Md. Mahmud Alam

Numerical study of transient magnetohydrodynamic radiative free convection nanofluid flow from a stretching permeable surface

Transient mixed convective laminar boundary layer flow of an incompressible, viscous, dissipative, electrically conducting nanofluid from a continuously stretching permeable surface in the presence of magnetic field and thermal radiation flux is studied. The model used for the unsteadiness in the momentum, temperature, and concentration fields is based on the time-dependent stretching velocity and surface temperature and concentration. Similarity transformations are used to convert the governing time-dependent nonlinear boundary layer equations for momentum, thermal energy, and concentration to a system of nonlinear ordinary coupled differential equations with appropriate boundary conditions. The transformed model is shown to be controlled by a number of thermophysical parameters, namely the magnetic parameter, thermal convective parameter, mass convective parameter, suction parameter, radiation-conduction parameter, Eckert number, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, and the unsteadiness parameter. Numerical solutions are obtained with the robust Nactsheim–Swigert shooting technique together with Runge–Kutta sixth-order iteration schemes. Comparisons with previously published work are performed and are found to be in excellent agreement. The effects of selected parameters on velocity, temperature, and concentration distributions and furthermore on skin friction coefficients, heat transfer rate (Nusselt number), and mass transfer rate (Sherwood number) are presented graphically. The current study has applications in high-temperature nano-technological materials processing.

Explicit numerical study of unsteady hydromagnetic mixed convective nanofluid flow from an exponentially stretching sheet in porous media

A numerical investigation of unsteady magnetohydrodynamic mixed convective boundary layer flow of a nanofluid over an exponentially stretching sheet in porous media, is presented. The transformed, non-similar conservations equations are solved using a robust, explicit, finite difference method (EFDM). A detailed stability and convergence analysis is also conducted. The regime is shown to be controlled by a number of emerging thermophysical parameters i.e. combined porous and hydromagnetic parameter (R), thermal Grashof number (Gr), species Grashof number (Gm), viscosity ratio parameter (Λ), dimensionless porous media inertial parameter (∇), Eckert number (Ec), Lewis number (Le), Brownian motion parameter (Nb) and thermophoresis parameter (Nt). The flow is found to be accelerated with increasing thermal and species Grashof numbers and also increasing Brownian motion and thermophoresis effects. However, flow is decelerated with increasing viscosity ratio and combined porous and hydromagnetic parameters. Temperatures are enhanced with increasing Brownian motion and thermophoresis as are concentration values. With progression in time the flow is accelerated and temperatures and concentrations are increased. EFDM solutions are validated with an optimized variational iteration method. The present study finds applications in magnetic nanomaterials processing.

MHD Mixed Convective Boundary Layer Flow of a Nanofluid through a Porous Medium due to an Exponentially Stretching Sheet

Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.

Flow Through a Rotating Curved Duct with Square Cross-Section

The incompressible viscous steady flow through a curved duct of square cross-section driven by a pressure gradient along the duct is considered. The rotation of the duct about the centre of the curvature is imposed to investigate the combined effects of rotation (Coriolis force) and curvature (centrifugal force) on the flow. The numerical calculations covering a wide range of rotational speed are carried out for the Dean numbers, D n , of 400, 642 and 800. When the rotation is in the same as the main flow direction, multiple solutions with 2-cell and 4-cell secondary flow patterns are obtained in case of D n =400 and 642, while only 4-cell solution is obtained in case of D n =800. When the rotation is opposite to the main flow direction, the 6-cell secondary flow pattern is obtained for D n =400, 642 and D n =800 with increasing the rotational speed gradually. For all cases, the total flux through the duct has a sharp peak, where the 6-cell pattern appears.

Flow through a rotating helical pipe with circular cross-section

Abstract The incompressible viscous steady flow through a helical pipe of circular cross-section rotating at a constant angular velocity about the centre of curvature is investigated numerically to examine the combined effects of rotation (Coriolis force), torsion and curvature (centrifugal force) on the flow. It is found that the variation of the total flux with rotation shows a sharp peak when the direction of rotation is negative, that is, in the opposite direction to the pressure-driven flow. The total flux decreases at large rotation. As the torsion increases, the flux first decreases from that of the toroidally curved pipe, reaches a minimum and then increases when the rotation is positive or negative large value. The secondary flow structure in the cross-section of the helical pipe is one cell type when the flux is close to the maximum. There is no bifurcation of the flow.

SPECTRAL NUMERICAL SIMULATION OF MAGNETO-PHYSIOLOGICAL LAMINAR DEAN FLOW

A computational simulation of magnetohydrodynamic laminar blood flow under pressure gradient through a curved bio-vessel, with circular cross-section is presented. Electrical conductivity and other properties of the biofluid (blood) are assumed to be invariant. A Newtonian viscous flow (Navier–Stokes magnetohydrodynamic) model is employed which is appropriate for large diameter blood vessels, as confirmed in a number of experimental studies. Rheological effects are therefore neglected as these are generally only significant in smaller diameter vessels. Employing a toroidal coordinate system, the steady-state, three-dimensional mass and momentum conservation equations are developed. With appropriate transformations, the transport model is non-dimensionalized and further simplified to a pair of axial and secondary flow momenta equations with the aid of a stream function. The resulting non-linear boundary value problem is solved with an efficient, spectral collocation algorithm, subject to physically appropriate boundary conditions. The influence of magnetic body force parameter, Dean number and vessel curvature on the flow characteristics is examined in detail. For high magnetic parameter and Dean number and low curvature, the axial flow is observed to be displaced toward the center of the vessel with corresponding low fluid particle vorticity strengths. Visualization is achieved with the MAPLE software. The simulations are relevant to cardiovascular biomagnetic flow control.

MHD boundary layer flow and heat transfer characteristics of a nanofluid over a stretching sheet

Abstract The study of radiative heat transfer in a nanofluid with the influence of magnetic field over a stretching surface is investigated numerically. Physical mechanisms responsible for magnetic parameter, radiation parameter between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. The parameters for Prandtl number Pr, Eckert number Ec, Lewis number Le, stretching parameter b/a and constant parameter m are examined. The governing partial differential equations were converted into nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with previously published work and the results are found to be in excellent agreement. Numerical results for velocity, temperature and concentration distributions as well as skin-friction coefficient, Nusselt number and Sherwood number are discussed at the sheet for various values of physical parameters.

Numerical simulation and stability analysis on MHD free convective heat and mass transfer unsteady flow through a porous medium in a rotating system with induced magnetic field

A numerical study of Soret and Dufour effects on MHD free convective heat and mass transfer unsteady high speed flow of viscous fluid through a porous medium with induced magnetic field is investigated in a rotating system. In this observation, heat and mass fluxes from the medium are considered to be constant for cooling problem with lighter and heavier particles. Numerical values of velocity, induced magnetic field, temperature and concentration are computed by the conditionally stable explicit finite difference method with stability and convergence analysis. The shear stress, current density, Nusselt number and Sherwood number are also calculated here. Effects of associated parameters on the above mentioned quantities are shown graphically and physical aspects of the problem are discussed in detail. Finally, both the qualitative and quantitative comparisons of present results with previous work are presented in tabular form.

Radiation and thermal diffusion effect on a steady MHD free convection heat and mass transfer flow past an inclined stretching sheet with Hall current and heat generation

In the present paper is an investigation of steady MHD free convection, heat and mass transfer flow of an incompressible electrically conducting fluid past an inclined stretching sheet under the influence of an applied uniform magnetic field with Hall current and radiation effect. Using suitable similarity transformations the governing fundamental boundary layer equations are transformed to a system of non-linear similar ordinary differential equations for momentum, thermal energy and concentration equations which are then solved numerically by the shooting method along with Runge- Kutta fourth-fifth order integration scheme. The results presented graphically illustrate that primary velocity field decrease due to increase of magnetic parameter, Angle of inclination, Dufour number, Prandtl number, Heat generation and Soret number while secondary velocity also decrease for Hall parameter . Other parameters increase the velocities of the fluid flow. Temperature field increases in the presence of Dufour number, heat generation, Schmidt number, Magnetic parameter, Grashof number & Modified Grashof number and decreases for other parameters. Also, concentration profiles decreases for increasing the values of Dufour number, Schmidt number, Heat generation, Soret number, Grashof number & Modified Grashof number but concentration increases for other parameters. The numerical results concerned with the primary velocity, secondary velocity, temperature and concentration profiles effects of various parameters on the flow fields are investigated and presented graphically. Also the skin friction coefficient, the local Nusselt number and the local Sherwood number are presented in Tables 1-3.

Transient Heat and Mass Transfer Flow through Salt Water in an Ocean by Inclined Angle

Abstract In the present computational study, the inclined angle effect of unsteady heat and mass transfer flow through salt water in an ocean was studied. The governing equations together with continuity, momentum, salinity and temperature were developed using the boundary layer approximation. Cartesian coordinate system was introduced to interpret the physical model where x-axis chosen along the direction of salt water flow and y-axis is inclined to x-axis. Two angle of inclination was considered such as 90° and 120°. The time dependent governing equations under the initial and boundary conditions were than transformed into the dimensionless form. A numerical solution approach so-called explicit finite difference method (EFDM) was employed to solve the obtained dimensionless equations. Different physical parameter was found in the model such as Prandtl number, Modified Prandtl number, Grashof number, Heat source parameter and Soret number. A stability and convergence analysis was developed in this study to describe the aspects of the finite difference scheme and this analysis is significant due to accuracy of the EFDM approach. The convergence criteria were observed to be in terms of dimensionless parameter as Pr ≥ 0.0128 and Ps ≥ 0.016. The distributions of the temperature and salinity profiles of salt water flow over different time steps were investigated for the effect of different dimensionless parameters and shown graphically.