Laminar flow in a uniformly porous pipe

This study focused on fully laminar flow of an incompressible viscous fluid in a uniformly porous pipe with suction and injection. An exact solution of the Navier-Stokes equations is given. The velocity field can be expressed in a series form in terms of modified Bessel function of the first kind of order n. The volume flux across a plane normal to the flow, the vorticity and the stress on the boundary are presented. The flow properties depend on the Reynolds number, U a / ,where U is the suction velocity, a is the radius of the pipe and is the kinematic viscosity. It is found that for large values of the cross-Reynolds number, the flow near the region of the suction shows a boundary layer character. In this region the velocity and vorticity vary sharply. Outside the boundary layer, the velocity and the vorticity do not show an appreciable change

Mathematical Model of Simultaneous Flow between Casson Fluid and Dust Particle over a Vertical Stretching Sheet

The process involving multiphase flow generally can be found in natural phenomena and many industrial applications. It might be between solid-liquid flow, liquid-liquid flow, gas-solid flow or gas-liquid flow. Their interaction is significant and able to influence the flow characteristics. The experimental work for this topic has been widely performed in order to obtain the best interaction output but it is still incomplete due to the limitation in term of cost and safety issue. Since then, the mathematical model is proposed to counter that constraint. This paper is aims to propose the mathematical model representing the two-phase flow which the interaction of non-Newtonian Casson fluid and solid particles is examined. The flow is investigated moving over a stretching sheet and the combined convection is considered together with the influence of heat generation in fluid phase. The governing equations representing the two-phase model are first transformed into the ordinary differential equations using established similarity transformations where the complexity of the model is reduced. The resulting equations are then solved by employing the Keller-box method with the help of Matlab software. The numerical output in term of velocity and temperature distribution for both phases are illustrated graphically and the value of skin friction and heat transfer coefficients are presented in tabular form for various value of mixed convection parameter, heat generation parameter and Casson parameter. Findings reveal that, the parameter under investigation affects the flow characteristics and present a significant impact to both phases except for mixed convection parameter

Aligned magnetic field of two-phase mixed convection flow in dusty Casson fluid over a stretching sheet with Newtonian heating

The effect of aligned magnetic field is numerically investigated for mixed convection flow of dusty Casson fluid over a stretching sheet. The governing equations of flow and heat transfer for the two-phase model (fluid and dust) with an appropriate thermal boundary condition which is Newtonian heating (NH) is presented. The similarity transformation is employed to transform the nonlinear governing equations for each phase into the ordinary differential equations which then solved numerically using Runge-Kutta Fehlberg (RKF45) method. Numerical solutions obtained for velocity and temperature distributions are illustrated through graph by varying several physical parameters. It is observed that the fluid velocity decreases with an increase in aligned magnetic field and particle-fluid interaction parameter

Fluid-particle interaction with buoyancy forces on jeffrey fluid with newtonian heating

The numerical results of fluid flow problem that being embedded with the dust particles is presented in this paper. In order to analyze such problem, a two-phase model is constructed by introducing a fluid-particle interaction forces in the momentum equations of fluid and dust phases. The buoyancy forces and aligned magnetic field are considered on the fluid flow. Also, the Newtonian heating boundary condition is induced on the vertical stretching sheet. The suitable similarity transformation is applied to the governing equations of the model which then produces the ordinary differential system. The results are obtained by adapting the Runge-Kutta Fehlberg (RKF45) method whereby the solutions are interpreted in terms of velocity and temperature profiles for Jeffrey fluid and dust particles respectively. The influences of assorted physical parameters are visualized graphically to clarify the flow and heat transfer characteristic for both phases. The discovery found that the presence of the dust particles have an effect on the fluid motion which led to decelerate the fluid transference. The present flow model can match to the single phase fluid cases if the fluid particle interaction parameter is ignored

Inclined magnetic field on second grade nanofluid flow from an inclined stretching sheet with nonlinear mixed convection

Present investigation aims to probe into the problem of nonlinear mixed convection flow of second grade nanofluid flow due to an inclined stretching sheet. The simultaneous impacts of inclined magnetic field of acute angle and convective boundary conditions are taken into deliberation. The system of highly nonlinear partial differential equations is transformed into non-linear ordinary differential equations with the aid of similarity transformation variables. The solutions are generated numerically via the Runge-Kutta-Fehlberg Method (RKF 45) and then presented in the form of graph. Obtained results are first authenticated by way of comparison with the documented results of previous publications. Finding reveals that the inclined angle together with magnetic parameter have decelerated the fluid flow. Besides, escalating both Brownian motion and thermophoresis diffusion parameters have enhanced the temperature. In contrast, the concentration profile has reduced owing to incremented Lewis number

Flow of Jeffrey fluid over a horizontal circular cylinder with suspended nanoparticles and viscous dissipation effect : Buongiorno model

Mathematical model of Jeffrey fluid describes the property of viscoelastic that clarifies the two components of relaxation and retardation times. Nevertheless, the poor thermal performance of Jeffrey fluid has been a key issue facing the public. This issue can be accomplished by the use of nanofluid that has superior thermal performance than the conventional fluids. A better cooling rate in industry is in fact not appropriate to attain by the thermal conductivity of the conventional fluids. On that account, the present study aims to delve into the impact of viscous dissipation and suspended nanoparticles on mixed convection flow of Jeffrey fluid from a horizontal circular cylinder. A concise enlightenment on the separation of boundary layer flow is included and discussed starting from the lower stagnation point flow up to the separation point only. The non-dimensional and non-similarity transformation variables are implemented to transform the dimensional nonlinear partial differential equations (PDEs) into two nonlinear PDEs, and then tackled numerically through the Keller-box method. Representation of tabular and graphical results are executed for velocity and temperature profiles as well as the reduced skin friction coefficient, Nusselt number and Sherwood number to investigate the physical insight of emerging parameters. It was found that the incremented ratio of relaxation to retardation, Deborah number and Eckert number have delayed the boundary layer separation up to 120°

Influence of viscous dissipation on the flow and heat transfer of a Jeffrey fluid towards horizontal circular cylinder with free convection: A numerical study

This paper focuses on the numerical solution of free convection boundary layer flow past a horizontal circular cylinder in non-Newtonian Jeffrey fluid. The impact of viscous dissipation is discussed. The non-dimensional variables and non-similar transformations are implemented to transform the dimensional partial differential equations into two nonlinear partial differential equations (PDEs). Then, the implicit, unconditionally stable and well-tested Keller-box method is used to solve the PDEs by adding an extra boundary condition at infinity. The impacts of emerging parameters such as ratio of relaxation to retardation times, Deborah number, Prandtl number and Eckert number towards the quantities of physical interest are deliberated through graphical representation. The critical point for Prandtl number and ratio of relaxation to retardation times are investigated to achieve the physically acceptable solutions. It appears from this study that a rise in ratio of relaxation to retardation times tends to boost the velocity profile while declining the temperature profile. The opposite trend of graph is observed for the Deborah number where an increase in Deborah number give rise to decrement in velocity profile but increment in temperature profile. For increasing values of the Eckert number, the skin friction coefficient is found to increase while the Nusselt number is decreased. This study also reveals that for different values of Eckert number, the non-Newtonian Jeffrey fluid pronounces an effective heat transfer rate in comparison to Newtonian fluid

Non-similarity solutions of non-Newtonian Brinkman–viscoelastic fluid

The exploration of heat transference in relation to fluid flow problems is important especially for non-Newtonian type of fluid. The use of the particular fluid can be found in many industrial applications such as oil and gas industries, automotives and manufacturing processes. Since the experimental works are costly and high-risk procedures, the mathematical study is proposed to counter the limitations. Therefore, this work aims to study the characteristics of a fluid that combines the properties of viscosity and elasticity, together with the porosity conditions, called the Brinkman–viscoelastic model. The flow is assumed to move over a horizontal circular cylinder (HCC) under consideration of the convective thermal boundary condition. The mathematical model is transformed to the less complex form by utilising a non-dimensionless and non-similarity variable. The resulting equations are in the partial differential equation (PDE) form. Subsequently, the equations are required to be solved by employing the Keller-box method (KBM). The solutions were conveniently evaluated by observing the plotted graphs in order to capture the propensity of the fluid’s behavior in response to the adjusting parameters. The study discovered that the viscoelastic and Brinkman variables had the impact of decreasing the fluid’s velocity and increasing the temperature distribution. Nevertheless, when mixed convection and Biot numbers increased, the velocity profile exhibited the opposite pattern. Furthermore, increasing the Biot number raises the Nusselt number while decreasing the skin friction coefficient. These numerical results are critical for assisting engineers in making heat transfer process decisions and accurately verifying experimental investigations

Aligned MHD jeffrey fluid flow containing carbon nanoparticles over exponential stretching sheet with viscous dissipation and newtonian heating effects

This study investigates the influence of viscous dissipation on aligned Magnetohydrodynamic (MHD) flow of Jeffry fluid containing Carbon Nanoparticles (CNTs) over an exponential stretching sheet with boundary condition of Newtonian Heating (NH). The model proposed by Tiwari and Das is adopted. The numerical computation using Runge-Kutta Fehlberg (RKF45) method is used to generate the results. The numerical solutions of the several parameters on the velocity and temperature profiles are analysed and presented graphically. It is revealed that an increase in aligned angle, magnetic field, and ratio of relaxation to retardation times leads to the decreasing in velocity and increasing in temperature profiles. Meanwhile, both velocity and temperature profiles increase with a rise in volume fraction parameter

Dusty casson fluid flow containing single-wall carbon nanotubes with aligned magnetic field effect over a stretching sheet

Two-phase flow is the mutual interaction between solid and fluid phases which encountered in real life applications, such as sedimentation, blood flow, water pollution, fluidized bed and to name a few. In the theoretical study, this binary mixture is represented by partial differential equations that denotes its physical properties of all phases. Therefore, the interaction between three important elements over a stretching sheet is examined in this study where the focus is on Casson fluid, single-wall carbon nanotubes (SWCNTs) and dust particles. Moreover, the aligned magnetic field effect and Newtonian heating (NH) are associate together to influence the flow region. In order to generate the results, the equations that governed the current model must therefore employ the similarity variables to produce the ordinary differential equations. Formulation of the problem is then continued by solving the resulting equations using Runge-Kutta Fehlberg (RKF45) method. Significant outputs for considered parameters are presented through graph. It is found that, the growing effect of fluid-particle interaction particle decreases the fluid phase distribution which contributes to the opposite trend in dust phase