This paper studies the unsteady magnetohydrodynamics (MHD) thin film flow of an incompressible Oldroyd-B fluid over an oscillating inclined belt making a certain angle with the horizontal. The problem is modeled in terms of non-linear partial differential equations with some physical initial and boundary conditions. This problem is solved for the exact analytic solutions using two efficient techniques namely the Optimal Homotopy Asymptotic Method (OHAM) and Homotopy Perturbation Method (HPM). Both of these solutions are presented graphically and compared. This comparison is also shown in tabular form. An excellent agreement is observed. The effects of various physical parameters on velocity have also been studied graphically.
The present work is concerned with exact solutions of Stokes second problem for magnetohydrodynamics (MHD) flow of a Burgers' fluid. The fluid over a flat plate is assumed to be electrically conducting in the presence of a uniform magnetic field applied in outward transverse direction to the flow. The equations governing the flow are modeled and then solved using the Laplace transform technique. The expressions of velocity field and tangential stress are developed when the relaxation time satisfies the condition γ = λ²/4 or γ> λ²/4. The obtained closed form solutions are presented in the form of simple or multiple integrals in terms of Bessel functions and terms with only Bessel functions. The numerical integration is performed and the graphical results are displayed for the involved flow parameters. It is found that the velocity decreases whereas the shear stress increases when the Hartmann number is increased. The solutions corresponding to the Stokes' first problem for hydrodynamic Burgers' fluids are obtained as limiting cases of the present solutions. Similar solutions for Stokes' second problem of hydrodynamic Burgers' fluids and those for Newtonian and Oldroyd-B fluids can also be obtained as limiting cases of these solutions.
In this paper, the heat transfer effect on the unsteady boundary layer flow of a Casson fluid past an infinite oscillating vertical plate with Newtonian heating is investigated. The governing equations are transformed to a systems of linear partial differential equations using appropriate non-dimensional variables. The resulting equations are solved analytically by using the Laplace transform 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 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 velocity decreases as Casson parameters increases and thermal boundary layer thickness increases with increasing Newtonian heating parameter.
The steady, two-dimensional laminar flow of a power-law fluid over a permeable shrinking sheet of constant surface temperature is investigated. The governing partial differential equations were transformed into a system of nonlinear ordinary differential equations using a similarity transformation, before being solved numerically by the Runge-Kutta- Fehlberg method with shooting technique. The results are presented graphically and the effects of the power-law index n, suction parameter fw and Prandtl number Pr were discussed. It was found that stronger suction is necessary for the solution to exist for a pseudoplastic fluid (n<1) compared to a dilatant fluid (n>1).
This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD) flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over a vertical plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in details.
This paper presents the preliminary steps required for conducting experiments to obtain the optimal operating conditions of a hybrid impeller mixer and to determine the residence time distribution (RTD) using computational fluid dynamics (CFD). In this paper, impeller speed and clearance parameters are examined. The hybrid impeller mixer consists of a single Rushton turbine mounted above a single pitched blade turbine (PBT). Four impeller speeds, 50, 100, 150, and 200 rpm, and four impeller clearances, 25, 50, 75, and 100 mm, were the operation variables used in this study. CFD was utilized to initially screen the parameter ranges to reduce the number of actual experiments needed. Afterward, the residence time distribution (RTD) was determined using the respective parameters. Finally, the Fluent-predicted RTD and the experimentally measured RTD were compared. The CFD investigations revealed that an impeller speed of 50 rpm and an impeller clearance of 25 mm were not viable for experimental investigations and were thus eliminated from further analyses. The determination of RTD using a k-ε turbulence model was performed using CFD techniques. The multiple reference frame (MRF) was implemented and a steady state was initially achieved followed by a transient condition for RTD determination.
The scour phenomenon around bridge piers causes great quantities of damages annually all over the world. Collars are considered as one of the substantial methods for reducing the depth and volume of scour around bridge piers. In this study, the experimental and numerical methods are used to investigate two different shapes of collars, i.e, rectangular and circular, in terms of reducing scour around a single bridge pier. The experiments were conducted in hydraulic laboratory at university of Malaya. The scour around the bridge pier and collars was simulated numerically using a three-dimensional, CFD model namely SSIIM 2.0, to verify the application of the model. The results indicated that although, both types of collars provides a considerable decrease in the depth of the scour, the rectangular collar, decreases scour depth around the pier by 79 percent, and has better performance compared to the circular collar. Furthermore, it was observed that using collars under the stream's bed, resulted in the most reduction in the scour depth around the pier. The results also show the SSIIM 2.0 model could simulate the scour phenomenon around a single bridge pier and collars with sufficient accuracy. Using the experimental and numerical results, two new equations were developed to predict the scour depth around a bridge pier exposed to circular and rectangular collars.
In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD) third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM). In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM). The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.
The majority of the eye models developed in the late 90s and early 00s considers only heat conduction inside the eye. This assumption is not entirely correct, since the anterior and posterior chambers are filled aqueous humor (AH) that is constantly in motion due to thermally-induced buoyancy. In this paper, a three-dimensional model of the human eye is developed to investigate the effects AH hydrodynamics have on the human eye temperature under exposure to external heat sources. If the effects of AH flow are negligible, then future models can be developed without taking them into account, thus simplifying the modeling process. Two types of external thermal loads are considered; volumetric and surface irradiation. Results showed that heat convection due to AH flow contributes to nearly 95% of the total heat flow inside the anterior chamber. Moreover, the circulation inside the anterior chamber can cause an upward shift of the location of hotspot. This can have significant consequences to our understanding of heat-induced cataractogenesis.
Magnetic field influence on unsteady free convection flow of a second grade fluid near an infinite vertical flat plate with ramped wall temperature embedded in a porous medium is studied. It has been observed that magnitude of velocity as well as skin friction in case of ramped temperature is quite less than the isothermal temperature. Some special cases namely: (i) second grade fluid in the absence of magnetic field and porous medium and (ii) Newtonian fluid in the presence of magnetic field and porous medium, performing the same motion are obtained. Finally, the influence of various parameters is graphically shown.
In this article, an approximate analytical solution of flow and heat transfer for a viscoelastic fluid in an axisymmetric channel with porous wall is presented. The solution is obtained through the use of a powerful method known as Optimal Homotopy Asymptotic Method (OHAM). We obtained the approximate analytical solution for dimensionless velocity and temperature for various parameters. The influence and effect of different parameters on dimensionless velocity, temperature, friction factor, and rate of heat transfer are presented graphically. We also compared our solution with those obtained by other methods and it is found that OHAM solution is better than the other methods considered. This shows that OHAM is reliable for use to solve strongly nonlinear problems in heat transfer phenomena.
The hot water sprays are an important part of many industrial processes, where the detailed knowledge of physical phenomena involved in jet transportation, interaction, secondary breakup, evaporation, and coalescence of droplets is important to reach more efficient processes. The objective of the work was to study the water spray jet breakup dynamics, vortex cloud formation, and droplet size distribution under varying temperature and load pressure. Using a high speed camera, the spray patterns generated by axisymmetric full cone nozzles were visualized as a function water temperature and load pressure. The image analysis confirmed that the spray cone angle and width do not vary significantly with increasing Reynolds and Weber numbers at early injection phases leading to increased macroscopic spray propagation. The formation and decay of semitorus like vortex clouds were also noticed in spray structures generated at near water boiling point temperature. For the nozzle with smallest orifice diameter (1.19 mm), these vortex clouds were very clear at 90°C heating temperature and 1 bar water load pressure. In addition, the sauter mean diameter (SMD) of the spray droplets was also measured by using Phase Doppler Anemometry (PDA) at different locations downstream of the nozzle exit. It was noticed that SMD varies slightly w.r.t. position when measured at room temperature whereas at higher temperature values, it became almost constant at distance of 55 mm downstream of the nozzle exit.
The steady boundary layer flow of a viscous and incompressible fluid over a moving vertical flat plate in an external moving fluid with viscous dissipation is theoretically investigated. Using appropriate similarity variables, the governing system of partial differential equations is transformed into a system of ordinary (similarity) differential equations, which is then solved numerically using a Maple software. Results for the skin friction or shear stress coefficient, local Nusselt number, velocity and temperature profiles are presented for different values of the governing parameters. It is found that the set of the similarity equations has unique solutions, dual solutions or no solutions, depending on the values of the mixed convection parameter, the velocity ratio parameter and the Eckert number. The Eckert number significantly affects the surface shear stress as well as the heat transfer rate at the surface.
The magnetohydrodynamic (MHD) stagnation point flow of a nanofluid over a permeable stretching/shrinking sheet is studied. Numerical results are obtained using boundary value problem solver bvp4c in MATLAB for several values of parameters. The numerical results show that dual solutions exist for the shrinking case, while for the stretching case, the solution is unique. A stability analysis is performed to determine the stability of the dual solutions. For the stable solution, the skin friction is higher in the presence of magnetic field and increases when the suction effect is increased. It is also found that increasing the Brownian motion parameter and the thermophoresis parameter reduces the heat transfer rate at the surface.
This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed.
Therapies with magnetic/electromagnetic field are employed to relieve pains or, to accelerate flow of blood-particles, particularly during the surgery. In this paper, a theoretical study of the blood flow along with particles suspension through capillary was made by the electro-magneto-hydrodynamic approach. Analytical solutions to the non-dimensional blood velocity and non-dimensional particles velocity are obtained by means of the Laplace transform with respect to the time variable and the finite Hankel transform with respect to the radial coordinate. The study of thermally transfer characteristics is based on the energy equation for two-phase thermal transport of blood and particles suspension with viscous dissipation, the volumetric heat generation due to Joule heating effect and electromagnetic couple effect. The solution of the nonlinear heat transfer problem is derived by using the velocity field and the integral transform method. The influence of dimensionless system parameters like the electrokinetic width, the Hartman number, Prandtl number, the coefficient of heat generation due to Joule heating and Eckert number on the velocity and temperature fields was studied using the Mathcad software. Results are presented by graphical illustrations.
We propose a strategy for optimizing distribution of flow in a typical benchtop microfluidic chamber for dielectrophoretic application. It is aimed at encouraging uniform flow velocity along the whole analysis chamber in order to ensure DEP force is evenly applied to biological particle. Via the study, we have come up with a constructive strategy in improving the design of microfluidic channel which will greatly facilitate the use of DEP system in laboratory and primarily focus on the relationship between architecture and cell distribution, by resorting to the tubular structure of blood vessels. The design was validated by hydrodynamic flow simulation using COMSOL Multiphysics v4.2a software. Simulations show that the presence of 2-level bifurcation has developed portioning of volumetric flow which produced uniform flow across the channel. However, further bifurcation will reduce the volumetric flow rate, thus causing undesirable deposition of cell suspension around the chamber. Finally, an improvement of microfluidic design with rounded corner is proposed to encourage a uniform cell adhesion within the channel.
In this paper, the problem of steady laminar boundary layer flow of an incompressible viscous fluid over a moving thin needle is considered. The governing boundary layer equations were first transformed into non-dimensional forms. These non-dimensional equations were then transformed into similarity equations using the similarity variables, which were solved numerically using an implicit finite-difference scheme known as the Keller-box method. The solutions were obtained for a blunt-nosed needle. Numerical computations were carried out for various values of the dimensionless parameters of the problem which included the Prandtl number Pr and the parameter a representing the needle size. It was found that the heat transfer characteristics were significantly
influenced by these parameters. However, the Prandtl number had no effect on the flow characteristics due to the decoupled boundary layer equations.
The drying of Piper betle Linn (betel) leaf extract using a lab scale spray dryer was simulated using Computational Fluid Dynamics (CFD). Three different turbulent models (standard k-ε, RNG k-ε and realizable k-ε) were used in the present study to determine the most suitable model for predicting the flow profile. Parametric studies were also conducted to evaluate the effect of process variables on the final moisture content. Four different initial droplet sizes (36, 79, 123 and 166 μm) were tested with four sets of combination of hot air temperature (140 and 160°C) and feed rate (4, 9.5 and 15 ml/min). It was found that standard k-ε is the most suitable turbulent model to predict the flow behaviour Moreover, the lowest final moisture content present in samples was obtained at 140°C and a feed rate of 15.0 ml/min.
In this study, the numerical simulation in a mixing vessel agitated by a six bladed Rushton turbine has
been carried out to investigate the effects of effective parameters to the mixing process. The study is intended to screen the potential parameters which affect the optimization process and to provide the detail insights into the process. Three-dimensional and steady-state flow has been performed using the fully predictive Multiple Reference Frame (MRF) technique for the impeller and tank geometry. Process optimization is always used to ensure the optimum conditions are fulfilled to attain industries’ satisfaction or needs (ie; increase profit, low cost, yields, etc). In this study, the range of recommended speed to accelerate optimization is 100, 150 and 200rpm respectively and the range of recommended clearance is 50, 75 and 100mm respectively for dual Rushton impeller. Thus, the computer fluid dynamics (CFD) was introduced in order to screen the suitable parameters efficiently and to accelerate optimization. In this study,