Mixed convection non-axisymmetric Homann stagnation-point flow

2017 ◽  
Vol 812 ◽  
pp. 418-434 ◽  
Author(s):  
Y. Y. Lok ◽  
J. H. Merkin ◽  
I. Pop
Keyword(s):  
Mixed Convection ◽  
Incompressible Fluid ◽  
Strain Rate ◽  
Stagnation Point ◽  
Similarity Solution ◽  
Rate Ratio ◽  
Numerical Solutions ◽  
Stagnation Point Flow ◽  
Asymptotic Results ◽  
Convection Parameter

The steady mixed convection non-axisymmetric (Homann, Z. Angew. Math. Mech., vol. 16, 1936, pp. 153–164) stagnation-point flow over a vertical flat wall placed in a viscous and incompressible fluid is considered. A similarity solution is derived which involves the dimensionless parameters $\unicode[STIX]{x1D6FE}$, representing the shear-to-strain-rate ratio, and $\unicode[STIX]{x1D706}$, a mixed convection parameter. Forced convection, $\unicode[STIX]{x1D706}=0$, is treated first where solutions additional to those given previously by Weidman (J. Fluid Mech., vol. 702, 2012, pp. 460–469) are found arising from singularities as $\unicode[STIX]{x1D6FE}\rightarrow \pm 1$. Numerical solutions are obtained for representative values of both $\unicode[STIX]{x1D6FE}$ and $\unicode[STIX]{x1D706}$. Critical values $\unicode[STIX]{x1D706}_{c}$ of $\unicode[STIX]{x1D706}$ are seen in opposing flow and these are treated in detail. Asymptotic results for large $\unicode[STIX]{x1D706}$ and $\unicode[STIX]{x1D6FE}$ are derived.

MHD mixed convection oblique stagnation-point flow on a vertical plate

2017 ◽  
Vol 27 (12) ◽  
pp. 2744-2767
Author(s):  
Giulia Giantesio ◽  
Anna Verna ◽  
Natalia C. Roşca ◽  
Alin V. Rosca ◽  
Ioan Pop
Keyword(s):  
Mixed Convection ◽  
Stagnation Point ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Similarity Transformations

Purpose This paper aims to study the problem of the steady plane oblique stagnation-point flow of an electrically conducting Newtonian fluid impinging on a heated vertical sheet. The temperature of the plate varies linearly with the distance from the stagnation point. Design/methodology/approach The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB. Findings An exact similarity solution of the magnetohydrodynamic (MHD) Navier–Stokes equations under the Boussinesq approximation is obtained. Numerical solutions of the relevant functions and the structure of the flow field are presented and discussed for several values of the parameters which influence the motion: the Hartmann number, the parameter describing the oblique part of the motion, the Prandtl number (Pr) and the Richardson numbers. Dual solutions exist for several values of the parameters. Originality value The present results are original and new for the problem of MHD mixed convection oblique stagnation-point flow of a Newtonian fluid over a vertical flat plate, with the effect of induced magnetic field and temperature.

Non-axisymmetric Homann stagnation-point flows

2012 ◽  
Vol 702 ◽  
pp. 460-469 ◽  
Author(s):  
P. D. Weidman
Keyword(s):  
Shear Stress ◽  
Shear Rate ◽  
Strain Rate ◽  
Stagnation Point ◽  
Rate Ratio ◽  
Numerical Solutions ◽  
New Family ◽  
Outer Potential ◽  
Asymptotic Behaviours ◽  
Stress Parameters

AbstractA modification of Homann’s axisymmetric outer potential stagnation-point flow of strain rate $a$ is obtained by adding periodic radial and azimuthal velocities of the form $b\hspace{0.167em} r\sin 2\theta $ and $b\hspace{0.167em} r\cos 2\theta $, respectively, where $b$ is a shear rate. This leads to the discovery of a new family of asymmetric viscous stagnation-point flows depending on the shear-to-strain-rate ratio $\gamma = b/ a$ that exist over the range $\ensuremath{-} \infty \lt \gamma \lt \infty $. Numerical solutions for the wall shear stress parameters and the displacement thicknesses are given and compared with their large-$\gamma $ asymptotic behaviours. Sample similarity velocity profiles are also presented.

Thermal Radiation Effects on the Mixed Convection Stagnation-Point Flow in a Jeffery Fluid

2011 ◽  
Vol 66 (10-11) ◽  
pp. 606-614 ◽  
Author(s):  
Tasawar Hayat ◽  
Sabir Ali Shehzad ◽  
Muhammad Qasim ◽  
Saleem Obaidat
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Radiation Effects ◽  
Numerical Solutions ◽  
Mathematical Formulation ◽  
Deborah Number ◽  
Stagnation Point Flow ◽  
Suction Parameter

This study describes the mixed convection stagnation point flow and heat transfer of a Jeffery fluid towards a stretching surface. Mathematical formulation is given in the presence of thermal radiation. The Rosseland approximation is used to describe the radiative heat flux. Similarity transformations are employed to reduce the partial differential equations into the ordinary differential equations which are then solved by a homotopy analysis method (HAM). A comparative study is made with the known numerical solutions in a limiting sense and an excellent agreement is noted. The characteristics of involved parameters on the dimensionless velocity and temperature are also examined. It is noticed that the velocity increases with an increase in Deborah number. Further, the temperature is a decreasing function of mixed convection parameter. We further found that for fixed values of other parameters, the local Nusselt number increases by increasing suction parameter and Deborah number.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

Numerical analysis of time-dependent stagnation point flow of Oldroyd-B fluid subject to modified Fourier’s law

2021 ◽  
pp. 2150187
Author(s):  
Foukeea Qasim ◽  
Tian-Chuan Sun ◽  
S. Z. Abbas ◽  
W. A. Khan ◽  
M. Y. Malik
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Nonlinear Partial Differential Equation ◽  
Thermal Relaxation ◽  
Stagnation Point Flow ◽  
Time Dependent ◽  
Parameter Values

This paper aims to investigate the time-dependent stagnation point flow of an Oldroyd-B fluid subjected to the modified Fourier law. The flow into a vertically stretched cylinder at the stagnation point is discussed. The heat flux model of a non-Fourier is intended for the transfer of thermal energy in fluid flow. The study is carried out on the surface heating source, namely the surface temperature. The developed nonlinear partial differential equation for regulating fluid flow and heat transport is transformed via appropriate similarity variables into a nonlinear ordinary differential equation. The development and analysis of convergent series solutions were considered for velocity and temperature. Prandtl number numerical values are computed and investigated. This study’s findings are compared to the previous findings. By making use of the bvp4c Matlab method, numerical solutions are obtained. Besides, high buoyancy parameter values are found to increase the fluid velocity for the stimulating approach. By improving the thermal relaxation time parameter values, heat transfer in the fluid flow decreases. The temperature field effects are displayed graphically.

Effects of Second-Order Slip and Magnetic Field on Mixed Convection Stagnation-Point Flow of a Maxwellian Fluid: Multiple Solutions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
M. M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Reverse Flow ◽  
Second Order ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Variable Surface

In this paper, we investigate the effects of second-order slip and magnetic field on the nonlinear mixed convection stagnation-point flow toward a vertical permeable stretching/shrinking sheet in an upper convected Maxwell (UCM) fluid with variable surface temperature. Numerical results are obtained using the bvp4c function from matlab for the reduced skin-friction coefficient, the rate of heat transfer, the velocity, and the temperature profiles. The results indicate that multiple (dual) solutions exist for a buoyancy opposing flow for certain values of the parameter space irrespective to the types of surfaces whether it is stretched or shrinked. It is found that an applied magnetic field compensates the suction velocity for the existence of the dual solutions. Depending on the parametric conditions; elastic parameter, magnetic field parameter, first- and second-order slip parameters significantly controls the flow and heat transfer characteristics. The illustrated streamlines show that for upper branch solutions, the effects of stretching and suction are direct and obvious as the flow near the surface is seen to suck through the permeable sheet and drag away from the origin of the sheet. However, aligned but reverse flow occurs for the case of lower branch solutions when the mixed convection effect is less significant.

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