Mathematics

A two-dimensional MHD free convection heat and mass transfer flow of viscous, incompressible and electrically conducting fluid past a vertical flat plate embedded in porous medium in the presence of hall current under the influence of uniform magnetic field applied normal to the flow is studied analytically. In this research work, we make the governing equations dimensionless by usual non-dimensional variables and we obtained a set of ordinary differential equations. Then these obtained ordinary differential equations are solved analytically by using perturbation technique. The expressions for velocity field, temperature distribution, concentration field, skin friction, the rate of heat transfer and the rate of mass transfer are derived. Finally the results are discussed in detailed with the help of graphs and tables to observe the effect of different parameters like Magnetic parameter (M), radiation parameter (F), Grashof number (Gr), modified Grashof number (Gm),  Prandtl number (Pr), permeability parameter (k), Eckert number (Ec) and the chemical reaction parameter (Kc).

A two-dimensional MHD free convection heat and mass transfer flow of viscous,
incompressible and electrically conducting fluid past a vertical flat plate embedded in
porous medium in the presence of hall current under the influence of uniform
magnetic field applied normal to the flow is studied analytically. In this research
work, we make the governing equations dimensionless by usual non-dimensional
variables and we obtained a set of ordinary differential equations. Then these
obtained ordinary differential equations are solved analytically by using perturbation
technique. The expressions for velocity field, temperature distribution, concentration
field, skin friction, the rate of heat transfer and the rate of mass transfer are derived.
Finally the results are discussed in detailed with the help of graphs and tables to
observe the effect of different parameters like Magnetic parameter (M), radiation
parameter (F), Grashof number (Gr), modified Grashof number (Gm), Prandtl
number (Pr), permeability parameter (k), Eckert number (Ec) and the chemical
reaction parameter (Kc).

This article is related with the simulation of mass and heat relocation behavior of viscous dissipative chemically reacted Casson fluid which is flowing with impact of suction, thermal conductivity and fickle viscosity. Current conductivity along with temperature dependent viscosity changes as a linear function of temperature. First of all, leading equations are converted into dimensionless form via suitable transformations. Therefore explicit finite differential technique has solved the obtained non-dimensional, non-similar mixed nonlinear and partial differential equations with the support of Compaq Visual Fortran 6.6.a, a very well-known programing language. The behavior of various relevant parameters in the boundary profile velocity, temperature and concentration was considered realistically. Therefore, these variables have a diagrammatic influence on skin friction and the heat transference coefficient profiles. Stability and convergence tests are also carried out for the accuracy of implemented numerical scheme. One of the significant attainment is the Casson fluid parameter displayed quite interesting behavior on the velocity fields as it represented provoking behavior close to the boundary but it behaved oppositely away from the boundary surface. However, a comparison is also presented with good agreement for the validation of the current investigation.

This study presents the exploration of unsteady magnetohydrodynamic (MHD) free convection flow of tangent hyperbolic nano-fluid flow on a moving cylinder with Brownian motion and thermophoresis effects. The current flow analysis yields nonlinear partial differential equations. The governing equations such as continuity, momentum, temperature and concentration are converted into dimensionless form and then solved numerically by adopting explicit finite difference method where Compaq Visual FORTRAN 6.6.a was also used for simulating the fluid flow system. The numerical outcomes are showed graphically to understand the result clearly. For the accurateness of the numerical technique a stability and convergence analysis was carried out. The aim was to illustrate the physical impacts of chemical reaction parameter, thermal radiation and viscous dissipation on various fluid fields along with the advanced visualization through streamlines. By comparing with the previous studies it was found that this fluid influenced the mass and heat properties more significantly rather than the other fluid. Additionally, this model predicts the shear thinning attitude significantly and describes the blood flow accurately. It has also applications in biological sciences, bio-engineering maneuver, and petroleum industries. Eventually the obtained outcomes were validated with previously published articles. Keywords Tangent hyperbolic fluid • Nanoparticle • EFDM • Chemical reaction • MHD List of symbols B 0 External magnetic field (Wb m −2) C P Specific heat at constant pressure (J kg −1 K −1) C Concentration component C w Concentration of the cylinder (mol.) C ∞ Concentration away from the cylinder C f Skin friction (-) D B Brownian diffusion coefficient D T Thermophoresis diffusion coefficient g Gravitational acceleration (m s −2) Gr Thermal Grashof number (-) Gm Mass Grashof number (-) Kr Chemical reaction parameter (-) Le Lewis number (-) M Magnetic parameter (-) n Power low index (-) Nb Brownian parameter (-) Nt Thermophoresis parameter (-) Nu Nusselt number (-) Pr Prandlt number (-) q r Radiative heat flux (kg m −2) Ra Radiation parameter (-) Sh Sherwood number (-) T Temperature (K)

Magnetohydrodynamic (MHD) unsteady flow of incompressible, electrically conducting, and viscous fluid passing through a vertical porous plate is explored in this investigation where the impact of thermal radiation and chemical reaction are presented. A nonlinear two-dimensional unsteady flow model is created to decompose heat and mass transfer of this fluid, which is shaped by taking appropriate boundary conditions. The governing equations are solved analytically with satisfactory boundary conditions by using a two-term perturbation technique. The analytical outcomes are illustrated graphically by using MATHEMATICA 7.0. The fundamental equations are also solved numerically by utilizing explicit finite difference methodology (EFDM) with the help of Compaq Visual Fortran 6.6a. The numerical arrangement is also depicted graphically to examine the outcomes. The acquired pertinent parameters are analysed conveniently, including thermal Grashof number, thermal radiation parameter, and che...

In this paper we further improve the modified extended tanh-function method to obtain new exact solutions for nonlinear partial differential equations. Numerical applications of the proposed method are verified by solving the improved Boussinesq equation and the system of variant Boussinesq equations. The new exact solutions for these equations include Jacobi elliptic doubly periodic type,Weierstrass elliptic doubly periodic type, triangular type and solitary wave solutions

An exploration has been perpetrated to study the heat and mass transfer flow of an incompressible electrically conducting Maxwell fluid past a stretching sheet in the presence of nanoparticle with Soret and Dufour effects. The governing partial differential equations are transformed into dimensionless momentum, energy and concentration equations and are solved numerically by using explicit finite difference method (EFDM) by employing Compact visual FORTRAN 6.6a programming algorithm. For optimizing the system parameter and accuracy of the system the stability and convergence analysis was carried out. It was observed that with the initial boundary conditions, for = 0.0005, = 0.67, = 0.167, the system converged at prandtl number ≥ 0.044 and Schmidt number ≥ 0.036 .The dominance of various physical parameters on the flow, heat and mass translation characteristics are speculated through diagram and tables.

Minutiae based feature extraction methods are used for fingerprint matching. This method is mainly depending on the characteristics of minutiae of the individuals. The minutiae are ridge endings or bifurcations on the fingerprints. Their coordinates and direction are most distinctive features to represent the fingerprint. Most fingerprint matching systems store only the minutiae template in the database for further usage. The conventional methods to utilize minutiae information are treating it as a point set and finding the matched points from different minutiae sets. This kind of minutiae-based fingerprint recognition/matching systems consists of two steps: minutiae extraction and minutiae matching. Image enhancement, histogram equalization, thinning, binarization, smoothing, block direction estimation, image segmantation, ROI extraction etc. are discussed in the minutiae extraction step. After the extraction of minutiae the false minutiae are removed from the extraction to get the accurate result. In the minutiae matching process, the minutiae features of a given fingerprint are compared with the minutiae template and the matched minutiae will be found out. The final template used for fingerprint matching is further utilized in the matching stage to enhance the system’s performance. Two fingerprint images always give two different matrices, the matrix equalization method is also used for matching two fingerprint images after the final template.

Combined heat and mass transfer of a viscous fluid along a semi-infinite vertical plate with large suction is studied analytically. Perturbation technique is used as main tool for the analytical approach. Viscous fluid behavior of heat and mass transfer over a vertical plate with large suction has been considered and its similarity equations have been obtained. Similarity equations of the corresponding momentum, temperature and concentration equations are derived by employing the usual similarity technique. The dimensionless similarity equations for momentum, temperature and concentration equation solved analytically by perturbation technique. The obtained numerical values of fluid velocity, temperature and concentration are drawn in figures. The results are discussed in detailed with the help of graphs to observe the effects of various parameters on the flow variables. Lastly, the important findings are concluded here.

The effects of temperature dependent viscosity and thermal conductivity on a two dimensional unsteady laminar MHD free convective flow over a vertical plate immersed in a porous medium with viscous dissipation and heat generation have been studied in the current work. The governing boundary layer equations are converted into a system of coupled nonlinear ordinary partial differential equations by using non-dimensional parameters and then solved numerically using finite difference method. Effects of variable viscosity, variable thermal conductivity, and the other parameters engaged in the study on the velocity, temperature and concentration profiles are investigated graphically. Skin friction and Nusselt number profiles have been also illustrated graphically.

Free convection and mass transfer flow through a porous medium with variable temperature has been investigated. Here we consider temperature dependent viscosity as well as thermal conductivity varies as a linear function of temperature. Then we have considered  the effects of radiation and chemical reaction in both the cases. The governing equations are transformed into non-dimensional form by using appropriate coordinate transformations. Then the obtained non-dimensional, non-similar coupled non-linear and partial differential equations have been solved by explicit finite difference technique. Numerical solutions for velocity, temperature and concentration distributions are obtained graphically for various parameters by using the above-mentioned technique. The skin friction and Nusselt number are also illustrated graphically for all the cases.

High order chemically reactive micropolar fluid flow through an infinite vertical porous medium with thermal diffusion, mass diffusion, MHD, thermal radiation and heat sink has been studied. A flow model is established by employing the well-known boundary layer approximations. In order to obtain non-dimensional system of equations, a similarity transformation is applied on the flow model. The stability and convergence analysis have been analyzed. The obtained non-dimensional equations have been solved by explicit finite difference method. The effects of various parameters entering into the problem on velocity, angular velocity, temperature and concentration are shown graphically.

Present study concerned with the theoretical work with numerical investigation of MHD transient naturally convective and higher order chemically reactive viscoelastic fluid with nano-particle flow through a vertical porous stretching sheet with the effects of heat generation and radiation absorption. A boundary layer approximation is carried out to develop a flow model representing time dependent momentum, energy, and concentration equations. The governing model equations in partial differential equations (PDEs) form were transformed into a set of nonlinear ordinary differential equation (ODEs) by using non-similar technique. Explicit Finite Difference Method (EFDM) was employed by implementing an algorithm in Compaq Visual Fortran 6.6a to solve the obtained set of nonlinear coupled ODEs. For optimizing the system parameter and accuracy of the system, the stability and convergence analysis (SCA) was carried out. It was observed that with initial boundary conditions, the system converged at Prandtl number>= 0.253 and Lewis number >=0.16. The velocity, temperature and concentration flow are investigated and shown graphically with the effect of system parameters and numerical comparison.

A two-dimensional (2D) flow of an incompressible Williamson fluid of Cattaneo–Christov heat flux type over a linearly stretched surface with the influence of magnetic field, thermal radiation-diffusion, heat generation and viscous dissipation is carried out in the present study. To develop a Williamson flow model, a boundary layer approximation is taken into account. The non-dimensional, nonlinear, coupled ordinary differential equations with boundary condition are solved numerically using Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme. The influences of physical parameters on the velocity, temperature, concentration is analysed through graphical consequences. To validate the accuracy of the numerical simulations scheme, comparisons is carried out with the previous studies and are found in an excellent agreement.