Unsteady MHD free convection flow of Jeffrey fluid and Jeffrey nanofluid along a vertical plate with radiation effect

Fluid is a substance that continuously deform under the influence of shear stress. Basically, fluid can be classified into two categories which are Newtonian and non-Newtonian. In reality, most fluids belong to the class of non-Newtonian fluids and one of them is Jeffrey fluid. Jeffrey fluid is also known as viscoelastic fluid that exhibits both viscous and elastic characteristics. Recently, this type of fluid have received considerable attention due to their numerous applications in industries especially in polymer industries. Due to this reason, many investigations have been made to study the Jeffrey fluid in various aspects from both analytical and numerical methods. Therefore, in this thesis, the effect of thermal radiation on unsteady magnetohydrodynamics (MHD) free convection flow of Jeffrey fluid with and without nanoparticles past an infinite vertical plate are studied. The fluid is taken electrically conducting in the presence of uniform transverse magnetic field applied in a direction perpendicular to the flow. Specifically, focused of this study is to obtain an exact solution for velocity and temperature distributions under conditions of ramped wall temperature and isothermal plate. Using the constitutive relation of Jeffrey fluid and some assumptions of physical conditions, five specific problems are modelled as partial differential equations. For the first three problems, the fluid is considered as non-rotating fluid, while in the fourth and fifth problems the rotating fluid is analyzed. An appropriate dimensionless variables are employed to the dimensional governing equations and solved analytically with the help of Laplace transform technique. The effect of pertinent parameters such as Jeffrey fluid parameter, rotation parameter, phase angle, Hartmann number, permeability parameter, nanoparticles volume fraction, Grashof number, Prandtl number, radiation parameter and time on velocity and temperature are plotted graphically and discussed in details. Numerical results of Nusselt number and skin friction for various emerging parameters are calculated and presented in tabular forms. In order to authenticate the present results, the limiting cases are provided, where an excellent agreement are found. Results obtained show that, increasing of Hartmann number tends to retard the fluid flow due to the Lorentz force effect. Increasing the values of radiation parameter led to an increase in velocity and temperature fields. Further, in the case of rotating fluid, large values of rotation parameter reduces the primary velocity but enhance in the secondary velocity. On the other hand, increasing nanoparticles volume fraction causes the velocity of non-rotating fluid increases but decreases for rotating fluid. It also found that, the fluid motion for ramped wall temperature is always slower compared to an isothermal plate. Interestingly, Jeffrey fluid can be reduced to a Second grade fluid in the absence of material parameter

Unsteady Free Convection Flow past a Vertical Plate with Heat and Mass Fluxes in the Presence of Thermal Radiation

The problem of unsteady free convection flow past an infinite vertical plate with heat and mass fluxes in the presence of thermal radiation is studied. The dimensionless coupled linear partial differential equations governing the flow are solved by employing the Laplace transform technique. Exact solutions have been obtained for the fluid velocity, temperature and mass concentration for the cases of both uniform heat flux (UHF) and uniform wall temperature (UWT). The numerical results for the fluid velocity, temperature and mass concentration are presented graphically for various pertinent flow parameters and discussed in detail

Effect of Radiation and Chemical Reaction on Transient MHD Free Convective Flow over a Vertical Plate Through Porous Media

This paper analyzed the Magneto hydrodynamic, Radiation and chemical reaction effects on unsteady flow, heat and mass transfer characteristics in a viscous, in compressible and electrically conduction fluid over a semi-infinite vertical porous plate through porous media. The porous plate is subjected to a transverse variable suction velocity. The transient, non-linear and coupled governing equations have been solved adopting a perturbative series expansion about a small parameter, ε. The effects of governing parameters on the flow variables are discussed graphically. Keywords: Transient velocity, MHD, Chemicalreaction, Radiation and Rarefaction Parameter

Hall effects on unsteady MHD natural convective flow past an impulsively moving plate with ramped temperature and concentration

517-534This paper deals with the study of an unsteady magnetohydrodynamic natural convective flow of a viscous incompressible electrically conducting fluid past an impulsively moving infinite vertical plate with ramped temperature and mass concentration taken into account the Hall effects. A uniform magnetic field is applied transversely to the direction of the flow. The flow consideration is subjected to small magnetic Reynolds number. Induced magnetic field is absent. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. Analytical solution of the governing equations has been obtained by employing the Laplace transform technique. The influences of the pertinent parameters on the velocity field, temperature distribution, mass concentration in fluid, shear stress and rate of heat and mass transfer are discussed with the help of graphs. Hall current is found to elevate the fluid velocity components. It is observed that significant difference can be observed between the velocity profiles due to ramped and isothermal boundary conditions

Heat and Mass Transfer to Unsteady MHD Viscoelastic Slip Flow through a Porous Medium with Chemical Reaction

In the present paper, an analysis is carried out to heat and mass transfer to unsteady flow of an electrically conducting incompressible non-Newtonian viscoelastic fluid filled in a vertical channel in the presence of transverse magnetic field through porous medium with heat source. The fluid and the channel rotate as a solid body with constant angular velocity, about an axis perpendicular to the planes of the plates. The effects of thermal radiation and chemical reaction are taken into account embedded with slip boundary condition. The momentum, energy and concentration equations are solved by using closed-from of analytical solution. The influences of the various parameters entering into the problem are illustrated with the help of graphs. Possible applications of the present study include engineering science and applied mathematics in the context of aerodynamics, geophysics and aeronautics

Inclined Magneticfield and Chemical Reaction Effects on Flow over a Semi Infinite Vertical Porous Plate through Porous Medium

We analyse the MHD, Radiation and chemical reaction effects on unsteady flow, heat and mass transfer characteristics in a viscous, incompressible and electrically conducting fluid over a semi infinite vertical porous plate through porous media in presence of inclined magnetic field. The porous plate is subjected to a transverse variable suction velocity. The transient, non-linear and coupled governing equations have been solved adopting a perturbative series expansion about a small parameter, ε. The effects of governing parameters on the flow variables are discussed graphically

Numerical study of heat transfer enhancement in MHD free convection flow over vertical plate utilizing nanofluids

AbstractA comprehensive numerical study of heat transfer enhancement in MHD free convection flow over vertical plate utilizing nanofluids has been carried out. Problem is formulated by using nanofluid volume fraction model by considering water based nanofluids containing copper and aluminum oxide. The transformed coupled, nonlinear dimensionless partial differential equations are solved numerically by using finite element method. The influence of pertinent physical parameters on velocity and temperature profiles is discussed and depicted with the aid of graphs. Finally, the numerical values of skin friction and Nusselt number within the flow regime are compared with the previously published work to ensure the correctness of this numerical scheme and an excellent agreement is obtained

Effect of porosity on unsteady MHD convection flow Past a moving vertical plate with ramped wall temperature

The unsteady MHD convective flow of an electrically conducting fluid embedded in a porous medium along moving infinite vertical plate with ramped wall temperature and radiation in a rotating system is investigated here. The fluid taken is incompressible and viscous. The governing PDE’s of the model are solved by using integral transform method. The analytical solutions for the velocity, concentration and temperature are obtained. The expressions for skin friction, rate of mass transfer and heat transfer near the plate are obtained. The effects of various parameters like porosity of the medium, magnetic field, Soret number, thermal radiation, rotation, radiation and Hall current on the flow field are discussed. It is observed that velocity increases with the increase in the porosity parameter K. It reveals that a porous medium having large permeability supports the movement of the fluid in the system. Also, it is noticed that Hall parameter reduces the resistive effect of the applied magnetic field. Such a study assumes importance because both rotation and Hall current induce secondary flow in the flow-field. The results of the research may be useful in many industrial applications

Numerical computation of buoyancy and radiation effects on MHD micropolar nanofluid flow over a stretching/shrinking sheet with heat source

Abstract In this mathematical study, the effect of buoyancy parameters along with radiation on magneto-hydrodynamic (MHD) micro-polar nano-fluid flow over a stretching/shrinking sheet is taken into consideration. Suitable similarity variables are used to convert the governing non-linear partial differential equations into a system of coupled non-linear ordinary differential equations which are then numerically solved by R.K method with shooting scheme. The influence of pertinent parameters on the velocity profile, temperature profile, micro-rotation profile, and concentration profile is investigated. It is founded that the velocity profile is decreased with the increment in the values of M and the opposite behavior is noticed for micro-rotation, thermal, and concentration profiles. It is also founded that an increase in the values of buoyancy parameters causes an increase in velocity profile while micro-rotation, thermal, and concentration profiles are decreased. The results are exposed and discussed through tables and graphs