Numerical simulation of MHD flow of micropolar fluid inside a porous inclined cavity with uniform and non-uniform heated bottom wall

2018 ◽  
Vol 96 (6) ◽  
pp. 576-593 ◽  
Author(s):  
Mubbashar Nazeer ◽  
N. Ali ◽  
Tariq Javed
Keyword(s):  
Magnetic Field ◽  
Temperature Distribution ◽  
Micropolar Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Numerical Data ◽  
Mhd Flow ◽  
Bottom Wall ◽  
Nusselt Numbers ◽  
Two Dimensional Flow ◽  
Inclined Cavity

Buoyancy-driven, incompressible, two-dimensional flow of a micropolar fluid inside an inclined porous cavity in the presence of magnetic field is investigated. The nonlinear partial differential equations are solved by employing a robust Galerkin finite element scheme. The pressure term in this scheme is eliminated by using the penalty method. The results are exhibited in the form of streamlines, isotherms, and local and average Nusselt numbers for two cases, namely, the constant and the sinusoidal heated lower wall of the conduit. In both cases, the side walls of the cavity are cold and the upper side is insulated. The main difference between the two cases is observed from temperature contours. For constant heated bottom wall a finite discontinuity appears in the temperature distribution at the corners of the bottom wall. In contrast, no such discontinuity appears in the temperature distribution for non-uniform heated bottom wall. The quantitative changes in temperature contours in different portions of the cavity are identified by comparing the results for both cases. The code is also validated and benchmarked with the previous numerical data available in the literature. It is found that the magnetic field inclined at a certain angle either suppresses or enhances the intensity of primary circulations depending on the inclination of the cavity. Further, the average Nusselt number at the bottom wall is higher when magnetic field is applied vertically irrespective of the inclination of cavity. The analysis presented here has potential application in solar collectors and porous heat exchangers.

scholarly journals Analysis of Chemical Reaction on MHD Micropolar Fluid Flow over a Shrinking Sheet near Stagnation Point with Nanoparticles and External Heat

2021 ◽  
Vol 39 (1) ◽  
pp. 262-268
Author(s):  
Krishnandan Verma ◽  
Debozani Borgohain ◽  
Bishwaram Sharma
Keyword(s):  
Stagnation Point ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Numerical Data ◽  
Mhd Flow ◽  
Heat Transfer Process ◽  
External Heat ◽  
Shrinking Sheet ◽  
Similarity Transformations ◽  
Micropolar Nanofluid

The present study investigates numerically MHD flow near the stagnation point of micropolar fluid through a shrinking sheet containing nanoparticles under the influence of chemical reaction and external heat. The study is an attempt to investigate the flow behaviour of micropolar nanofluid because of its importance in heat transfer process in industries as well as cooling systems. The governing equations are converted to nonlinear ordinary differential equations by implementing similarity transformations. Numerical results are investigated in the form of figures and tables by using MATLAB built in solver bvp4c for various dimensionless parameters. The impacts of external heat parameter on temperature and chemical reaction factor on concentration of the nanofluid are illustrated in the form of graphs. It is observed that the temperature of the nanofluid and nanoparticle volume distributions increase when Biot number attain larger values. Rise in Thermophoretic parameter increases the nanoparticles concentration in the boundary layer. Numerical data are presented for Nusselt number and Sherwood number.

scholarly journals Heat transfer effect on MHD flow of a micropolar fluid through porous medium with uniform heat source and radiation

2019 ◽  
Vol 8 (1) ◽  
pp. 65-73 ◽  
Author(s):  
S.R. Mishra ◽  
Mohammad Mainul Hoque ◽  
B. Mohanty ◽  
N.N. Anika
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Velocity Profile ◽  
Micropolar Fluid ◽  
Magnetic Parameter ◽  
Flow Direction ◽  
Coupling Parameter ◽  
Mhd Flow ◽  
Physical Parameters ◽  
Nusselt Numbers

Abstract The present study examines the effect of heat transfer on electrically conducting MHD micropolar fluid flow along a semi-infinite horizontal plate with radiation and heat source. The uniform magnetic field has applied along the principal flow direction. The obtained governing equations have been converted into a set of dimensionless differential equations and then numerically solved by using a well-known Runge-Kutta method with shooting technique. The velocity, microrotation, and temperature distribution are presented for various physical parameters. The numerical values of skin friction and Nusselt numbers at the plates are shown in tabular form, and the obtained results are compared with the results of a previous study. It has been found that the magnetic parameter increases the velocity profile whereas the boundary layer thickness reduces due to the inclusion of coupling parameter and inertia effect. The presence/absence of magnetic parameter and coupling parameter enable to enhance the angular velocity profile while it is worth to note that the backflow has generated in the vicinity of the plate.

scholarly journals Hydromagnetic Dissipative and Radiative Graphene Maxwell Nanofluid Flow Past a Stretched Sheet-Numerical and Statistical Analysis

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1929 ◽  
Author(s):  
Syed M. Hussain ◽  
Rohit Sharma ◽  
Manas R. Mishra ◽  
Sattam S. Alrashidy
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Physical Parameters ◽  
Maxwell Nanofluid ◽  
Nusselt Numbers ◽  
Highly Nonlinear ◽  
Numeric Data ◽  
The Relationship ◽  
The Magnetic Field

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

scholarly journals Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

2016 ◽  
Vol 26 (8) ◽  
pp. 2370-2392 ◽  
Author(s):  
Ioan Pop ◽  
Siti Suzilliana Putri Mohamed Isa ◽  
Norihan M. Arifin ◽  
Roslinda Nazar ◽  
Norfifah Bachok ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Flow Characteristics ◽  
Mhd Flow ◽  
Integration Scheme ◽  
Shrinking Sheet ◽  
Content Type

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

Effects of Thermal Radiation on Unsteady Magnetohydrodynamic Flow of a Micropolar Fluid with Heat and Mass Transfer

2010 ◽  
Vol 65 (11) ◽  
pp. 950-960 ◽  
Author(s):  
Tasawar Hayat ◽  
Muhammad Qasim
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat And Mass Transfer ◽  
Micropolar Fluid ◽  
Radiation Effects ◽  
Nonlinear Partial Differential Equations ◽  
Numerical Data ◽  
Surface Shear Stress ◽  
Surface Shear

An analysis has been carried out to study the combined effects of heat and mass transfer on the unsteady flow of a micropolar fluid over a stretching sheet. The thermal radiation effects are presented. The arising nonlinear partial differential equations are first reduced to a set of nonlinear ordinary differential equations and then solved by the homotopy analysis method (HAM). Plots for various interesting parameters are presented and discussed. Numerical data for surface shear stress, Nusselt number, and Sherwood number in steady case are also tabulated. Comparison between the present and previous limiting results is given.

scholarly journals MHD Stagnation Point Flow over a Nonlinear Stretching/Shrinking Sheet in Nanofluids

2020 ◽  
Vol 76 (3) ◽  
pp. 139-152
Author(s):  
Nor Hathirah Abd Rahman ◽  
Norfifah Bachok ◽  
Haliza Rosali
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Mhd Flow ◽  
Problem Solver ◽  
Shrinking Sheet ◽  
The Impact ◽  
The Magnetic Field

In this study, an investigation of the steady 2-D magnetohydrodynamiic (MHD) flow of stagnation point past a nonlinear sheet of stretching/shrinking within of a non-uniform transverse magnetic intensity in nanofluids had been analysed. Considered material of nanoparticles such as copper (Cu) in water base fluid with Pr = 6.2 to analyze the influence of volume fraction parameter of nanoparticles and the stretching/shrinking sheet parameter. The governing nonlinear partial differential equations (PDEs) are converted in to the nonlinear ordinary differential equations (ODEs) and use the boundary value problem solver bvp4c in Matlab program to solve numerically through the use of a similarity transformation. The impact of the parameter of the magnetic field on the coefficient of skin friction, the local number of Nusselt and the profiles of velocity and temperature are portrayed and explained physically. The analysis reveals that the magnetic field and volume fraction of nanoparticles affect the velocity and temperature. The dual solutions are achieved where for the shrinking sheet case and the solutions are non-unique, different from a stretching sheet.

scholarly journals Effects of Variable Viscosity and Thermal Conductivity on Micropolar Fluid Flow Due to a Stretching Cylinder in Presence of Magnetic Field

2019 ◽  
Vol 4 (3) ◽  
pp. 745-760 ◽  
Author(s):  
Surajit Dutta ◽  
Bishwaram Sharma ◽  
Gopal Chandra Hazarika
Keyword(s):  
Magnetic Field ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Variable Viscosity ◽  
Skin Friction Coefficient ◽  
Linear Functions ◽  
Stretching Cylinder ◽  
Nusselt Numbers ◽  
Similarity Transformations

In the presence of magnetic field, steady flow of a micropolar fluid due to a stretching cylinder is studied. Viscosity and thermal conductivity are assumed to be inverse linear functions of temperature. The governing partial differential equations are converted into ordinary differential equations using suitable similarity transformations and then solved by fourth order Runge-Kutta shooting method and developing Matlab programme. The graphs show the effects of different parameters and the skin friction coefficient and Nusselt numbers are shown in tabular form.

scholarly journals Effect of Nonlinear Thermal Radiation, Heat Source on MHD 3D Darcy-Forchheimer Flow of Nanofluid Over Aa Porous Medium with Chemical Reaction

2018 ◽  
Vol 7 (4.10) ◽  
pp. 605 ◽  
Author(s):  
Nainaru Tarakaramu ◽  
K. Ramesh Babu ◽  
P. V. Satyanarayana
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Skin Friction ◽  
Chemical Reaction ◽  
Transverse Velocity ◽  
Nonlinear Partial Differential Equations ◽  
Numerical Data ◽  
Mhd Flow ◽  
Nonlinear Thermal Radiation

The present work nonlinear thermal radiation and chemical reaction effect on three-dimensional MHD flow of permeable medium analysed. We are considering introduce the Darcy-Forchheimer law along with axial and transverse velocity. Using suitable transportations the nonlinear partial differential equations are converted into ordinary differential equations. These equations are solved numerically by 4th Runge-Kutta-Fehlberg scheme with shooting procedure. We are getting unique numerical solution for distinct physical variables temperature and concentration fields are depicted. Also the heat transfer and skin friction coefficients drawn through numerical data. We are finding great results of the velocity profiles behaviors opposite trend of porosity and Forchheimer parameters, the profiles of and behavior reverse trend follows other than chemical reaction parameter, both directions of skin friction coefficient and heat transfer rates reduction.  

Aligned Magnetic Field Effect on Radiative Bioconvection Flow Past a Vertical Plate with Thermophoresis and Brownian Motion

2017 ◽  
Vol 377 ◽  
pp. 127-140 ◽  
Author(s):  
K. Avinash ◽  
N. Sandeep ◽  
Oluwole Daniel Makinde ◽  
Isaac Lare Animasaun
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Vertical Plate ◽  
Magnetic Field Effect ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Magnetic Field Effects ◽  
Gyrotactic Microorganisms ◽  
And Brownian Motion ◽  
Nusselt Numbers

This study covers a numerical investigation of gyrotactic microorganisms contained MHD flow over a vertical plate bearing thermal radiation, thermophoresis, Brownian motion, chemical reaction and inclined magnetic field effects. With the assistance of similarity transforms, the derived governed equations are transformed as set of ODEs and solved numerically by R-K and Newton’s methods. Graphs are exhibited and explained for various parameters of interest. For engineering interest, we mainly talked about the Skin friction coefficient, reduced Sherwood, Nusselt numbers and density of motile microorganisms. We noticed a rise in the heat transfer rate of motile microorganisms for rising values of the thermophoresis and Brownian motion parameters. Increasing values of the aligned angle hikes the drag force.

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