# M. Ferdows

## Publications

##### 3 Numerical Solution of Steady Magnetohydrodynamic Boundary Layer Flow Due to Gyrotactic Microorganism for Williamson Nanofluid over Stretched Surface in the Presence of Exponential Internal Heat Generation

**Authors:**
M. Ferdows,
M. A. Talha,
M. Osman Gani

**Abstract:**

This paper focuses on the study of two dimensional magnetohydrodynamic (MHD) steady incompressible viscous Williamson nanofluid with exponential internal heat generation containing gyrotactic microorganism over a stretching sheet. The governing equations and auxiliary conditions are reduced to a set of non-linear coupled differential equations with the appropriate boundary conditions using similarity transformation. The transformed equations are solved numerically through spectral relaxation method. The influences of various parameters such as Williamson parameter γ, power constant λ, Prandtl number P_{r}, magnetic field parameter M, Peclet number P_{e}, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

**Keywords:**
Numerical Analysis,
similarity,
internal heat generation,
spectral method,
convection flow,
Williamson nanofluid

##### 2 Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**Abstract:**

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

**Keywords:**
slip parameter,
biomagnetic fluid,
FHD,
nonlinear stretching sheet

##### 1 A Note on MHD Flow and Heat Transfer over a Curved Stretching Sheet by Considering Variable Thermal Conductivity

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**Abstract:**

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

**Keywords:**
MHD,
finite difference method,
variable thermal conductivity,
curved stretching sheet

## Abstracts

##### 6 A Note on MHD Flow and Heat Transfer over a Curved Stretching Sheet by Considering Variable Thermal Conductivity

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**Abstract:**

**Keywords:**
MHD,
finite difference method,
variable thermal conductivity,
curved stretching sheet

##### 5 Similarity Solutions of Nonlinear Stretched Biomagnetic Flow and Heat Transfer with Signum Function and Temperature Power Law Geometries

**Authors:**
M. G. Murtaza,
E. E. Tzirtzilakis,
M. Ferdows

**Abstract:**

**Keywords:**
MHD,
biomagnetic fluid,
FHD,
nonlinear stretching sheet

##### 4 Existence and Stability of Periodic Traveling Waves in a Bistable Excitable System

**Authors:**
M. Ferdows,
M. Osman Gani,
Toshiyuki Ogawa

**Abstract:**

**Keywords:**
bistable system,
Eckhaus bifurcation,
excitable media,
FitzHugh-Nagumo model,
periodic traveling waves

##### 3 Simulation to Detect Virtual Fractional Flow Reserve in Coronary Artery Idealized Models

**Authors:**
M. Ferdows,
Nabila Jaman,
K. E. Hoque,
S. Sawall

**Abstract:**

**Keywords:**
CAD,
CHD,
vFFR,
bifurcation angles,
coronary stenosis

##### 2 Numerical Solution of Steady Magnetohydrodynamic Boundary Layer Flow Due to Gyrotactic Microorganism for Williamson Nanofluid over Stretched Surface in the Presence of Exponential Internal Heat Generation

**Authors:**
M. Ferdows,
M. A. Talha,
M. Osman Gani

**Abstract:**

_{r}, magnetic field parameter M, Peclet number P

_{e}, Lewis number Le, Bioconvection Lewis number Lb, Brownian motion parameter Nb, thermophoresis parameter Nt, and bioconvection constant σ are studied to obtain the momentum, heat, mass and microorganism distributions. Moment, heat, mass and gyrotactic microorganism profiles are explored through graphs and tables. We computed the heat transfer rate, mass flux rate and the density number of the motile microorganism near the surface. Our numerical results are in better agreement in comparison with existing calculations. The Residual error of our obtained solutions is determined in order to see the convergence rate against iteration. Faster convergence is achieved when internal heat generation is absent. The effect of magnetic parameter M decreases the momentum boundary layer thickness but increases the thermal boundary layer thickness. It is apparent that bioconvection Lewis number and bioconvection parameter has a pronounced effect on microorganism boundary. Increasing brownian motion parameter and Lewis number decreases the thermal boundary layer. Furthermore, magnetic field parameter and thermophoresis parameter has an induced effect on concentration profiles.

**Keywords:**
Numerical Analysis,
similarity,
internal heat generation,
spectral method,
convection flow,
Williamson nanofluid

##### 1 Power and Efficiency of Photovoltaic Module: Effect of Cell Temperature

**Authors:**
M. Ferdows,
R. Nasrin

**Abstract:**

**Keywords:**
Efficiency,
Solar Radiation,
PV module,
cell temperature