Rama Bhargava

Numerical solution for mixed convection boundary layer flow of a nanofluid along an inclined plate embedded in a porous medium

The steady mixed convection boundary layer flow of an incompressible nanofluid along a plate inclined at an angle @a in a porous medium is studied. The resulting nonlinear governing equations with associated boundary conditions are solved using an optimized, robust, extensively validated, variational finite-element method (FEM) and a finite-difference method (FDM) with a local non-similar transformation. The Nusselt number is found to decrease with increasing Brownian motion number (Nb) or thermophoresis number (Nt), whereas it increases with increasing angle @a. In addition, the local Sherwood number is found to increase with a rise in Nt, whereas it is reduced with an increase in Nb and angle @a. The effects of Lewis number, buoyancy ratio, and mixed convection parameter on temperature and concentration distributions are also examined in detail. The present study is of immediate interest in next-generation solar film collectors, heat-exchanger technology, material processing exploiting vertical and inclined surfaces, geothermal energy storage, and all those processes which are greatly affected by a heat-enhancement concept.

Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet

This paper presents a finite element solution for the mixed convection micropolar flow driven by a porous stretching sheet with uniform suction. The governing partial differential equations are solved numerically by the using finite element method and the results have been compared with those obtained by using the quasi-linearization method. The effect of surface conditions on the velocity, microrotation as well as for temperature functions has been studied. It is noticed that the micropolar fluids help in the reduction of drag forces and also act as a cooling agent.

Numerical solution of free convection MHD micropolar fluid flow between two parallel porous vertical plates

The fully developed electrically conducting micropolar fluid flow between two vertical porous parallel plates is studied in the presence of temperature dependent heat sources including the effect of frictional heating and in the presence of a magnetic field. Profiles for velocity, microrotation and temperature are presented for a wide range of Hartmann numbers and the micropolar parameter. The skin friction, couple stress and Nusselt numbers at the plates are shown in the tables.

Finite element solution of micropolar fluid flow and heat transfer between two porous discs

The problem of steady axisymmetric flow and heat transfer in an incompressible micropolar fluid between two porous discs has been studied. A finite element analysis of the resulting system of nonlinear coupled differential equations representing the velocity, microrotation and temperature is presented. The numerical results for the radial and axial velocities, microrotation, temperature, skin friction, couple stress coefficient and the rate of heat transfer on the discs for different values of the micropolar parameter and the injection Renolds number have been obtained. A comparison of the results is made with those obtained through the quasilinearisation method as well as the series solution for the viscous case, thus proving the versatility of the finite element method.

The onset of convection in a binary nanofluid saturated porous layer

The double-diffusive convection in a horizontal nanofluid saturated porous layer is studied analytically using a Brinkman-Darcy model. The model used for nanofluid includes the effects of Brownian motion and thermophoresis. The linear stability theory is employed to obtain the condition for the onset of convection. The effect of solute Rayleigh number, Soret parameter, Dufour parameter, Lewis number, nanoparticle Rayleigh number, nanoparticle Lewis number, modified particle-density increment parameter, modified diffusivity ratio, Darcy number and the porosity parameter have been analysed on the onset of convection. The sufficient conditions for the non-existence of overstability are also obtained.

Finite element solution of flow and heat transfer of a micropolar fluid over a stretching sheet

Abstract A steady, incompressible micropolar fluid flow and heat transfer over a stretching sheet has been analysed. The resulting system of non-linear ordinary coupled differential equations is solved by finite element method using variational Ritz model. Numerical results obtained for velocity, microrotation and temperature distributions are shown graphically.

Boundary layer flow and heat transfer of viscoelastic nanofluids past a stretching sheet with partial slip conditions

The aim of the paper is to analyze the effect of velocity slip boundary condition on the flow and heat transfer of non-Newtonian nanofluid over a stretching sheet. The Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations with the help of group theory transformations. The obtained ordinary differential equations are solved by variational finite element method (FEM). The effects of different controlling parameters, namely, the Brownian motion parameter, the thermophoresis parameter, viscoelastic parameter, Prandtl number, Lewis number and the slip parameter on the flow field and heat transfer characteristics are examined. The numerical results for the dimensionless velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically. The present study is of great interest in the fields of coatings and suspensions, cooling of metallic plates, oils and grease, paper production, coal water or coal–oil slurries, heat exchangers’ technology, and materials’ processing and exploiting.

Finite element simulation of unsteady magneto-hydrodynamic transport phenomena on a stretching sheet in a rotating nanofluid

This study examines theoretically and computationally the transient magneto-hydrodynamic boundary layer flow and heat transfer in an incompressible rotating nanofluid over a stretching continuous sheet, with a transverse magnetic field applied normal to the sheet plane. The three-dimensional conservation equations for mass, momentum, energy and species (nanoparticle) diffusion, are normalized into a system of two-dimensional dimensionless boundary layer equations, using appropriate scaling transformations. The resulting nanofluid transport model incorporates a Brownian motion parameter, thermophoresis parameter, rotation parameter, unsteady parameter, Prandtl number, Hartmann magnetic parameter and Lewis number, and physically realistic boundary conditions at the sheet surface and in the free stream. The nonlinear two-point boundary value problem is solved using a robust, efficient finite element method based on the variational formulation. A detailed evaluation of the effects of the governing physical parameters on the velocity components, temperature and nanoparticle concentration via graphical plots is conducted. Primary velocity is strongly retarded with increasing Hartmann number and there is also a reduction in secondary velocity magnitude. Both temperature and nanoparticle concentration are positively affected by the Hartmann number. Increasing rotational parameter decreases both primary and secondary velocity, and also depresses temperature and nanoparticle concentration. Unsteadiness parameter is generally found to enhance primary velocity and temperatures but exhibits a varied influence on secondary velocity and nanoparticle concentration. The reduced Nusselt number (wall temperature gradient) is observed to be depressed with both Brownian motion and thermophoresis effects, whereas the contrary behaviour is computed for the reduced Sherwood number (wall mass transfer gradient). The reduced Nusselt number and the Sherwood number also show a steady decrease with increasing rotational parameter. The present finite element method solutions have been validated extensively with the previously published results, demonstrating excellent correlation. The study has important applications in the manufacture and electromagnetic control of complex magnetic nanofluid materials of relevance to biomedical, energy systems and aerospace systems technologies.

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

Abstract The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy–Brinkman–Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.

Numerical study of heat transfer characteristics of the micropolar boundary layer near a stagnation point on a moving wall

The present paper presents a numerical study of heat transfer of a micropolar boundary layer flow near a stagnation point on a moving wall. The governing differential equations are solved numerically and the temperature profiles are shown graphically for different values of material parameters and wall velocity. The heat transfer rate has been obtained for both the isothermal and the adiabatic case. It is concluded that the temperature in the boundary layer increases for the micropolar flows, as compared to the Newtonian flows.