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Forced convective heat and mass transfer flow of hydromagnetic, radiating and dissipative fluid over a porous nonlinear stretching sheet in the presence of non-uniform heat generation/absorption is investigated numerically. The system of nonlinear partial differential equations governing the physical problem is reduced to nonlinear ordinary differential equations by means of suitable similarity transformations and are solved numerically using Nachtsheim Swigert shooting iteration scheme together with fourth order Runge Kutta method. The effects of various physical parameters on velocity, temperature and concentration distributions are depicted graphically. The important findings of this study exhibited that the effect of non-uniform heat generation/absorption parameter and radiation parameter have significant role in controlling thermal boundary layer thickness and temperature. Numerical values of the skin friction coefficient, temperature and concentration at the wall are shown in a tabular form. A comparison is made with previously published data which results in good agreement.

Hydromagnetic flow of water based nanofluids over a nonlinearly stretching sheet in the presence of velocity slip, temperature jump, magnetic field, nonlinear thermal radiation, thermophoresis and Brownian motion has been studied. The article focuses on Cu water nanofluid and Ag water nanofluid. The similarity transformation technique is adopted to reduce the governing nonlinear partial differential equations into nonlinear ordinary differential equations and then they are solved numerically utilizing the Nachistem – Swigert shooting method along with the fourth order Runge Kutta integration technique. The influence of physical parameters on the flow, temperature and nanoparticle volume fraction are presented through graphs. Also the values of the skin friction coefficient at the wall and nondimensional rate of heat transfer are given in a tabular form. A comparative study with previous published results is also made.

In this paper, the effects of viscous and Ohmic heating on magneto hydrodynamic forced convection flow due to a permeable shrinking surface in the presence of internal heat generation and radiation is investigated. The shrinking surface subjected to suction is prescribed with non uniform temperature which varies with the quadratic power of x. Momentum boundary layer equation takes into account of transverse magnetic field effect. Thermal boundary layer equation considered the effects of viscous and Ohmic heating due to transverse magnetic field, radiation and internal heat generation. Numerical results are obtained for various values of governing physical parameters. To access the accuracy of the numerical solution, the present results are checked against previously published work and the analytical solution of the problem obtained using Kummer’s function. Table values show that the analytical and numerical solutions are found to be in excellent agreement. J. Wilfred Samuel Raj | S. P. Anjali Devi "Viscous and Ohmic Heating Effects on Hydromagnetic Convective-Radiative Boundary Layer Flow Due to a Permeable Shrinking Surface with Internal Heat Generation" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-3 , April 2020, URL: https://www.ijtsrd.com/papers/ijtsrd30524.pdf Paper Url :https://www.ijtsrd.com/mathemetics/applied-mathamatics/30524/viscous-and-ohmic-heating-effects-on-hydromagnetic-convectiveradiative-boundary-layer-flow-due-to-a-permeable-shrinking-surface-with-internal-heat-generation/j-wilfred-samuel-raj

The aim of present investigation was to study the effects of thermal radiation, viscous dissipation, ohmic dissipation and mass transfer effects on unsteady hydromagnetic boundary layer flow over a stretching surface. The governing equations of momentum, thermal and concentration boundary layers are reduced to a set of ordinary differential equations by means of suitable similarity transformations. Those equations are solved numerically for some arbitrary values of the governing physical parameters such as the Unsteadiness parameter (A), Magnetic interaction parameter (M2), Prandtl number (Pr), Radiation parameter (Rd), Eckert number (Ec) and Schmidt number (Sc) using Runge Kutta method of fourth order along with an efficient shooting method called Nachtsheim Swigert integration technique for the satisfaction of asymptotic boundary conditions. The results obtained are discussed with the help of graphical illustrations. Important physical concepts such as skin friction coefficient, Nusselt number and Sherwood number are also obtained and are discussed in detail. Keywords: Unsteady stretching surface, Radiation heat transfer, Mass transfer, MHD, Viscous dissipation, Ohmic dissipation

In this paper, an investigation is made to analyze the effects of radiation on an MHD boundary layer flow and heat transfer over a nonlinear stretching surface with variable wall temperature and non-uniform heat source/sink. A suitable similarity transformation is used to transform the governing nonlinear partial differential equations into a system of nonlinear ordinary differential equations by using the Nachtsheim Swigert shooting iteration technique together with the fourth order Runge Kutta method. The effects of various physical parameters over a dimensionless velocity and dimensionless temperature are presented graphically. The numerical results for the skin friction co-efficient and non-dimensional rate of heat transfer are presented and discussed for several sets of values of the parameters. Comparisons of numerical results are made with the earlier published results under limiting cases.

Heat and mass transfer characteristics of water based nanofluids over a nonlinear shrinking surface with suction is studied numerically in the incidence of magnetic field, thermal radiation under the boundary conditions heat flux and mass flux. Similarity transformations are used to renovate the governing partial differential equations into higher order nonlinear ordinary differential equations. These equations are numerically solved using fourth order Runge Kutta technique along with Nachistem - Swigert shooting method. Numerical results are achieved for the nanofluid velocity, nanofluid temperature and nanoparticle concentration as well as for the skin friction coefficient, wall temperature and concentration of the wall for various values of governing physical parameters viz. magnetic interaction parameter, suction parameter, shrinking parameter, thermal radiation parameter, temperature ratio parameter and solid volume fraction of the nanoparticles such as copper and silver. Mekala Selvaraj | S. P. Anjali Devi "Hydromagnetic Flow of Nanofluids over a Nonlinear Shrinking Surface with Heat Flux and Mass Flux" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-1 | Issue-6 , October 2017, URL: https://www.ijtsrd.com/papers/ijtsrd5793.pdf

In recent days, nanofluids have derived the attention of researchers, scientists and engineers due to their abundant applications in Engineering and technology and specific applications such as Electronics cooling, vehicle cooling, medical applications including cancer therapy and so on. Motivated by these applications of nanofluids, this work is mainly concerned with the convective heat transfer of nanofluids. MHD slip flow of nanofluids with heat absorption over a rotating disk subjected to suction has been analyzed. Two types of nanofluids such as copper-water nanofluid and silver-water nanofluid are considered for the present study. The system of axisymmetric nonlinear partial differential equations governing the hydromagnetic steady flow and heat transfer are reduced to nonlinear ordinary differential equations by introducing suitable similarity transformations. The resulting non-linear ordinary differential equations are solved numerically by most efficient Nachtsheim-Swigert shooting iteration technique for satisfaction of asymptotic boundary conditions along with Runge – Kutta Fehlberg Method. The flow field is affected by the presence of physical parameters, such as magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, whereas the temperature field is addionally affected by magnetic interaction parameter, suction parameter, internal heat absorption parameter and solid volume fraction. With the amplifying effect in magnetic interaction parameter, suction parameter, slip parameter and solid volume fraction, the radial and tangential velocities decline. Axial velocity gets decelerated for increasing magnetic interaction parameter and slip parameter whereas it gets accelerated for growing effect of suction parameter and solid volume fraction. The temperature of the fluid within the boundary layer enhances with the increasing effect of magnetic interaction parameter and solid volume fraction while it reduces for increasing values of the suction parameter and internal heat absorption parameter. Also the values of radial and tangential skin friction coefficients and Nusselt number are obtained numerically and are tabulated.

An emerging concept of hybrid nanofluid with a new improved model of its thermophysical properties are introduced in the present work. Hybrid nanofluid is an advanced type of conventional heat transfer fluids, which has been employed for the enhancement of heat transfer rate. Two distinct fluids, namely hybrid nanofluid ( C u − A l 2 O 3 / w a t e r ) $({\rm{Cu - A}}{{\rm{l}}_{\rm{2}}}{{\rm{O}}_{\rm{3}}}{\rm{/water}})$ and nanofluid (Cu/water) are used to investigate the parametric features of the flow and heat transfer phenomena over a permeable stretching sheet in the presence of magnetic field. The effects of various physical parameters and effecting physical quantities of interest are analyzed. From this study it is observed that the heat transfer rate of hybrid nanofluid ( C u − A l 2 O 3 / w a t e r ) $({\rm{Cu - A}}{{\rm{l}}_{\rm{2}}}{{\rm{O}}_{\rm{3}}}{\rm{/water}})$ is higher than that of Nanofluid (Cu/water) under magnetic field environment. More combinations of different nanocomposites can be tried so that the desired heat transfer rate can be achieved.

This work compares the heat transfer characteristics of traditional nanofluid with that of emerging hybrid nanofluid. Hybrid nanofluid, a new type of conventional fluid, has been used toward the enhancement of heat transfer in the boundary layer flow. A new model of thermophysical properties is employed to investigate the effects of Lorentz force over a three-dimensional stretching surface subject to Newtonian heating. Comparisons are obtained through the numerical parametric study, which has been carried out to explore the effects of various physical parameters involved in the problem. From this study it is observed that the heat transfer rate of hybrid nanofluid (Cu–Al2O3/water) is higher than nanofluid (Cu/water) even in the presence of a magnetic field environment. By opting to use different and appropriate nanoparticle proportions in hybrid nanofluid, the desired heat transfer rate can be achieved.

This paper presents a mathematical analysis on the effects of viscous dissipation over unsteady MHD flow and radiation heat transfer past a stretching surface subjected to suction embedded in a porous medium. The governing nonlinear partial differential equations of the problem are transformed into nonlinear ordinary differential equations adopting suitable similarity transformations. The numerical solution is obtained by employing Nachtsheim-Swigert shooting iteration method together with Fourth order Runge-kutta integration method. Numerical results for the dimensionless velocity and temperature distribution as well as for the local skin friction coefficient and nondimensional rate of heat transfer are obtained and displayed graphically for pertinent physical parameters.

The main objective of this work is to analyze how the heat transfer rate of variable thickness stretching sheet gets influenced by the thermal radiation environment in the presence of magnetic field. For which, steady, two-dimensional, nonlinear, hydromagnetic laminar flow of an incompressible, viscous, radiating and electrically conducting fluid over a stretching sheet with variable thickness in the presence of variable magnetic field and thermal radiation are considered. The physical model was solved numerically using Nachtsheim–Swigert shooting iteration technique along with fourth order Runge–Kutta integration method. Numerical solutions are obtained for various values of the physical parameters involved in the problem. The heat transfer rate gets suppressed due to significant effect of magnetic field strength and radiation.

This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The result- ing non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various val- ues of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

An analysis is carried out to study the problem of the steady flow and heat transfer over a rotating disk with a prescribed heat flux in nanofluid. Nanofluid considered is Copper (Cu) with water as the base fluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, which are then solved using the Nachtsheim-Swigert Shooting iteration technique along with the fourth order Runga Kutta method. The features of the flow and heat transfer characteristics are analyzed and discussed. The radial velocity, tangential velocity and the axial velocity for copper-water nanofluid are calculated and are represented graphically. Numerical results for dimensionless temperature, the radial skin friction coefficient and the tangential skin friction coefficient of the nanofluid flows are obtained and computations are carried out for the various values of Prandtl number. It is found that for the prescribed heat flux case (PHF case), the effect of Prandtl number is to reduce the temperature as it increases for copper-water nanofluid.

In this investigation, thermal radiation effect over an electrically conducting, Newtonian fluid in a steady laminar magnetohydrodynamic convective flow over a porous rotating infinite disk with the consideration of heat and mass transfer in the presence of Soret and Dufour diffusion effects is investigated. The partial differential equations governing the problem under consideration are transformed by a similarity transformation into a system of ordinary differential equations which are solved numerically using fourth order Runge–Kutta based shooting method. The effects of the magnetic interaction parameter, slip flow parameter, Soret number, Dufour number, Schmidt number, radiation parameter, Prandtl number and suction parameter on the fluid velocity, temperature and concentration distributions in the regime are depicted graphically and are analyzed in detail. The corresponding skin-friction coefficients, the Nusselt number and the Sherwood number are also calculated and displayed in tables showing the effects of various parameters on them.

The effect of thermal radiation on the steady laminar convective hydromagnetic flow of a viscous and electrically conducting fluid due to a rotating disk of infinite extend is studied. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The governing Navier–Stokes and Maxwell equations of the hydromagnetic fluid, together with the energy equation, are transformed into nonlinear ordinary differential equations by using the von Karman similarity transformations. The resulting nonlinear ordinary differential equations are then solved numerically subject to the transformed boundary conditions by Runge–Kutta based shooting method. Comparisons with previously published works are performed and the results are found to be in excellent agreement. Numerical and graphical results for the velocity and temperature profiles as well as the skin friction and Nusselt number are presented and discussed for various parametric conditions.

The Rayleigh–Taylor instability (RTI) of a ferrofluid has been the subject of recent research, because of its implications on the stability of stellar and planetary interiors. This paper analyzes the effects of rotation and magnetic field on nonlinear RTI of two superposed ferrofluids. It is considered that the system is subjected to uniform parallel rotation and normal magnetic field. Surface tension acts at the interface. The method of multiple scales is utilized to obtain the solutions and dispersion relations are obtained for the nonlinear problem of RTI of magnetic fluids. Finally the stability of the problem is discussed.

The steady nonlinear hydromagnetic flow of an incompressible, viscous and electrically conducting fluid with heat transfer over a surface of variable temperature stretching with a power-law velocity in the presence of variable transverse magnetic field is analysed. Utilizing similarity transformation, governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations and they are numerically solved using fourth-order Runge–Kutta shooting method. Numerical solutions are illustrated graphically by means of graphs. The effects of magnetic field, stretching parameter and Prandtl number on velocity, skin friction, temperature distribution and rate of heat transfer are discussed.

An approximate numerical solution for thermal stratification on MHD steady laminar boundary-layer flow over a wall of the wedge with suction or injection. The fluid is assumed to be viscous and electrically conducting Boussinesq fluid. A magnetic field is applied transversely to the direction of the flow. The governing partial differential equations of the problem subject to their boundary conditions are solved using R.K.Gill numerical method. Numerical calculations up to third level of truncation are carried out for different values of dimensionless parameters in the problem

An approximate numerical solution for the steady MHD laminar boundary-layer flow over an accelerating vertical surface with suction or injection in the presence of species concentration and mass diffusion has been obtained by solving the governing equations using R.K. Gill method. The fluid is assumed to be viscous, incompressible and electrically conducting with a magnetic field applied transversely to the direction of the flow. It has been observed that in the presence of mass diffusion: (i) in the case of suction, the velocity decreases and the temperature distribution and concentration of the fluid increase and for injection, the velocity increases and the temperature distribution and concentration of the fluid decrease with increase of thermal stratification parameter, (ii) in the presence of thermal stratification parameter in both the cases of suction and injection, the skin friction and rate of mass transfer decrease and the rate of heat transfer of the fluid increases with increase of chemical reaction effects, (iii) in the cases of suction and injection, an increase in the strength of magnetic field leads to fall in the velocity and rise in the temperature and concentration of the fluid along the surface. Copyright © 2003 John Wiley & Sons, Ltd.

An approximate numerical solution for the steady MHD laminar boundary-layer flow over a wall of the wedge with suction or injection in the presence of species concentration and mass diffusion has been obtained by solving the governing equations using R.K.Gill method.The fluid is assumed to be viscous and electrically conducting Boussinesq fluid. A magnetic field is applied transversely to the direction of the flow. Numerical calculations up to third level of truncation are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow field is influenced appreciably by the magnetic field,chemical reaction and suction or injection at the wall of the wedge

The interface of two superposed viscous ferrofluids of infinite depth in the presence of an uniform magnetic field oblique to the interface is considered. The fluids are assumed to be incompressible and a surface tension T acts on the interface. Solutions of the linear problem and the linear dispersion relation are found. Exchange of stabilities are discussed for various cases.

An approximate numerical solution for the steady MHD flow over an infinite horizontal plate in the presence of species concentration and chemical reaction has been obtained by solving the non-linear governing equations using R. K. Gill's method. The fluid is assumed to be viscous, incompressible, and electrically conducting. A uniform transverse magnetic field is applied. It has been observed that in the presence of chemical reaction (1) the velocity and the concentration decrease with increase of the chemical reaction parameter and vice versa, (2) the velocity decreases and the concentration is uniform with increase of the magnetic parameter and vice versa.

The hydromagnetic slip flow of a viscous incompressible and electrically conducting fluid through an inclined channel of rectangular cross section in the presence of a transverse magnetic field has been analysed. The walls of the channel are assumed to have prescribed temperatures and finite conductivities. The boundary conditions for both velocity and temperature are properly rectified. The expressions for the velocity, induced magnetic field and the temperature are obtained both analytically and numerically.

Heat transfer in unsteady MHD channel flow (of an incompressible viscous and electrically conducting fluid) under oscillatory pressure gradient when the channel surfaces are conducting and moving with time-dependent velocities has been analysed. The velocity, magnetic field and temperature distributions have been obtained and their numerical results are shown graphically.

The nonlinear, steady, mixed convective, two-dimensional laminar hydromagnetic boundary layer flow of copper-water and alumina-water nanofluids over an inclined flat plate with an angle of inclination α in the presence of uniform transverse magnetic field is investigated in this work. The governing nonlinear partial differential equations of the problem are transformed into nonlinear ordinary differential equations by utilizing suitable similarity transformations and the resulting nonlinear ordinary differential equations are solved numerically using MATLAB. Numerical results for dimensionless velocity and temperature of the nanofluid flows are obtained and computations for the various values of Magnetic interaction parameter, angle of inclination, volume fraction, Prandtl number and mixed convection parameter. The range of volume fraction of nanofluids and the angle of inclination under study are as follows: 0.00 ≤ φ ≤ 0.10 and 0° ≤ α ≤ 60°. The results are displayed graphically to show the interesting aspects of the nanofluids.

This paper investigates the influence of both viscous and joules dissipation on the problem of magnetohydrodynamic flow past a stretching porous surface embedded in a porous medium. Analytic solutions of the resulting nonlinear non-homogeneous boundary value problem in the case when the plate stretches with a velocity varying linearly with distance, expressed in terms of confluent hypergeometric functions, are presented for the case of prescribed surface temperature. Numerical calculations have been carried out for various values of suction parameter, magnetic field, Prandtl number, Eckert number and Schmidt number. The results show that increases in magnetic parameter decrease both the dimensionless transverse velocity, longitudinal velocity and also the skin friction coefficient. Also, formation of thin boundary layer is observed for higher value of magnetic parameter.

In hypersonic flights, two vital problems are drag and aerodynamic heating. Both problems can be palliated by modifying the flow field at nose region of the hypersonic blunt body by using jet. In this study, feasibility of utilising a counter flow jet for the reduction of total drag and aerodynamic heating around coneogive blunt body in hypersonic turbulent flow is investigated. Flow field around the blunt body is calculated numerically in the free stream of Mach number of 6.5. Computation of drag and aerodynamic heating is made in the absence of jet and in the presence of jet. Contours of Mach number, temperature and density are presented to describe the flow patterns. Effective jet conditions for reduction of drag and aerodynamic heating are obtained. Eventually, a code is developed based on adaptive neuro-fuzzy inference system (ANFIS) for validating the numerical results obtained through CFD software.

The vertical (upwards) flow of an incompressible, Newtonian, viscous, stratified, diffusive, electrically conducting fluid embedded with a uniform magnetic field that is applied in the vertical direction, past a non-conducting sphere is considered. Quasisteady approximation is made allowing for a time dependent buoyancy force. Method of matched asymptotic expansions is employed to obtain the drag exerted on the sphere, for small values of a stratification parameter α such that α≪1,Re≪α1/3,\(F_{\tau ^2 }\) ≪α−1/3,Pe≫α2/3 andRm=O(α2/3). The drag is computed for certain typical values of the magnetic interaction parameter and diffusivity parameter. The results reveal the fact that while the stratification and magnetic field have the enhancing effect over the drag, the effect of diffusivity is to decrease it.

The primary focus of this work is to numerically investigate the influence of temperature dependent viscosity and thermal conductivity on hydromagnetic flow over slendering stretching sheet. In the process held at high temperature like glass blowing, the fluid properties like viscosity and thermal conductivity may gets influenced in such temperature which motivated us to analyze those kind of problem. Considering steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness in the presence of variable magnetic field. Numerical computations are carried out for various values of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained and presented in tabulated form. It is noticed that, in additional to the magnetic field there are two more regulators which can manipulate to maintain the optimal heat for the glass blowing process to attain required shapes.