Increase In Suction Parameter Research Articles

Modeling and Solution of an Unsteady Flow of a Third Grade Fluid Over an Infinite Parallel Rigid Plate Within a Porous Medium

It is known by many researchers that non-Newtonian fluids are regarded as important and appropriate in technological techniques and several industrial manufacturing processes such as in polymer sheet extrusion from dye, drilling of oil and gas well to mention a few. Due to such reason a model of such type of fluid called the differential type model in which the third grade fluid is categorized. The skin friction, Nusselt number, and Sherwood number through the graphs obtained, were also obtained. The nonlinear partial differential equations were solved using He – Laplace method. He – laplace method is a combination of Homotopy perturbation method with the Laplace transform method which is used in determining linear together with the nonlinear partial differential equations, and the use of He’s polynomials for the nonlinear term. Amongst many results obtained; the velocity, temperature and concentration profiles diminish due to the increase in suction parameter. Higher values of magnetic parameter decreases the fluid velocity. The temperature distribution is enhanced by the increment in radiation parameter. Upsurging values of chemical reaction decline the concentration of the fluid.

Dual solutions of a nanofluid flow past a convectively heated nonlinearly shrinking sheet

Effects of magnetic field, convective heating and thermal radiation on the dual solutions and boundary layer separations of nanofluid flow over a nonlinearly shrinking sheet are investigated. Shrinking sheet problems may have applications in polymer technology where one deals with stretching/shrinking of plastic sheets and in metallurgy that involves the cooling of continuous strips. The new type of shrinking sheet flow is essentially a backward flow and it shows physical phenomena quite distinct from the stretching flow case. Governing equations of the problem are reduced to a system of dimensionless equations using similarity transformations. The resulting equations are solved using the well-known shooting method. A comparison between the present solutions and the available data shows a good agreement. Higher volume fraction of nanoparticles causes a decrease in skin friction coefficient and local Nusselt number. The converse is observed for increasing suction parameter. Local Nusselt number is substantially increased by larger shrinking index parameter and Biot number. An increase in suction parameter and magnetic parameter leads to diminish the boundary layer separation and the domain of existence of dual solutions. But the reverse is observed with higher volume fraction of nanoparticles and shrinking index parameter. For increasing nanoparticle volume fraction and decreasing suction parameter the velocity decreases and the temperature increases.

Radiative and MHD Effects on Time-Dependent Thermal-Material Transfer by Micropolar Binary Mixture

Radiation is an important branch of thermal engineering which includes geophysical thermal insulation, ground water pollution, food processing, cooling of electronic components, oil recovery processes etc. An analysis of unsteady magneto-convective heat-mass transport by micropolar binary mixture of fluid passing a continuous permeable surface with thermal radiation effect has been introduced in this paper. The governing equations are transformed into coupled ordinary differential equations along with Boussinesq approximation by imposing the similarity analysis. Applying the shooting technique, the obtained non-linear coupled similarity equations are solved numerically with the help of “ODE45 MATLAB” software. The results of the numerical solutions to the problem involving velocity, temperature, concentration and micro-rotation are presented graphically for different dimensionless parameters and numbers encountered. With an increase of suction parameter, the velocity distributions very closed to the inclined permeable wall decrease slightly where 0 ≤ η ≤ 0.3 . But for the uplifting values of sunction, both micro-rotation profile and species concentration enhance through the boundary layer. The skin-friction coefficient increases about 61%, 13%, 27% for rising values of Prandtl number (0.71-7), radiation effect (0 - 1) and thermal Grashof number (5-10), respectively, but an adverse effect is observed for magnetic field (1 - 4), inclined angle 0 0 − 60 0 and Schmidt number (0.22 - 0.75). Heat transfer and mass transfer reduce about 82%, 53%, respectively, in increasing of Pr (0.71-1) and 36%, 11%, respectively, in increasing of thermal radiation (0 - 1). The surface couple stress increases about 26%, 49%, 64% and 30% with the increasing values of magnetic field (1-4), inclination angle 0 0 − 60 0 , suction (0-1) and Schmidt number (0.22-0.75), respectively. Finally, the present study has been compared with the earlier published results. It is observed that the comparison bears a good agreement.

Mathematical Model and Solution for an Unsteady MHD Fourth Grade Fluid Flow over a Vertical Plate in a Porous Medium with Magnetic Field and Suction/Injection Effects

This work investigates the mathematical model and solution for an unsteady MHD fourth grade fluid flow over a vertical plate in a porous medium with the effects of the magnetic field and suction/injection parameters using Homotopy Perturbation Method. The flow is considered to satisfy the constitutive equations of fourth grade fluid flow model and because of the Homotopy Perturbation Method used, only the momentum equation with initial and boundary conditions are solved as governing equations. After initializing stability test, the convergence of the governing equations are observed graphically using the results of Homotopy Perturbation Method with the new analytical method used by Yurusoy in literature and there is a perfect agreement in results. The impact of dimensionless second, third and fourth grade parameters with the effects of magnetic field and suction/injection parameters on the velocity field are displayed graphically and discussed. Increase in suction parameter decreases the momentum boundary layer thickness while injection parameter enhances velocity distribution in the boundary layer. Magnetic field reduces velocity throughout the boundary layer because the Lorentz force which acts as retarding force reduces the boundary layer thickness.

MHD heat transfer flow of Casson fluid past a stretching wedge subject to suction and injection

The steady two dimensional incompressible hydromagnetic boundary layer flow caused by stretching wedge immersed in Casson fluid with heat transfer and suction/injection is investigated numerically. The governing nonlinear partial differential equations are transformed into nonlinear ordinary differential equations using suitable transformations and then solved numerically via Keller-box method. Numerical results for local skin friction coefficient are compared with the existing literature and observed in closed agreement with those results. The effects of pertinent parameters on flow fields are displayed graphically and discussed. It is found that velocity decreases with increase of Casson parameter and wedge angle parameter when the wedge is stretching faster than free stream. It is also observed that rate of heat transfer at surface increases with the increase of Prandtl number and Casson fluid parameter. Moreover, with increase of suction parameter the fluid velocity decreases and rate of shear stress increases.

Flow and heat transfer past a permeable nonlinearly stretching/shrinking sheet in a nanofluid: A revised model with stability analysis

This article presents a realistic approach for flow and heat transfer over a nonlinearly permeable stretching/shrinking sheet in a nanofluid. Practically, this approach is more acceptable as compared to the previous one where we have to assume the nanoparticle fraction control on boundaries. By doing this, nanoparticle flux is considered zero and nanoparticle fraction adjusts itself accordingly on the boundaries. Now the impact of Buongiorno's model can be applied in a more effective way. With this revised model, we have discussed the impact of numerous parameters on the skin friction coefficient, the local Nusselt number, and the velocity, temperature, and nanoparticle concentration profiles while finding dual solutions. To determine which solution is physically stable and realizable, we performed the stability analysis. Then the flow pattern is observed by drawing streamlines. It is observed that the first solution is stable and thus, physically realizable. The correlation based estimation for the local Nusselt number has also been carried out. The Brownian motion effect becomes negligible for the new revised model. It is found that the local Nusselt number is almost independent of the Brownian motion while the heat transfer rate reduces with the rise in Lewis number and thermophoresis parameter. For the impermeable case, the streamlines are similar to the normal stagnation point flow but the streamlines contract with the increase of suction parameter as the density of streamline increases and is proportional to the fluid velocity.

Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium

This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter.

Effect of viscous dissipation and suction/injection on MHD nanofluid flow over a wedge with porous medium and slip

The purpose of present study is to identify the effects of viscous dissipation and suction/injection on MHD flow of a nanofluid past a wedge with convective surface in the appearance of slip flow and porous medium. The basic non-linear PDEs of flow and energy are altered into a set of non-linear ODEs using auxiliary similarity transformations. The system of equations together with coupled boundary conditions have been solved numerically by applying Runge-Kutta-Fehlberg procedure via shooting scheme. The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and investigated in detail. The results elucidate that as enhance in the Eckert number, the skin friction coefficient increases, while heat transfer rate decreases. The outcomes also specify that thermal boundary layer thickness declines with an increase in suction parameter. Moreover, it is accelerated with augment in injection parameter. The results are analogized with the study published earlier and it creates a fine concord.

Double diffusive unsteady convective micropolar flow past a vertical porous plate moving through binary mixture using modified Boussinesq approximation

Abstract The problem of unsteady convective with thermophoresis, chemical reaction and radiative heat transfer in a micropolar fluid flow past a vertical porous surface moving through binary mixture considering temperature dependent dynamic viscosity and constant vortex viscosity has been investigated theoretically. For proper and correct analysis of fluid flow along vertical surface with a temperature lesser than that of the free stream, Boussinesq approximation and temperature dependent viscosity model were modified and incorporated into the governing equations. The governing equations are converted to systems of ordinary differential equations by applying suitable similarity transformations and solved numerically using fourth-order Runge–Kutta method along with shooting technique. The results of the numerical solution are presented graphically and in tabular forms for different values of parameters. Velocity profile increases with temperature dependent variable fluid viscosity parameter. Increase of suction parameter corresponds to an increase in both temperature and concentration within the thin boundary layer.

A study of the effect of magnetic field on the rotation of a viscous fluid near a porous medium with a constant suction

The problem of a rotating fluid bounded by one or two rotating disks is model of several complicated problems of practical interest in geophysics, biomechanics and many other engineering problems. In the present investigation the effect of transverse magnetic field on the rotating flow of a viscous fluid near a porous medium is discussed. The problem is solved by using Stuart’s method of expanding the entities in the inverse powers of the suction parameter. Two cases are considered for the porous medium (i) it is unbounded (ii) it is bounded by a parallel impervious surface. The solutions are governed by parameters including magnetic parameter, rotating parameter, porous parameter and suction parameter. The values of shearing stress for the second case increase with the increase of magnetic parameter as well as porous parameter but decrease with the increase of suction parameter. The analytical computed results for the normal and transverse velocities are shown graphically. Keywords : Magnetic field, Porous medium, Rotation, Suction.

On a Homotopy Perturbation Treatment of Steady Laminar Forced Convection Flow over a Nonlinearly Stretching Porous Sheet

The steady two-dimensional laminar forced convection boundary layer flow of an incompressible viscous Newtonian fluid over a nonlinearly stretching porous (permeable) sheet with suction is considered. The sheet’s permeability is also considered to be nonlinear. The boundary layer equations are transformed by similarity transformations to a nonlinear ordinary differential equation (ODE). Then the homotopy perturbation method (HPM) is used to solve the resultant nonlinear ODE. The dimensionless entrainment parameter and the dimensionless sheet surface shear stress are obtained for various values of the suction parameter and the nonlinearity factor of sheet stretching and permeability. The results indicate that the dimensionless sheet surface shear stress decreases with the increase of suction parameter. The results of present HPM solution are compared to the values obtained in a previous study by the homotopy analysis method (HAM). The HPM results show that they are in good agreement with the HAM results within 2% error.

Influence of convective boundary condition on double diffusive mixed convection from a permeable vertical surface

The main objective of the present paper is to obtain non-similar solutions numerically for steady two dimensional double diffusive mixed convection boundary layer flows along a vertical semi-infinite permeable surface under the influence of convective boundary condition along with surface mass transfer. The nonlinear partial differential equations governing the flow, temperature, and species concentration fields are expressed in non-dimensional form using suitable non-similar transformations. The final non-dimensional set of coupled nonlinear partial differential equations is solved by using an implicit finite difference scheme in combination with quasi-linearization technique. The effects of various governing parameters involved on the velocity, temperature and species concentration profiles are discussed in the present paper. The results show that the streamwise co-ordinate ξ significantly influences the flow, thermal, and concentration fields which indicate the importance of non-similar solutions. Results indicate that buoyancy parameter (Ri) and the ratio of buoyancy forces parameter (N) enhance the skin friction coefficient and decrease the heat transfer coefficient. Also, it is observed that the increase of suction parameter (A=1) causes the decrease in the magnitude of temperature and concentration profiles from their values for injection parameter (A=−1). In the present investigation, dual solutions are also obtained under similarity assumptions and compared with previously published work.

Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation

The present paper aims at investigating the boundary layer flow of a non-Newtonian fluid accompanied by heat transfer toward an exponentially stretching surface in presence of suction or blowing at the surface. Casson fluid model is used to characterize the non-Newtonian fluid behavior. Thermal radiation term is incorporated into the equation for the temperature field. With the help of similarity transformations, the governing partial differential equations corresponding to the momentum and heat transfer are reduced to a set of non-linear ordinary differential equations. Numerical solutions of these equations are then obtained. The effect of increasing values of the Casson parameter is seen to suppress the velocity field. But the temperature is enhanced with increasing Casson parameter. Thermal radiation enhances the effective thermal diffusivity and the temperature increases. It is found that the skin-friction coefficient increases with the increase in suction parameter.

Heat Transfer from Rotating Porous Plate Using Homotopy Perturbation Method

The homotopy perturbation method is employed to solve the nonlinear energy equation due to temperaturedependent thermal conductivity. The effects of variable thermal conductivity and otherparameters onheat transfer are investigated for a hydromagnetic flow of an incompressible viscous electrically conducting fluid past a rotating porous plate. The plate is rotating with a uniform angular velocity about an axis normal to the plate, and the fluid is rotating at infinity with the same angular velocity about a noncoincident parallel axis. It is demonstrated that the dimensionless heat transfer decreases along the vertical distance from the plate surface with the decrease in thermal conductivity and increases with the increase in suction parameter, Brinkman number, magnetic parameter, or Prandtl numbers, while the others are kept constant.

Hydrodynamic effect on the three‐dimensional flow past a vertical porous plate

The study of unsteady hydrodynamic free convective flow of a viscous incompressible fluid past a vertical porous plate in the presence of a variable suction has been made. Approximate solutions have been derived for the velocity and temperature fields, shear stress, and rate of heat transfer using perturbation technique. It is observed that main fluid velocity decreases with increase in Prandtl number, while it increases with increase in suction parameter. The cross‐velocity decreases near the plate and increases away from the plate with increase in suction parameter. On the other hand, it increases near the plate and decreases away from the plate with increase in frequency parameter. The amplitude and the tangent of phase shift of the shear stress due to main flow decrease with increase in either Prandtl number, Grashof number, or frequency parameter. It is seen that the temperature decreases with increase in either suction parameter, Prandtl number, or frequency parameter. It is also seen that the amplitude of the rate of heat transfer increases and the tangent of phase shift of rate of heat transfer decreases with increase in Prandtl number.

PRESSURE DROP IN DOWNWARD FLOW OF CONDENSING STEAM OVER A HORIZONTAL BUNDLE OF SQUARE PITCHED TUBES

Pressure drop measurements in a 15-row steam condenser configured with in-line tubes, p/D < 1.33, are described. Pressures from 50 to 100 mb and Remax in the range 1,000-18,000 were imposed. It is shown that pressure loss coefficients for the bundle and for two-row pairs were lower than predictions for equivalent single-phase tests except near the bottom of the bundle. There was some evidence that increase in suction parameter increased this effect in the top rows. Taken together with previous investigations [3, 4], a falling trend of suction effect is evident the more closely packed the tubes are. The discrepancy between these findings and the results of simulation experiments [7] is noted.

Free convection along a vertical wall in a porous medium with periodic permeability variation

AbstractThis communication investigates the effect of permeability variation on free convection flow and heat transfer in a porous medium bounded by a vertical porous wall. A transverse periodic variation in permeability is considered to study the effect on heat transfer rate and skin friction. The problem becomes three‐dimensional due to the variation in permeability. Analytical expressions for velocity, temperature, skin friction and rate of heat transfer are obtained using the perturbation technique. Effects of permeability and suction parameters on skin friction and heat transfer is studied and it is found that the increase in permeability creates a higher heat transfer rate and greater skin friction. However, the increase in suction parameter causes the skin friction values to decrease. The results obtained will be useful in the design of steam displacement processes in oil recovery and various geothermal systems.