M.A. Alim

NUMERICAL SIMULATION OF NON-DARCY FORCED CONVECTION THROUGH A CHANNEL WITH NONUNIFORM HEAT FLUX IN AN OPEN CAVITY USING NANOFLUID

This article aims to numerically investigate forced convection heat transfer phenomena in a two-dimensional horizontal channel having an open cavity with porous medium. A nonuniform heat flux is considered to be located on the bottom surface of the cavity. Three different heating modes are considered at this wall. The rest of the surfaces are taken to be perfectly adiabatic. The physical domain is filled with water based nanofluid containing TiO2 naparticles. The fluid enters from left and exits from right with initial velocity U i and temperature T i . Governing equations are discretized using the penalty finite element method. The simulation is carried out for a range of Prandtl number Pr(=5.2–12.2) and solid volume fraction φ (=0%–15%). Results are presented in the form of streamlines, isothermal lines, local and average Nusselt number, average temperature of the fluid, horizontal and vertical velocities at mid-height of the channel, and mean velocity field for various Pr and φ. It is found that increasing Pr and φ cause the enhancement of the heat transfer rate.

Transient Analysis on Forced Convection Phenomena in a Fluid Valve Using Nanofluid

A transient numerical study is conducted to investigate the transport mechanism of forced convection in a fluid valve filled with water-CuO nanofluid. The flow enters from one inlet at the left with uniform temperature and velocity T i and U i , respectively, but can leave the valve through two outlets at the right. The upper and lower boundaries of the valve are heated with constant temperature T h , while the remaining walls are perfectly insulated. The numerical approach is based on the finite element technique with Galerkins weighted residual simulation. Solutions are obtained for fixed Prandtl number (Pr = 1.47), Reynolds number (Re = 100), and solid volume fraction (φ = 5%). The streamlines, isotherm plots, flow rate and the local Nusselt number (Nu local ) at both heated phases, the average Nusselt number (Nu) for base fluid, and nanofluid with the variation of nondimensional time (τ) are presented and discussed. It is found that the rate of heat transfer in the fluid valve reduces for longer time periods.

Effect of Temperature-Dependent Variable Viscosity on Magnetohydrodynamic Natural Convection Flow along a Vertical Wavy Surface

The effect of temperature dependent variable viscosity on magnetohydrodynamic (MHD) natural convection flow of viscous incompressible fluid along a uniformly heated vertical wavy surface has been investigated. The governing boundary layer equations are first transformed into a nondimensional form using suitable set of dimensionless variables. The resulting nonlinear system of partial differential equations are mapped into the domain of a vertical flat plate and then solved numerically employing the implicit finite difference method, known as Keller-box scheme. The numerical results of the surface shear stress in terms of skin friction coefficient and the rate of heat transfer in terms of local Nusselt number, the stream lines and the isotherms are shown graphically for a selection of parameters set consisting of viscosity parameter (𝜀), magnetic parameter (𝑀), and Prandtl number (Pr). Numerical results of the local skin friction coefficient and the rate of heat transfer for different values are also 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.

A New Geometric Average Technique to Solve Multi-Objective Linear Fractional Programming Problem and Comparison with New Arithmetic Average Technique

In this paper, we have suggested a new technique to solve a MOLFPP by using new geometric averaging method. An algorithm is suggested for its solution. We have used some other techniques such as arithmetic averaging, geometric averaging, and new arithmetic averaging method to solve the same problem. New geometric averaging method gives better result than all those methods.

Numerical Study of Blood Flow through Symmetry and NonSymmetric Stenosis Artery under Various Flow Rates

This study investigated the significance of symmetry and non-symmetry stenosis effects of blood flow and quantifies some of the most relevant non Newtonian characteristics of blood flow in blood vessels. The models studied in this work are the Newtonian and Non-Newtonian (Oldroyd-B) models, as well as their generalized (shear-thinning) modifications. The governing system of equations is based on incompressible Navier-Stokes equations which are generalized to take into account viscoelasticity and shear-thinning properties of blood flow. Finite element method is used for the solution of the governing system of equations. Mathematical tests are performed on an idealized symmetric stenosis and a realistic stenosed carotid bifurcation reconstructed from medical images. Model sensitivity tests are achieved with respect to the characteristic flow rate to evaluate its impact on the observed non-Newtonian effects. The numerical simulation is performed for various flow rates 0.05 to 2 cm 3 /s at Reynold numbers, Re =10 2 and Weissenberg numbers, Wi= 0.6 with good convergence of the iterative scheme. Results from the blood flow simulations indicate that non-Newtonian behavior has considerable effects on instantaneous flow patterns. Different effects for these models are presented numerically.

Finite Element Analysis of MHD Natural Convection in a Rectangular Cavity and Partially Heated Wall

In this paper numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within rectangular enclosures. A finite element analysis is performed to investigate the effects of uniform heating and is also used for solving the Navier-Stokes and Energy balance equations. The horizontal bottom wall is divided into three sections. The middle section of the horizontal bottom wall was kept temperature at Th and the other two parts of the horizontal bottom wall were kept thermal insulation while the left and right vertical walls and the top wall of the cavity were maintained constant temperature Tc with Th>Tc. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number (Ha = 0, 50, 100), Rayleigh number (Ra = 103 – 106) and Prandtl number Pr=0.71. The streamlines, isotherms, average Nusselt number at the hot wall and velocity profiles and temperature distribution of the fluid in the enclosure are presented for the parameters. The numerical results indicated that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. Also the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the enclosure.

MHD free convection heat and mass transfer flow through a porous medium in a rotating system with hall current and heat generation

The present work is the focused on steady Magneto hydrodynamics (MHD) free convection boundary layer flow of an incompressible electrically conducting fluid through a porous medium over a semi-infinite vertical plate in a rotating system with heat generation and the effects of Hall current are taken into account. The governing boundary layer equations are transformed into a set of non-linear ordinary differential equations for primary velocity, secondary velocity, temperature and concentration equations which are then solved numerically by the shooting method along with Runge-Kutta fourth-fifth order integration scheme. The effect of entering parameters on the primary velocity, secondary velocity, the temperature and concentration profiles are presented graphically. Therefore, the results of primary velocity field and secondary velocity field increases for increasing values of Hall parameter and permeability parameter but other parameters decrease the velocities of the fluid flow. The temperature field decreases in the presence of magnetic parameter, heat generation parameter, Prandtl number, Soret & Dufour numbers and Grashof number and negligible decreasing effect for rotational parameter. Also, concentration profile decreases for increasing the values of heat generation parameter, magnetic parameter, Prandtl number and Schmidt number but concentration increases for the effect of Grashof number, Soret number & Hall parameter. The numerical results for the rate of heat transfer are compared with other authors when the magnetic field, Grashof number, rotational parameter, heat generation parameter and Dufour number are absent and found almost similar result.

Finite Element Analysis of MHD Free Convection within Trapezoidal Enclosures with Uniformly Heated Side Walls

A numerical study is presented of two-dimensional laminar steady-state on megneto-hydrodynamics (MHD) free convection for heat flow patterns within trapezoidal enclosures. A finite element analysis is performed to investigate the effects of unifor heating and is also used for solving the Navier-Stokes and Energybalance equations.In this study, cold bottom walls, uniformly heated left and right (side) walls and insulated top walls with inclination angles (ф) are considered in a trapezoidal enclosure. The present numerical procedure adopted in this investigation yields consistent performance over a wide range of parameters, Prandtl numbers, (Pr = 0.026 - 0.7), and Rayleigh numbers (Ra = 10 3 - 10 5 ), Hartmann number (Ha = 50) with various tilt angles Ф = 45 0 , 30 0 and 0 0 (square).Numerical results are presented in terms of streamlines, isotherms, heat