Effects of heat source/sink,radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a stretching sheet

This paper presents a study of the flow and heat transfer of an incompressible homogeneous second-grade fluid over a non-isothermal stretching sheet. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation, work due to deformation, internal heat generation/absorption and thermal radiation are considered in the energy equation, and the variations of dimensionless surface temperature and dimensionless surface temperature gradient as well as the heat transfer characteristics with various physical parameters are graphed and tabulated. Two cases are studied, namely, (i) a sheet with prescribed surface temperature (PST case) and (ii) a sheet with prescribed heat flux (PHF case).     

Melting heat transfer in boundary layer stagnation-point flow towards a stretching/shrinking sheet in a micropolar fluid

The steady boundary layer stagnation-point flow of a micropolar fluid towards a horizontal linearly stretching/shrinking sheet is investigated. A mathematical model is developed to study the heat transfer characteristics occurring during the melting process due to a stretching/shrinking sheet. The transformed non-linear ordinary differential equations governing the flow are solved numerically by the Runge–Kutta–Fehlberg method with shooting technique. It is found that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique.     

Thermal radiation and slip effects on MHD stagnation point flow of non-Newtonian nanofluid over a convective stretching surface

The present analysis examines the combine effects of thermal radiation and velocity slip along a convectively nonlinear stretching surface. Moreover, MHD effects are also considered near the stagnation point flow of Casson nanofluid. Slipped effects are considered with the porous medium to reduce the drag reduction at the surface of the sheet. Main structure of the system is based upon the system of partial differential equations attained in the form of momentum, energy, and concentration equations. To determine the similar solution system of PDEs is rehabilitated into the set of nonlinear ordinary differential equations (ODEs) by employing compatible similarity transformation. Important physical parameters are acquired through obtained differential equations. To determine the influence of emerging parameters, resulting set of ODE’s in term of unknown function of velocity, temperature, and concentration are successfully solved via Keller’s box-scheme. All the obtained unknown functions are discussed in detail after plotting the results against each physical parameter. To analyze the behavior at the surface: skin friction, local Nusselt and Sherwood numbers are also illustrated against the velocity ratio parameter A, Brownian motion Nb, thermophoresis Nt, and thermal radiation parameters R. Results obtained from the set of equations described that skin friction is decreasing function of A, and local Nusselt and Sherwood number demonstrate the significant influenced by Brownian motion Nb, thermophoresis Nt, and radiation parameters R.

     

The effects of MHD and buoyancy on Hematite water-based fluid past a convectively heated stretching sheet

Neural Computing and Applications - In the present paper, we examined the buoyancy effects on MHD two-dimensional boundary layer flow in the presence of heat transfer of Hematite–water...     

MHD flow with heat and mass transfer of Williamson nanofluid over stretching sheet through porous medium

Microsystem Technologies - Two-dimensional hydromagnetic flow of an incompressible Williamson nanofluid over a stretching sheet in a porous media is examined during this work. Convective heat and...     

Magnetohydrodynamic three-dimensional flow of nanofluids with slip and thermal radiation over a nonlinear stretching sheet: a numerical study

A numerical simulation for mixed convective three-dimensional slip flow of water-based nanofluids with temperature jump boundary condition is presented. The flow is caused by nonlinear stretching surface. Conservation of energy equation involves the radiation heat flux term. Applied transverse magnetic effect of variable kind is also incorporated. Suitable nonlinear similarity transformations are used to reduce the governing equations into a set of self-similar equations. The subsequent equations are solved numerically by using shooting method. The solutions for the velocity and temperature distributions are computed for several values of flow pertinent parameters. Further, the numerical values for skin-friction coefficients and Nusselt number in respect of different nanoparticles are tabulated. A comparison between our numerical and already existing results has also been made. It is found that the velocity and thermal slip boundary condition showed a significant effect on momentum and thermal boundary layer thickness at the wall. The presence of nanoparticles stabilizes the thermal boundary layer growth.

     

The extended homotopy perturbation method for the boundary layer flow due to a stretching sheet with partial slip

A fully analytical solution of the steady, laminar and axisymmetric flow of a Newtonian fluid due to a stretching sheet when there is a partial slip of the fluid past the sheet has been derived using the extended homotopy perturbation method. The solution differs from that obtained by the classical homotopy perturbation method in that it is capable of generating a totally analytical solution up to any desired degree of accuracy and is not limited to the first-order correction terms. For an eight-decimal accuracy, it is sufficient to take 12 terms in the power series in the perturbation parameter, provided that use is made of Shanks’ transformation. Unlike other similar problems involving mass transfer across the sheet and/or the presence of a transverse magnetic field, the solution for the present problem is relatively insensitive to the velocity slip parameter.     

Fluid flow and heat transfer past two spheres in a cylindrical tube

The fluid flow and the heat transfer for a row of spheres in a cylindrical tube is modelled by considering the flow past two spheres in a long tube. The problem is solved numerically by a finite element method, using a velocity-pressure formulation for the Navier-Stokes equations.Results are obtained for Reynolds number up to 200, with Prandtl numbers of 0.72 and 7.0, for a range of sphere sizes and sphere separations. It was found that as the distance between the spheres was decreased a circulatory region of flow appeared between the spheres for a given Reynolds number. This eddy led to poor heat transfer in this region. Increasing the Reynolds number was found not to improve the situation as the eddy grew in size and caused poorer heat transfer. This was found to be true with even the widest gap sizes considered.     

Nanofluid flow over a shrinking sheet with surface slip

In the present study, the effects of partial slip on mixed convection stagnation point flow and heat transfer of nanofluid impinging normally toward a shrinking sheet are investigated numerically. In particular, focus is on Cu–water and Al₂O₃–water nanofluids. Similarity transformation technique is adopted to obtain the self-similar ordinary differential equations and then solved numerically using Runge–Kutta–Fehlberg method with shooting technique. A parametric study is performed to explore the effects of various governing parameters on the fluid flow and heat transfer characteristics. Both the cases of assisting and opposing flows are considered. The physical aspects of the problem are highlighted and discussed.     

Effect of patchwise slip on fluid flow

In this paper, we show that large connected slip patches (hydrophobic patches) are a necessity to induce macroscopic slip effects of water flow in microchannels. For this purpose, the 2D fluid flow between a planar stationary surface with alternating stick and slip patches and a parallel planar surface moving with a constant relative velocity has been studied by computer simulations based on Navier–Stokes equations. A slip patch is defined as the slipping length in a 2D system or a slip area of the surface in a 3D system. The simulations reveal that the ratio (size of each slip patch)/(distance between the two parallel interfaces) has profound effect on the viscous stress on the moving surface when this ratio is around and above one. However, when the ratio is much below one, the effect of the slip patches are minor, even if the area fraction of slip patches are higher than 50 %. Obviously, the stick patches adjacent to the slip patches act as effective barriers, preventing the fluid velocity to increase near the surface with alternating stick and slip patches. The obtained results are scalable and applicable on all length scales, with an exception for narrow channels in the subnano regime, i.e. <1 nm where specific effects as the atomistic composition and the nanostructure of the wall as well as the interactions between the wall and the water molecules have an effect.     

Teaching computer-aided design of fluid flow and heat transfer engineering equipment

A teaching programme for fluid mechanics and heat transfer is described which contains a computer-aided learning (CAL) component and a computer-aided design (CAD) component. The first centres on a final-year lecture course on the fundamentals of the subject and is heavily supported by computer-based tutorial exercises, while the second consists of a CAD course and separate project work in which the students apply the knowledge acquired in the ‘fundamentals’ course to selected design probems. It is argued that the understanding of the physical and numerical modelling taught in the CAL course is essential to the proper implementation of CAD.     

Non-coaxial rotating flow of viscous fluid with heat and mass transfer

Heat and mass transfer in unsteady non-coaxial rotating flow of viscous fluid over an infinite vertical disk is investigated. The motion in the fluid is induced due to two sources. Firstly, due to the buoyancy force which is caused because of temperature and concentration gradients. Secondly, because of non-coaxial rotation of a disk such that the disk executes cosine or since oscillation in its plane and the fluid is at infinity. The problem is modeled in terms of coupled partial differential equations with some physical boundary and initial conditions. The dimensionless form of the problem is solved via Laplace transform method for exact solutions. Expressions for velocity field, temperature and concentration distributions are obtained, satisfying all the initial and boundary conditions. Skin friction, Nusselt number and Sherwood number are also evaluated. The physical significance of the mathematical results is shown in various plots and is discussed for several embedded parameters. It is found that magnitude of primary velocity is less than secondary velocity. In limiting sense, the present solutions are found identical with published results.

     

Transient flow and heat transfer mechanism for Williamson-nanomaterials caused by a stretching cylinder with variable thermal conductivity

The utilization of nanometre-sized solid particles in working fluids has been seriously recommended due to their enhanced thermal characteristics. This suspension of solid particles in base fluids can significantly enhance the physical properties, such as, viscosity and thermal conductivity. They are widely used in several engineering processes, like, heat exchangers, cooling of electronic equipment, etc. In this exploration, we attempt to deliver a numerical study to simulate the nanofluids flow past a circular cylinder with convective heat transfer in the framework of Buongiorno’s model. A non-Newtonian Williamson rheological model is used to describe the behavior of nanofluid with variable properties (i.e., temperature dependent thermal conductivity). The leading flow equations for nanofluid transport are mathematical modelled with the assistance of Boussinesq approximation. Numerical simulation for the system of leading non-linear differential equations has been performed by employing versatile, extensively validated, Runge–Kutta Fehlberg scheme with Cash–Karp coefficients. Impacts of active physical parameters on fluid velocity, temperature and nanoparticle concentration is studied and displayed graphically. It is worth to mention that the temperature of non-Newtonian nanofluids is significantly enhanced by higher variable thermal conductivity parameter. One major outcome of this study is that the nanoparticle concentration is raised considerably by an increasing values of thermophoresis parameter.

     

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the Keller-Box method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress.     

Flow and heat transfer of a MHD viscoelastic fluid in a channel with stretching walls: Some applications to haemodynamics

Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter’s liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agreement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.     

Analytical solution for suction and injection flow of a viscoplastic Casson fluid past a stretching surface in the presence of viscous dissipation

In this study, steady two-dimensional flow of a viscoplastic Casson fluid past a stretching surface is considered under the effects of thermal radiation and viscous dissipation. Both suction and injection flows situations are considered. The partial differential governing equations are transformed into ordinary differential equations and solved analytical. Analytical solutions for velocity and temperature are obtained in terms of hypergeometric function and discussed graphically. Moreover, numerical results are also obtained by Runge–Kutta–Fehlberg fourth–fifth-order (RKF45) method and compared with the analytical results. The results showed that the injection and suction parameter can be used to control the direction and strength of flow. The effects of Casson parameter on the temperature and velocity are quite opposite. The effects of thermal radiation on the temperature are much more stronger in case of injection. The heat transfer coefficient shows higher value for Casson fluid while for Newtonian fluid is the lowest.

     

Lie-group similarity solution and analysis for fractional viscoelastic MHD fluid over a stretching sheet

Lie-group is introduced for studying boundary layer flow and heat transfer of fractional viscoelastic MHD fluid over a stretching sheet. Fractional boundary layer equations, based on Riemann–Liouville operators, are reduced and solved numerically by Grünwald scheme approximation. Results show that the skin friction and thermal conductivity are strongly affected by magnetic field parameter, fractional derivative and wall stretching exponent. The bigger of the fractional order derivative leads to the faster velocity of viscoelastic fluids near the plate but not to hold near the outer flow. Skin friction increases with increase of magnetic field parameter $M$, while the heat transfer decreases. For wall stretching exponent parameter $\beta =1.0$, the velocity profile decreases with the increase of similarity variable $\eta$. However, for $\beta =?1.5$, the velocity profile increases initially and then decreases afterwards with the biggest velocity at the interior of boundary layer.     

Diffuse interface method for fluid flow and heat transfer in cellular solids

This work presents a contribution on the numerical modelling capabilities for the simulation of fluid flow and heat transfer in cellular solids – in particular we focus on open cell aluminium foams. Rather than applying one of the classical academical or commercial numerical finite volume (FV), finite difference (FD) or finite element (FE) interface tracking methods, we base our models on an interface capturing phase field method (Nestler, 2005). A coupled diffuse interface lattice Boltzmann fluid flow solver (Ettrich, 2014) and a diffuse interface heat transfer approach (Ettrich et al., 2014) are combined in view of dealing with even more convoluted geometries, incorporating the dynamics of interfaces and complex multiphysics applications. Numerical results for the combined fluid flow and heat transfer simulations in open cell metal foams are in very good agreement with experimental data (Ettrich and Martens, 2012; Ettrich et al., 2012).     

Effects of multiple slip on flow of magneto-Carreau fluid along wedge with chemically reactive species

Neural Computing and Applications - Of concern in this work is an investigation of the heat and mass transfer mechanisms in the presence of first-order chemical reaction for an incompressible flow...