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1

FEM simulation of triple diffusive natural convection along inclined plate in porous medium: prescribed surface heat, solute and nanoparticles flux

Goyal M., Goyal R, Bhargava R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

883–-900

EN

In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

2

Finite element solutions for two-phase magneto-heat transfer in a particle-suspension through a non-Darcian porous channel with heat source and buoyancy effects

Bhargava R., Rawat S., Takhar H. S., Beg T. A., Anwar Beg o.

International Journal of Applied Mechanics and Engineering

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2008

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Vol. 13, no 2

325-357

EN

We consider the steady, laminar natural convection heat transfer of a particulate suspension in an electrically-conducting fluid through a two-dimensional channel containing a non-Darcian porous material in the presence of a transverse magnetic field. The transport equations for both fluid and particle phases are formulated using a two-phase continuum model and a heat source term is included which simulates either absorption or generation. A set of transformations are implemented to reduce the partial differential equations for momentum and energy conservation (for both phases) from a two-dimensional coordinate system to a one-dimensional system. Finite element solutions are obtained for the transformed model. A comprehensive parametric study of the effects of the heat source parameter (E), Prandtl number (Pr), Grashof number (Gr), momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (PL), buoyancy parameter (B), Hartmann number (Ha), temperature inverse Stokes number (SkT), viscosity ratio [...], specific heat ratio [...], dimensionless particle-phase wall slip parameter [...] on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity ( ), dimensionless fluid phase temperature [...] and the dimensionless temperature of particle phase [...] are presented graphically. In addition, we also describe numerical solutions for several special cases of the model, for example, the inviscid hydromagnetic two phase non-Darcian free convection, heat transfer [...], forced convection case (GrŽ0) etc. Fluid phase velocities are found to be strongly reduced by the magnetic field, Darcian drag and also Forchheimer drag; a lesser reduction is observed for the particle phase velocity field. The Prandtl number is shown to depress both the fluid temperature and particle phase temperature in the left hand side of the channel but to boost both temperatures at the right hand side of the channel [...]. The inverse momentum Stokes number is seen to reduce fluid phase velocities and increase particle phase velocities. The influence of other thermophysical parameters is discussed in detail and computations compared with previous studies. The model finds applications in MHD plasma accelerators, astrophysical flows, geophysics, geothermics and industrial materials processing.

3

Modified strip saturation model for a cracked piezoelectric strip

Bhargava R., Setia A.

Archives of Materials Science and Engineering

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2008

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Vol. 30, nr 1

33-36

EN

Purpose: The investigations aim to propose a model for arresting an electrical opening of a crack which weakens a narrow, poled and infinite piezoelectric strip. The edges of the strip are subjected to uniform, constant anti-plane stresses and in-plane electrical displacements. Design/methodology/approach: The loads applied at the edges of the strip open the crack in a self-similar fashion. Consequently at each tip of the crack a saturation zone protrudes. To stop the crack from further opening the rims of developed saturation zones are subjected to normal, cohesive linearly varying saturation limit electric displacement. The edges of the strip are subjected to anti-plane deformation and in-plane electrical displacement. Fourier integral transform method employed reduces the problem to the solution of a Fredholm integral equation of second kind. Findings: The electrical displacement, stress intensity factor, the saturation zone length, crack opening displacement and crack growth rate have been calculated. The results obtained presented graphically, analysed and concluded. Research limitations/implications: The ceramic used for strip is being assumed to be electrically more brittle. The investigations are carried at this level in the present paper. Also the small scale electrical yielding is considered. Consequently the developed saturation zone is proposed to lie in a line segment ahead of crack. Practical implications: Piezoelectric ceramics being widely used as transducers. Their wide utility has prompted to study many attires of such ceramic and one such attire is fracture mechanics of these ceramics. Originality/value: The paper gives an assessment of the electrical load necessary to arrest the electrical crack opening. The investigations are useful to smart material design technology where sensors and actuators are manufactured.

4

Finite element modeling of laminar flow of a third grade fluid in a Darcy-Forcheimmer porous medium with suction effects

Takhar H. S., Bhargava R., Rawat S., Beg T. A., Beg O. A.

International Journal of Applied Mechanics and Engineering

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2007

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Vol. 12, no 1

215-233

EN

A mathematical model to simulate the steady laminar flow of an incompressible, third grade, non-Newtonian fluid past an infinite porous plate embedded in a Darcy-Forcheimmer porous medium is presented. A number of special cases are examined for the governing nonlinear differential equation. The model is solved with appropriate boundary conditions using the finite element method. Velocity and velocity gradient are plotted graphically for variation in permeability (k), Forcheimmer parameter (b), third grade materiaI parameter (f3 3 ) , and suction effect (Vo). It is shown that velocities are generally decreased transverse to the plate surface with increasing Forcheimmer parameter; increasing permeability conversely boosts the velocities, as this corresponds to an increasingly fluid (Le., progressively less porous) regime. The third grade material parameter is also seen to substantially increase the velocities in the direction normal to the plate surface. The special case of a second order viscoelastic flow is also studied. The flow scenario finds applications in polymer extrusion processes, and other important industrial rheology systems.

5

Finite element solution of mixed convection micropolar fluid flow between two vertical plates with varying temperature

Kumar L., Bhargava R., Bhargava P., Takhar H. S.

Archives of Mechanics

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2005

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Vol. 57, nr 4

251--264

EN

This paper presents a finite element solution for the mixed convection micropolar fluid flow between two parallel plates with varying temperature. The governing differential equations are solved numerically using the finite element method. The effect of important parameters, namely pressure gradient, micropolar parameter and surface, condition parameter on velocity, microrotation as well as on temperature functions has been studied. It is noticed that the micropolar fluids act as a cooling agent as well as a drag reducing fluids.