity. The results indicate that the present problem is strongly dependent on these parameters. The results demonstrate that by varying the dimensionless slip length from 0.001 to 0.01 while maintaining a curvature ratio of 0.5 there is a twofold increase in the maximum velocity. Moreover, this increase becomes more pronounced at higher curvature ratios. In addition, the velocity difference between the inner and outer radial regions increases with increasing slip length. Therefore, the incorporation of the slip boundary condition results in an augmented velocity and a more non-uniform velocity distribution. The findings presented here offer valuable insights into the design and optimization of EOF performance in curved hydrophobic microchannels featuring rectangular cross-sections.

Chemical Reaction on Williamson Nanofluid’s Radiative MHD Dissipative Stagnation Point Flow over an Exponentially Inclined Stretching Surface with Multi-Slip Effects

A wide range of technological and industrial domains,including heating processors,electrical systems,mechanical systems,and others,are facing issues as a result of the recent developments in heat transmission.Nanofluids are a novel type of heat transfer fluid that has the potential to provide solutions that will improve energy transfer.The current study investigates the effect of a magnetic field on the two-dimensional flow of Williamson nanofluid over an exponentially inclined stretched sheet.This investigation takes into account the presence of multi-slip effects.We also consider the influence of viscous dissipation,thermal radiation,chemical reactions,and suction on the fluid’s velocity.We convert the nonlinear governing partial differential equations(PDEs)of the fluid flow problem into dimensionless ordinary differential equations(ODEs)through the utilization of similarity variables.We then use the homotopy analysis method(HAM)to numerically solve the resulting ordinary differential equations(ODEs).We demonstrate the effects of numerous elements on a variety of profiles through graphical and tabular representations.We observe a drop in the velocity profile whenever we increase either the magnetic number or the suction parameter.Higher values of the Williamson parameter lead to an increase in the thermal profile,while the momentum of the flow displays a trend in the opposite direction.The potential applications of this unique model include chemical and biomolecule detection,environmental cleansing,and the initiation of radiation-induced chemical processes like polymerization,sterilization,and chemical synthesis.

Effects of Service Condition on Rolling Contact Fatigue Failure Mechanism and Lifetime of Thermal Spray Coatings——A Review

The service condition determines the Roiling Contact Fatigue（RCF） failure mechanism and lifetime under ascertain material structure integrity parameter of thermal spray coating. The available literature on the RCF testing of thermal spray coatings under various condition services is considerable; it is generally difficult to synthesize all of the result to obtain a comprehensive understanding of the parameters which has a great effect on a thermal spray coating＇s resistance of RCF. The effects of service conditions（lubrication states, contact stresses, revolve speed, and slip ratio） on the changing of thermal spray coatings＇ contact fatigue lifetime is introduced systematically. The effects of different service condition on RCF failure mechanism of thermal spray coating from the change of material structure integrity are also summarized. Moreover, In order to enhance the RCF performance, the parameter optimal design formula of service condition and material structure integrity is proposed based on the effect of service condition on thermal spray coatings＇ contact fatigue lifetime and RCF failure mechanism. The shortage of available literature and the forecast focus in future researches are discussed based on available research. The explicit result of RCF lifetime law and parameter optimal design formula in term of lubrication states, contact stresses, revolve speed, and slip ratio, is significant to improve the RCF performance on the engineering application.

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.