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.

scholarly journals Unsteady mixed convection stagnation-point flow over a plate moving along the direction of flow impingement

2017 ◽  
Vol 27 (1) ◽  
pp. 120-141 ◽  
Author(s):  
Siti Hidayah Muhad Saleh ◽  
Norihan Md. Arifin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Differential Equation ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Nonlinear Partial Differential Equation ◽  
Stagnation Point Flow ◽  
Transfer Coefficients ◽  
Content Type ◽  
Heat Transfer Coefficients ◽  
Similarity Transformations ◽  
Unsteady Mixed Convection

Purpose The purpose of this paper is to present the results of an analysis performed to study unsteady mixed convection at the stagnation point flow over a plate moving along the direction of flow impingement. The similarity transformations are used to transform the governing nonlinear partial differential equation to a system of an ordinary differential equation. Design/methodology/approach The transformed equations are then solved numerically by a shooting technique together with bvp4c function. Findings The numerical results are compared with the corresponding results from previous researchers. The effects of the unsteadiness Parameter A, Prandtl number Pr, mixed convection parameter λ for plane (m = 0) and axisymmetric (m = 1) flow on the shear stress or the skin friction and heat transfer coefficients, as well as the velocity and temperature profiles, are presented and discussed. Originality/value Dual solutions for the opposing flow and multiple solutions for the assisting flow are found.

Nonorthogonal Stagnation-point Flow of a Second-grade Fluid Past a Lubricated Surface

2016 ◽  
Vol 71 (3) ◽  
pp. 273-280 ◽  
Author(s):  
Khalid Mahmood ◽  
Muhammad Sajid ◽  
Nasir Ali
Keyword(s):  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Fluid Velocity ◽  
Weissenberg Number ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Grade Fluid

AbstractThe stagnation-point flow of a second-grade fluid past a power law lubricated surface is considered in this paper. It is assumed that the fluid impinges on the wall obliquely. A suitable choice of similarity transformations reduces the governing partial differential equations into ordinary differential equations. The thin lubrication layer suggests that the interface conditions between the fluid and the lubricant can be imposed on the boundary. An implicit finite difference scheme known as the Keller-Box method is employed to obtain the numerical solutions. The effects of slip parameter and Weissenberg number on the fluid velocity and streamlines is discussed in the graphs. The limiting cases of partial-slip and no-slip can be deduced from the present solutions.

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.

scholarly journals Nonviscous Oblique Stagnation Point Flow towards Riga Plate

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Sobia Akbar ◽  
Azad Hussain
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Differential Equations ◽  
Stagnation Point ◽  
Plane Surface ◽  
Equations Of Motion ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Riga Plate ◽  
Mathematical Techniques

Purpose. The flow of nonviscous Casson fluid is examined in this study over an oscillating surface. The model of the fluid flow has been inspected in the presence of oblique stagnation point flow. The scrutiny is subsumed for the Riga plate by considering the effects of magnetohydrodynamics. The Riga plate is considered as an electromagnetic lever which carries eternal magnets and a stretching line up of alternating electrodes coupled on a plane surface. We have considered nonboundary layer two-dimensional incompressible flow of the fluid. The fluid flow model is analyzed in the fixed frame of reference. Motivation. The motivation of achieving more suitable results has always been a quest of life for scientists; the capability of determining the boundary layer of flow on aircraft which either stays laminar or turns turbulent has encouraged the researcher to study compressible flow in depth. The compressible fluid with boundary layer flow has been utilized by numerous researchers to reduce skin friction and enhance thermal and convectional heat exchange. Design/Approach/Methodology. The attained partial differential equations will be critically inspected by using suitable similarity transformation to transform these flows thrived equations into higher nonlinear ordinary differential equations (ODE). Then, these equations of motion are intercepted by mathematical techniques such as the bvp4c method in Maple and Matlab. The graphical and tabular representation of different parameters is also given. Findings. The behavior of β and modified Hartmann number M increases by positively increasing the values of both parameters for F η , while ω decreases with increasing the values of ω for F η . The graph of β shows upward behavior for distinct values for both G η and G ′ η for velocity portray. Prandtl number and β for the temperature profile of θ η and θ 1 η goes downward with increasing parameters.

Fourier-Bessel Series Model for the Stefan Problem With Internal Heat Generation in Cylindrical Coordinates

2018 ◽  
Author(s):  
Lyudmyla Barannyk ◽  
John Crepeau ◽  
Patrick Paulus ◽  
Ali Siahpush
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Time Dependent ◽  
Cylindrical Coordinates ◽  
System Approaches ◽  
Melting And Solidification

A nonlinear, first-order ordinary differential equation that involves Fourier-Bessel series terms has been derived to model the time-dependent motion of the solid-liquid interface during melting and solidification of a material with constant internal heat generation in cylindrical coordinates. The model is valid for all Stefan numbers. One of the primary applications of this problem is for a nuclear fuel rod during meltdown. The numerical solutions to this differential equation are compared to the solutions of a previously derived model that was based on the quasi-steady approximation, which is valid only for Stefan numbers less than one. The model presented in this paper contains exponentially decaying terms in the form of Fourier-Bessel series for the temperature gradients in both the solid and liquid phases. The agreement between the two models is excellent in the low Stefan number regime. For higher Stefan numbers, where the quasi-steady model is not accurate, the new model differs from the approximate model since it incorporates the time-dependent terms for small times, and as the system approaches steady-state, the curves converge. At higher Stefan numbers, the system approaches steady-state faster than for lower Stefan numbers. During the transient process for both melting and solidification, the temperature profiles become parabolic.

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).

scholarly journals Hydromagnetic Stagnation-Point Flow towards a Radially Stretching Convectively Heated Disk

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
S. Shateyi ◽  
O. D. Makinde
Keyword(s):  
Stagnation Point ◽  
Numerical Solutions ◽  
Relaxation Method ◽  
Disk Surface ◽  
Stagnation Point Flow ◽  
Temperature Fields ◽  
Physical Parameters ◽  
Local Skin ◽  
Spectral Relaxation Method ◽  
Spectral Relaxation

The steady stagnation-point flow and heat transfer of an electrically conducted incompressible viscous fluid are extended to the case where the disk surface is convectively heated and radially stretching. The fluid is subjected to an external uniform magnetic field perpendicular to the plane of the disk. The governing momentum and energy balance equations give rise to nonlinear boundary value problem. Using a spectral relaxation method with a Chebyshev spectral collocation method, the numerical solutions are obtained over the entire range of the physical parameters. Emphasis has been laid to study the effects of viscous dissipation and Joule heating on the thermal boundary layer. Pertinent results on the effects of various thermophysical parameters on the velocity and temperature fields as well as local skin friction and local Nusselt number are discussed in detail and shown graphically and/or in tabular form.

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