scholarly journals Effect of a Convective Boundary Condition on Boundary Layer Slip Flow and Heat Transfer Over a Stretching Sheet in View of the Exact Solution

2016 ◽  
Vol 46 (4) ◽  
pp. 85-95 ◽  
Author(s):  
Mona D. Aljoufi ◽  
Abdelhalim Ebaid
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Exact Solutions ◽  
Shooting Method ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Convective Boundary Condition ◽  
Current Paper ◽  
Convective Boundary

Abstract The exact solutions of a nonlinear differential equations system, describing the boundary layer flow over a stretching sheet with a convective boundary condition and a slip effect have been obtained in this paper. This problem has been numerically solved by using the shooting method in literature. The aim of the current paper is to check the accuracy of these published numerical results. This goal has been achieved via first obtaining the exact solutions of the governing nonlinear differential equations and then, by comparing them with the approximate numerical results reported in literature. The effects of the physical parameters on the flow field and the temperature distribution have been re-investigated through the new exact solutions. The main advantage of the current paper is the simple computational approach that has been introduced to analyze exactly the present physical problem. This simple analytical approach can be further applied to investigate similar problems. Although no remarkable differences have been detected between the current figures and those obtained in literature, the authors believe that if some numerical calculations were available for the fluid velocity and the temperature in literature then the convergence criteria and the accuracy of the shooting method used in Ref. [15] can be validated in view of the current exact expressions.

scholarly journals MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Reda G. Abdel-Rahman
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

scholarly journals Influence of Variable Thermal Conductivity on MHD Boundary Layer Slip Flow of Ethylene-Glycol Based Cu Nanofluids over a Stretching Sheet with Convective Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
N. Bhaskar Reddy ◽  
T. Poornima ◽  
P. Sreenivasulu
Keyword(s):  
Thermal Conductivity ◽  
Boundary Layer ◽  
Boundary Condition ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Convective Boundary Condition ◽  
Variable Thermal Conductivity ◽  
Convective Boundary

An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.

Numerically framing the impact of magnetic field on nanofluid flow over a curved stretching surface with convective heating

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Sanatan Das ◽  
Akram Ali ◽  
Rabindra Nath Jana
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Magnetic Parameter ◽  
Convective Boundary Condition ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Convective Boundary ◽  
Content Type ◽  
Curvature Parameter

Purpose Outstanding features such as thermal conductivity and superior electrical conductivity of nanofluids unfold a new window in the context of their extensive applications in engineering and industrial domains. The purpose of this study to simulate numerically the magneto-nanofluid flow and heat transfer over a curved stretching surface. Heat transport is explored in the presence of viscous dissipation. At the curved surface, the convective boundary condition is adopted. Three different nanoparticles, namely, copper, aluminium oxide and titanium dioxide are taken into consideration because of easily available in nature. Design/methodology/approach The basic flow equations are framed in terms of curvilinear coordinates. The modelled partial differential equations are transformed into a system of non-linear ordinary differential equations by means of appropriate similarity transformation. The subsequent non-linear system of equations is then solved numerically by using the Runge–Kutta–Felhberg method with the shooting scheme via bvp4c MATLAB built-in function. Impacts of various physical parameters on velocity, pressure and temperature distributions, local skin-friction coefficient, local Nusselt number and wall temperature are portrayed through graphs and tables followed by a comprehensive debate and physical interpretation. Findings Graphical results divulge that augmenting values of the magnetic parameter cause a decline in velocity profiles and stream function inside the boundary layer. The magnitude of the pressure function inside the boundary layer reduces for higher estimation of curvature parameter, and it is also zero when the curvature parameter goes to infinity. Furthermore, the temperature is observed in a rising trend with growing values of the magnetic parameter and Biot number. Practical implications This research study is very pertinent to the expulsion of polymer sheet and photographic films, metallurgical industry, electrically-conducting polymer dynamics, magnetic material processing, rubber and polymer sheet processing, continuous casting of metals, fibre spinning, glass blowing and fibre, wire and fibre covering and sustenance stuff preparing, etc. Originality/value Despite the huge amount of literature available, but still, very little attention is given to simulate the flow configuration due to the curved stretching surface with the convective boundary condition. Very few papers have been examined on this topic and found that its essence inside the boundary layer is not any more insignificant than on account of a stretching sheet. A numerical comparison with the published works is conducted to verify the accuracy of the present study.

Effect of Convective Boundary Condition on MHD Carreau Dusty Fluid over a Stretching Sheet with Heat Source

2017 ◽  
Vol 377 ◽  
pp. 233-241 ◽  
Author(s):  
S.U. Mamatha ◽  
Mahesha ◽  
Chakravarthula S.K. Raju ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Heat Source ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Dusty Fluid ◽  
Similarity Transformations

The underlying intention of the present study is to analyze the steady incompressible magneto hydrodynamic Carreau Dusty fluid over a stretching sheet with exponentially decaying heat source. Convective conditions are considered to control the thermal boundary layer. Similarity transformations were used to convert partial differential equations (PDEs) to a system of nonlinear ordinary differential equations (NODEs) which are solved numerically by employing Runge-Kutta with Newton’s technique. The effect of pertinent parameters on velocity and temperature profiles of both fluid and dust phase within the boundary layer has been studied by considering various values of controlling parameters. In addition, skin friction coefficient and reduced heat transfer coefficient have been examined for various values of the governing parameters. It is observed that the rate of heat transfer depreciates with space dependent heat generation and enhanced with the existing convective condition.

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