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In this paper, we examine the hydromagnetic boundary layer flow and heat transfer characteristics of a laminar nano liquid film over an unsteady stretching sheet is presented. The highly nonlinear partial dierential equations governing flow and heat transport are simplified using similarity transformation. The analytical solutions of the resulting ODEs are obtained for some special case of nano liquid film using hypergeometric power series functions, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed analytically.

An analysis for the MHD boundary layer flow and heat transfer towards stretching sheet is carried out via symmetry analysis. A steady two-dimensional flow of an electrically conducting incompressible fluid flow over a stretching sheet. The flow permeated by a uniform transverse magnetic field. The governing partial dierential equations are reduced to a system of ordinarydierential equations by the scaling symmetries. The symmetry groups admitted by the corresponding boundary value problem are obtained by using special Lie group transformations. The scaling of group transformations is applied to the governing equations.The system remains invariant due to some relation among the parameters of the transformations. After finding two absolute invariants a third order ordinary dierential equation corresponding to momentum equation and second order dierential equation corresponding to energy equation are derived. The equations along with boundary conditions solved numerically. Numerical solutions of these equations are obtained by using Runge-Kutta-Fehlberg scheme. Further more attention is paid to the eects of some physical parameters magnetic field (Mn), Prandtl number (Pr), Eckert number (Ec) and uniform heat source/sink, on velocity and thermal boundary layer. The results thus obtained are presented graphically and discussed.

The influence of surface tension on the laminar flow of a thin film of a non-Newtonian nano liquid over an unsteady stretching sheet is considered. Surface tension is assumed vary linearly with temperature. An effective medium theory (EMT) based model is used for the thermal conductivity of the nano liquid. Metal and metal oxide nanoparticles are considered in carboxymethyl cellulose (CMC) – water base liquid. The unsteady boundary layer equations are transformed to a system of non-linear ordinary differential equations with the application of similarity transformations. Resultant two-point boundary value problem is solved numerically using a shooting method together with Runge-Kutta-Fehlberg and Newton-Raphson schemes. The effect of surface tension on the dynamics of the considered problem is presented graphically and analyzed in detail. The clear liquid results which form special case of the present study are in excellent agreement with the results reported in the literature

The objective of this paper is to study magnetohydrodynamic flow in a vertical double passage channel taking into account the presence of the first order chemical reaction. The channel is divided into two passages by means of a thin,perfectly conducting plane baffle and hence the velocity will be individual in each stream. The governing equations are solved by using regular perturbation technique valid for small values of the Brinkman number and differential transform method valid for all values of the Brinkman number. The results are obtained for velocity, temperature and concentration. The effects of various dimensionless parameters such as thermal Grashof number, mass Grashof number, Brinkman number, first order chemical reaction parameter, and Hartman number on the flow variables are discussed and presented graphically for open and short circuits. The validity of solutions obtained by differential transform method and regular perturbation method are in good agreement for small values of the Brinkman number. Further the effects of governing parameters on the volumetric flow rate, species concentration, total heart rate, skin friction and Nusselt number are also observed and tabulated.

The linear stability of Maxwell fluid-nanofluid flow in a saturated porous layer is examined theoretically when the walls of the porous layers are subjected to time-periodic temperature modulations. A modified Darcy-Maxwell model is used to describe the fluid motion, and the nanofluid model used includes the effects of the Brownian motion. The thermal conductivity and viscosity are considered to be dependent on the nanoparticle volume fraction. A perturbation method based on a small amplitude of an applied temperature field is used to compute the critical value of the Rayleigh number and the wave number. The stability of the system characterized by a critical Rayleigh number is calculated as a function of the relaxation parameter, the concentration Rayleigh number, the porosity parameter, the Lewis number, the heat capacity ratio, the Vad´asz number, the viscosity parameter, the conductivity variation parameter, and the frequency of modulation. Three types of temperature modulations are considered, and the effects of all three types of modulations are found to destabilize the system as compared to the unmodulated system.

We analyzed the boundary layer flow and heat transfer over a stretching sheet due to nanofluids with the effects of magnetic field, Brownian motion, thermophoresis, viscous dissipation and convective boundary conditions. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The highly nonlinear partial differential equations governing flow and heat transport are simplified using similarity transformation. Resultant ordinary differential equations are solved numerically using the Runge-Kutta-Fehlberg and Newton-Raphson schemes based on the shooting method. The solutions velocity temperature and nanoparticle concentration depend on parameters such as Brownian motion, thermophoresis parameter, magnetic field and viscous dissipation, which have a significant influence on controlling the dynamics of the considered problem. Comparison with known results for certain particular cases shows an excellent agreement.

We analyzed the boundary layer flow and heat transfer over a stretching sheet due to nanofluids with the effects of magnetic field, Brownian motion, thermophoresis, viscous dissipation and convective boundary conditions. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. The highly nonlinear partial differential equations governing flow and heat transport are simplified using similarity transformation. Resultant ordinary differential equations are solved numerically using the Runge–Kutta–Fehlberg and Newton–Raphson schemes based on the shooting method. The solutions velocity temperature and nanoparticle concentration depend on parameters such as Brownian motion, thermophoresis parameter, magnetic field and viscous dissipation, which have a significant influence on controlling the dynamics of the considered problem. Comparison with known results for certain particular cases shows an excellent agreement.

A mathematical analysis has been carried out to describe mixed convection heat transfer in MHD non-Darcian flow due to an exponential stretching sheet embedded in a porous medium in presence of non-uniform heat source/sink. Approximate analytical similarity solutions of the highly non-linear momentum and energy equations are obtained. The governing system of partial differential equations is first transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed equations are non-linear coupled differential equations and are solved very efficiently by using fifth order Runge–Kutta–Fehlberg method with shooting technique for various values of the governing parameters. The numerical solutions are obtained by considering an exponential dependent stretching velocity and prescribed boundary temperature on the flow directional coordinate. The computed results are compared with the previously published work on various special cases of the problem and are in good agreement with the earlier studies. The effect of various physical parameters, such as the Prandtl number,the Grashoff number, the Hartmann number, porous parameter, inertia coefficient and internal heat generation on flow and heat transfer characteristics are presented graphically to show some interesting aspects of the physical parameter.