scholarly journals A New Analytical Procedure for Solving the Non-Linear Differential Equation Arising in the Stretching Sheet Problem

2013 ◽  
Vol 18 (3) ◽  
pp. 955-964 ◽  
Author(s):  
P.G. Siddheshwar ◽  
U.S. Mahabaleswar ◽  
H.I. Andersson
Keyword(s):  
Boundary Layer ◽  
Stretching Sheet ◽  
Analytical Procedure ◽  
Boundary Layer Equation ◽  
Newtonian Liquid ◽  
Linear Boundary ◽  
Boundary Layer Equations ◽  
Non Linear ◽  
Clairaut Equation ◽  
Linear Differential

Abstract The paper discusses a new analytical procedure for solving the non-linear boundary layer equation arising in a linear stretching sheet problem involving a Newtonian/non-Newtonian liquid. On using a technique akin to perturbation the problem gives rise to a system of non-linear governing differential equations that are solved exactly. An analytical expression is obtained for the stream function and velocity as a function of the stretching parameters. The Clairaut equation is obtained on consideration of consistency and its solution is shown to be that of the stretching sheet boundary layer equation. The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem

scholarly journals MHD MIXED CONVECTION STAGNATION-POINT FLOW OF A MICROPOLAR FLUID IN A POROUS MEDIUM TOWARDS A HEATED STRETCHING SHEET WITH THERMAL RADIATION

2012 ◽  
Vol 17 (4) ◽  
pp. 498-518 ◽  
Author(s):  
Dulal Pal ◽  
Sewli Chatterjee
Keyword(s):  
Boundary Layer ◽  
Porous Medium ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Boundary Layer Equation ◽  
Physical Parameters ◽  
Ohmic Dissipation ◽  
Local Skin ◽  
Non Linear

The present investigation is concerned with the study of heat and mass transfer characteristics on MHD boundary layer flow of an electrically conducting micropolar fluid over a non-isothermal stretching sheet embedded in a porous medium of variable thermal conductivity by applying prescribed heat flux for the heating processes. The thermal boundary layer equation takes into account of Ohmic dissipation due to transverse magnetic and electric fields. The governing system of partial differential equations is transformed into a system of non-linear ordinary differential equations using similarity transformation. The transformed non-linear coupled differential equations are linearized by quasi-linearization method and then solved very efficiently by finite-difference method. Attention has been focused to study the effects of various physical parameters on velocity, temperature and concentration in the boundary layer. Numerical data for the local skin friction coefficient, surface temperature and surface solutal concentration have also been tabulated for various parametric conditions.

The laminar boundary-layer equations II. Integration of non-linear ordinary differential equations

1948 ◽  
Vol 192 (1031) ◽  
pp. 567-575 ◽  
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Differential Equations ◽  
Two Dimensions ◽  
Boundary Layer Problem ◽  
Linear Ordinary Differential Equations ◽  
Boundary Layer Equations ◽  
Non Linear ◽  
Independent Variable ◽  
Linear Differential

The aim of this paper is to find particular integrals of non-linear differential equations which satisfy certain boundary conditions and tend exponentially to zero at infinity. The equations arise in connexion with the problem of integration of the equations of laminar flow in two dimensions. The paper consists of two parts. In the first part the equation / " '+ / / ' = A ( 1 - /'2) is discussed, where A is generally a known parameter, and the primes denote deviations with respect to the independent variable, x. This is the well-known Falkner & Skan’s (1930) equation. It was derived in connexion with the solution of the boundary-layer problem for a particular distribution of the velocity outside the boundary layer. It appears, however, that this equation is of far more fundamental importance in the problem of laminar flow, although, of course, A has a different meaning in the general case than it has in Falkner & Skan’s treatment.

Unsteady Flow and Heat Transfer of a MHD Micropolar Fluid Over a Porous Stretching Sheet in the Presence of Thermal Radiation

2013 ◽  
Vol 29 (3) ◽  
pp. 559-568 ◽  
Author(s):  
G. C. Shit ◽  
R. Haldar ◽  
A. Sinha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Micropolar Fluid ◽  
Stretching Sheet ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Layer Flow

AbstractA non-linear analysis has been made to study the unsteady hydromagnetic boundary layer flow and heat transfer of a micropolar fluid over a stretching sheet embedded in a porous medium. The effects of thermal radiation in the boundary layer flow over a stretching sheet have also been investigated. The system of governing partial differential equations in the boundary layer have reduced to a system of non-linear ordinary differential equations using a suitable similarity transformation. The resulting non-linear coupled ordinary differential equations are solved numerically by using an implicit finite difference scheme. The numerical results concern with the axial velocity, micro-rotation component and temperature profiles as well as local skin-friction coefficient and the rate of heat transfer at the sheet. The study reveals that the unsteady parameter S has an increasing effect on the flow and heat transfer characteristics.

scholarly journals Computational study of unsteady couple stress magnetic nanofluid flow from a stretching sheet with Ohmic dissipation

2019 ◽  
Vol 233 (2-4) ◽  
pp. 49-63 ◽  
Author(s):  
Mahesh Kumar ◽  
G Janardhana Reddy ◽  
N Naresh Kumar ◽  
O Anwar Bég
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Couple Stress ◽  
Stretching Sheet ◽  
Magnetic Parameter ◽  
Aluminium Oxide ◽  
Ohmic Dissipation ◽  
Non Linear ◽  
Layer Flow ◽  
Sheet Stretching

To provide a deeper insight of the transport phenomena inherent to the manufacturing of magnetic nano-polymer materials, in the present work a mathematical model is developed for time-dependent hydromagnetic rheological nano-polymer boundary layer flow and heat transfer over a stretching sheet in the presence of a transverse static magnetic field. Joule heating (Ohmic dissipation) and viscous heating effects are included since these phenomena arise frequently in magnetic materials processing. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. The Tiwari–Das nanoscale model is adopted which permits different nanoparticles to be simulated (in this article, both copper–water and aluminium oxide–water nanofluids are considered). Similarity transformations are utilized to convert the governing partial differential conservation equations into a system of coupled, non-linear ordinary differential equations with appropriate wall and free stream boundary conditions. The shooting technique is used to solve the reduced non-linear coupled ordinary differential boundary value problem via MATLAB symbolic software. Validation with published results from the literature is included for the special cases of non-dissipative and Newtonian nanofluid flows. Fluid velocity and temperature profiles for both copper and aluminium oxide (Al2O3) nanofluids are observed to be enhanced with greater non-Newtonian couple stress parameter and magnetic parameter, whereas the opposite trend is computed with greater values of unsteadiness parameter. The boundary layer flow is accelerated with increasing buoyancy parameter, elastic sheet stretching parameter and convection parameter. Temperatures are generally increased with greater couple stress rheological parameter and are consistently higher for the aluminium oxide nanoparticle case. Temperatures are also boosted with magnetic parameter and exhibit an overshoot near the wall when magnetic parameter exceeds unity (magnetic force exceeds viscous force). A decrease in temperatures is induced with increasing sheet stretching parameter. Increasing Eckert number elevates temperatures considerably. With greater nanoparticle volume fraction, both skin friction and Nusselt number are elevated, and copper nanoparticles achieve higher magnitudes than aluminium oxide.

Radiative Unsteady Rarefied Gaseous Flow Over a Stretching Sheet with Velocity Slip and Temperature Jump Effects

2020 ◽  
Vol 87 (3-4) ◽  
pp. 261
Author(s):  
Ram Prakash Sharma ◽  
N. Indumathi ◽  
S. Saranya ◽  
B. Ganga ◽  
A. K. Abdul Hakeem
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Gaseous Flow ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In this study a mathematical analysis has been carried out to scrutinize the unsteady boundary layer flow of an incompressible, rarefied gaseous flow over a vertical stretching sheet with velocity slip and thermal jump boundary conditions in the presence of thermal radiation. Using boundary layer approach and suitable similarity transformations, the governing partial differential equations with the boundary conditions are reduced to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved with the help of fourth order Runge-Kutta method with shooting technique. The results obtained for the velocity profile, temperature profile, skin friction coefficient and the reduced Nusselt number are described through graphs. It is predicted that the velocity and temperature profiles are lower for unsteady flow and has an opposite effect for steady flow.

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