scholarly journals Analytical Investigation of Viscoelastic Stagnation-Point Flows with Regard to Their Singularity

2021 ◽  
Vol 11 (15) ◽  
pp. 6931
Author(s):  
Jie Liu ◽  
Martin Oberlack ◽  
Yongqi Wang
Keyword(s):  
Stress Distribution ◽  
Stress Field ◽  
Stagnation Point ◽  
Analytical Solutions ◽  
Wide Spectrum ◽  
Momentum Conservation ◽  
Stagnation Point Flow ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Special Cases

Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.

On the differential equation governing the rear stagnation point in magnetohydrodynamics and Goldstein's ‘backward’ boundary layers

1967 ◽  
Vol 63 (4) ◽  
pp. 1327-1330 ◽  
Author(s):  
S. Leibovich
Keyword(s):  
Differential Equation ◽  
Boundary Value Problem ◽  
Stagnation Point ◽  
Boundary Layers ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Stagnation Point Flow ◽  
Special Cases ◽  
Rear Stagnation Point

AbstractExistence and uniqueness proofs for a boundary-value problem associated with a magnetohydrodynamic Falkner–Skan equation are presented. Relevant special cases of the problem herein considered include the magnetohydrodynamic rear stagnation point flow, and the non-magnetic ‘backward boundary layers’ of Goldstein(2).

Rotational stagnation point flow

1964 ◽  
Vol 19 (3) ◽  
pp. 366-374 ◽  
Author(s):  
Wallace D. Hayes
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Constant Density ◽  
Rotational Flow ◽  
Boundary Layer Equations ◽  
Stagnation Points ◽  
Special Cases

The constant-density inviscid rotational flow in the neighbourhood of a general stagnation point on a wall is investigated. In all but very special cases, the solution is non-analytic and the vorticity at the wall is infinite; the stagnation streamline is tangent to the wall at the stagnation point; stagnation points of saddlepoint type cannot exist.The boundary-layer equations corresponding to the inviscid solutions studied are presented.

Stagnation-point flow of an aqueous titania-copper hybrid nanofluid toward a wavy cylinder

2018 ◽  
Vol 28 (7) ◽  
pp. 1716-1735 ◽  
Author(s):  
Mohammad Yousefi ◽  
Saeed Dinarvand ◽  
Mohammad Eftekhari Yazdi ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Base Fluid ◽  
Stagnation Point Flow ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Analytic Modeling ◽  
Flow And Heat Transfer ◽  
Special Cases ◽  
Hybrid Nanofluids

Purpose The purpose of this paper is to investigate analytically the steady general three-dimensional stagnation-point flow of an aqueous titania-copper hybrid nanofluid past a circular cylinder that has a sinusoidal radius variation. Design/methodology/approach First, the analytic modeling of hybrid nanofluid is presented, and using appropriate similarity variables, the governing equations are transformed into nonlinear ordinary differential equations in the dimensionless stream function, which is solved by the well-known function bvp4c from MATLAB. Findings The current solution demonstrates good agreement with those of the previously published studies in the special cases of regular fluid and nanofluids. Graphical results are presented to investigate the influences of the titania and copper nanoparticle volume fractions and also the nodal/saddle indicative parameter on flow and heat transfer characteristics. Here, the thermal characteristics of hybrid nanofluid are found to be higher in comparison to the base fluid and fluid containing single nanoparticles. An important point to note is that the developed model can be used with great confidence to study the flow and heat transfer of hybrid nanofluids. Originality/value Analytic modeling of hybrid nanofluid is the important originality of present study. Hybrid nanofluids are potential fluids that offer better heat transfer performance and thermophysical properties than convectional heat transfer fluids (oil, water and ethylene glycol) and nanofluids with single nanoparticles. In this investigation, titania (TiO2, 50 nm), copper (Cu, 20 nm) and the hybrid of these two are separately dispersed into the water as the base fluid and analyzed.

scholarly journals Heat transfer on magnetohydrodynamic stagnation point flow through a porous shrinking/stretching sheet: A numerical study

2020 ◽  
Vol 24 (2 Part B) ◽  
pp. 1335-1344 ◽  
Author(s):  
Munawwar Abbas ◽  
Muhammad Bhatti ◽  
Mohammad Rashidi
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Stretching Sheet ◽  
Numerical Study ◽  
Linearization Method ◽  
Stagnation Point Flow ◽  
Heat Transfer Analysis ◽  
Special Cases ◽  
Successive Linearization Method ◽  
Flow Through

This article examines the numerical study of heat transfer analysis on MHD stagnation point flow past a permeable shrinking/stretching sheet through a porous media. The governing equations have been reduced to the ODE by utilizing similarity variables. The obtained highly non-linear coupled differential equations have been solved by implementing a numerical scheme labeled as successive linearization method. The influences for the pertinent parameters on velocity profile and temperature profile is debated and demonstrated graphically. Numerical comparisons in some special cases have been brought along the prevailing literature, and it is noticed that the current outcomes are in good concord.

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