(R1894) Invariant Solution for Two-dimensional and Axisymmetric Jet of Power-Law Fluids

An invariant solution is derived using the Lie symmetry technique for steady laminar two-dimensional and axisymmetric boundary layer jet flow of incompressible power-law fluids with appropriate boundary conditions. Using symmetry, the nonlinear partial differential equation of the jet flow problem is transformed into a nonlinear ordinary differential equation. The resultant nonlinear ordinary differential equation with boundary conditions is converted to an initial value problem using the Lie symmetry technique. A numerical solution for the resulting initial value problem is derived using Fehlberg’s fourth-fifth order Runge-Kutta method through Maple software. The graphical representation of the characteristics of the velocity field for different physical parameters is also discussed

(R1978) Heated Laminar Vertical Jet of Psudoplastic Fluids-Against Gravity

A heated laminar jet of Pseudo-plastic fluid flowing vertically upwards from a long narrow slit into a region of the same fluid which is at a rest and at a uniform temperature is considered. The governing non-linear Partial differential equations (PDEs) for the defined flow problem are transformed into non-linear ordinary differential equations using the effective similarity technique-one parameter deductive group theory method. The obtained non-linear coupled Ordinary differential equations are solved and the results are presented by graphs. The effect of the Prandtl number and Grashof number on the velocity and temperature of the jet flow is discussed. Also, a detailed discussion of some interesting applications of the vertical jet flow of pseudoplastic fluids in different fields of engineering and geophysics are provided

Extension of Blasius Newtonian Boundary Layer to Blasius Non-Newtonian Boundary Layer

Blasius equation is very well known and it aries in many boundary layer problems of fluid dynamics. In this present article, the Blasius boundary layer is extended by transforming the stress strain term from Newtonian to non-Newtonian. The extension of Blasius boundary layer is discussed using some non-newtonian fluid models like, Power-law model, Sisko model and Prandtl model. The Generalised governing partial differential equations for Blasius boundary layer for all above three models are transformed into the non-linear ordinary differewntial equations using the one parameter deductive group theory technique. The obtained similarity solutions are then solved numerically. The graphical presentation is also explained for the same. It concludes that velocity increases more rapidly when fluid index is moving from shear thickninhg to shear thininhg fluid.MSC 2020 No.: 76A05, 76D10, 76M9

Non-Newtonian Prandtl fluid over stretching permeable surface

An analysis is made of the velocity and temperature distribution in the flow of a viscous incompressible fluid caused by the stretching permeable surface which issues in the Prandtl fluid. Parandtl fluid is a pseudoplastic visco-inelastic non-Newtonian fluid. The governing partial differential equations are reduced to ordinary differential equations using deductive group transformation and similarity solution is derived. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity and temperature profiles. The corresponding skin friction coefficient and the Nusselt number are also calculated

Local Non-Similar Solution of Powell-Eyring Fluid flow over a Vertical Flat Plate

Our objective is to obtain the non-similarity solution of non-Newtonian fluid for Powell-Eyring model by a local non-similarity method. Here, free stream velocity is considered in power-law form (=m). The governing equations are transformed using non-similar transformations and derived equations are treated as ordinary differential equations. Non-similar solutions are obtained for different values of power-law index and stream-wise location . Influence of various parameters on velocity and temperature field are presented graphically using MATLAB bvp4c solver

Laminar Boundary Layer Flow of Sisko Fluid

The problem of steady two dimensional laminar boundary layer flow of non-Newtonian fluid is analyzed in the present paper. Sisko fluid model, one of the various fluid models of non- Newtonian fluid, is considered for stress-strain relationship. Similarity and numerical solutions obtained for the defined flow problem

Numerical Solution of 3rd order ODE Using FDM: On a Moving Surface in MHD Flow of Sisko Fluid

A Similarity group theoretical technique is used to transform the governing nonlinear partial differential equations of two dimensional MHD boundary layer flow of Sisko fluid into nonlinear ordinary differential equations. Then the resulting third order nonlinear ordinary differential equation with corresponding boundary conditions is linearised by Quasi linearization method. Numerical solution of the linearised third order ODE is obtained using Finite Difference method (FDM). Graphical presentation of the solution is given

Similarity analysis of three dimensional nanofluid flow by deductive group theoretic method

The objective of this paper is to obtain similarity solution of three-dimensional nanofluid flow over flat surface stretched continuously in two lateral directions. Two independent variables from governing equations are reduced by applying deductive two parameter group theoretical method. Partial differential equations with boundary conditions are converted into ordinary differential equations with appropriate boundary conditions. Obtained equations are solved for temperature and velocity. The effect of nanoparticles volume fraction on temperature and velocity profile is investigated

Similarity Flow Solution of MHD Boundary Layer Model for Non-Newtonian Power-Law Fluids over a Continuous Moving Surface

Abstract In this paper, the problem of laminar boundary layer flow for non-Newtonian power-law fluid over a continuous moving surface in the presence of transverse magnetic field is studied by appropriate similarity transformation. The governing partial differential equations are transformed into non linear ordinary differential equations using deductive group theoretic method