Search results

1 – 10 of 933
Per page
102050
Citations:
Loading...
Access Restricted. View access options
Article
Publication date: 29 November 2018

Alin V. Roşca, Natalia C. Roşca and Ioan Pop

The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned…

137

Abstract

Purpose

The purpose of this study is to investigate the influence of the second order slip velocity on the boundary layer stagnation point flow of a nanofluid past a non-aligned stretching/shrinking sheet.

Design/methodology/approach

Proper similarity variables are used to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. This system is then solved numerically using the bvp4c solver in MATLAB software. As in the papers by Kuznetsov and Nield (2010, 2013) and Fang et al. (2009), the authors considered the stretching/shrinking parameter λ, the first-order (a1, a2) and second-order (b1) slip parameters and the Lewis number Le, Nb the Brownian parameter and Nt the thermophoresis parameter fixed at Le = 10, Nb = Nt = 0.5 when the Prandtl number Pr is fixed at Pr = 1.

Findings

Dual solutions are found as the sheet is shrunk in the horizontal direction. Stability analysis shows that the first solution is physically realizable, whereas the second solution is not practicable.

Originality/value

The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface, as they successfully extend the problem considered by Wang (2008) and Lok et al. (2011) to the case of nanofluids.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 2
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 4 December 2017

Giulia Giantesio, Anna Verna, Natalia C. Roşca, Alin V. Rosca and Ioan Pop

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…

113

Abstract

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.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 27 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 19 June 2019

Natalia C. Roşca, Alin V. Roşca and Ioan Pop

The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper…

77

Abstract

Purpose

The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das.

Design/methodology/approach

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters.

Findings

It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case.

Originality/value

The authors believe that all numerical results are new and original, and have not been published elsewhere.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 15 May 2009

Y.Y. Lok, I. Pop, D.B. Ingham and N. Amin

The purpose of this paper is to study theoretically the steady two‐dimensional mixed convection flow of a micropolar fluid impinging obliquely on a stretching vertical sheet. The…

417

Abstract

Purpose

The purpose of this paper is to study theoretically the steady two‐dimensional mixed convection flow of a micropolar fluid impinging obliquely on a stretching vertical sheet. The flow consists of a stagnation‐point flow and a uniform shear flow parallel to the surface of the sheet. The sheet is stretching with a velocity proportional to the distance from the stagnation point while the surface temperature is assumed to vary linearly. The paper attempts also to show that a similarity solution of this problem can be obtained.

Design/methodology/approach

Using a similarity transformation, the basic partial differential equations are first reduced to ordinary differential equations which are then solved numerically using the Keller box method for some values of the governing parameters. Both assisting and opposing flows are considered. The results are also obtained for both strong and weak concentration cases.

Findings

These results provide information about the effect of a/c (ratio of the stagnation point velocity and the stretching velocity), σ (shear flow parameter) and K (material parameter) on the flow and heat transfer characteristics in mixed convection flow near a non‐orthogonal stagnation‐point on a vertical stretching surface. The results show that the shear stress increases as K increases, while the heat flux from the surface of the sheet decreases with an increase in K.

Research limitations/implications

The results in this paper are valid only in the small region around the stagnation‐point on the vertical sheet. It is found that for smaller Prandtl number, there are difficulties in the numerical computation due to the occurrence of reversed flow for opposing flow. An extension of this work could be performed for the unsteady case.

Originality/value

The present results are original and new for the micropolar fluids. They are important in many practical applications in manufacturing processes in industry.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 3/4
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 11 January 2011

Y.Y. Lok, A. Ishak and I. Pop

The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of…

767

Abstract

Purpose

The purpose of this paper is to theoretically investigate the steady two‐dimensional magnetohydrodynamic (MHD) boundary layer flow over a shrinking sheet. The effects of stretching and shrinking parameter as well as magnetic field parameter near the stagnation point are studied.

Design/methodology/approach

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary differential equations which are then solved numerically using Keller‐box method.

Findings

The solution is unique for stretching case; however, multiple (dual) solutions exist for small values of magnetic field parameter for shrinking case. The streamlines are non‐aligned and a reverse flow is formed near the surface due to shrinking effect.

Practical implications

The flow due to a stretching or shrinking sheet is relevant to several practical applications in the field of metallurgy, chemical engineering, etc. For example, in manufacturing industry, polymer sheets and filaments are manufactured by continuous extrusion of the polymer from a die to a windup roller, which is located at a finite distance away. In these cases, the properties of the final product depend to a great extent on the rate of cooling which is governed by the structure of the boundary layer near the stretching surface.

Originality/value

The present results are original and new for the MHD flow near the stagnation‐point on a shrinking sheet. For shrinking case, the velocity on the boundary is towards a fixed point which would cause a velocity away from the sheet. Therefore, this paper is important for scientists and engineers in order to become familiar with the flow behaviour and properties of such MHD flow and the way to predict the properties of this flow for the process equipments.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 21 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 19 December 2023

Waqar Khan Usafzai, Emad H. Aly and Ioan Pop

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport…

72

Abstract

Purpose

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

Design/methodology/approach

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

Findings

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

Originality/value

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 34 no. 3
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 18 September 2007

Anati Ali, Norsarahaida Amin and Ioan Pop

The purpose of this paper is to study the unsteady boundary layer flow of a micropolar fluid past a circular cylinder which is started impulsively from rest.

811

Abstract

Purpose

The purpose of this paper is to study the unsteady boundary layer flow of a micropolar fluid past a circular cylinder which is started impulsively from rest.

Design/methodology/approach

The nonlinear partial differential equations consisting of three independent variables are solved numerically using the 3D Keller‐box method.

Findings

Numerical solutions for the velocity profiles, wall skin friction and microrotation profiles are obtained and presented for various values of time t and material parameter K with the boundary condition for microrotation n=0 (strong concentration of microelements) and n=1/2 (weak concentration of microelements). The results are presented along the points on the cylinder surface, starting from the forward to the rear stagnation point, for small time up to the time when the boundary layer flow separates from the cylinder.

Originality/value

It is believed that this is the first paper that uses the 3D Keller‐box method to study the unsteady boundary layer flow of micropolar fluids. In the last four decades, there has been overhelming interest shown by researchers in micropolar fluids and still many problems are unsolved. The paper shows not only the fundamental importance of this problem, but also the implications for situations of practical interest.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 17 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 27 September 2021

Ioan Pop, Mohammadreza Nademi Rostami and Saeed Dinarvand

The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical…

88

Abstract

Purpose

The purpose of this article is to study the steady laminar magnetohydrodynamics mixed convection stagnation-point flow of an alumina-graphene/water hybrid nanofluid with spherical nanoparticles over a vertical permeable plate with focus on dual similarity solutions.

Design/methodology/approach

The single-phase hybrid nanofluid modeling is based on nanoparticles and base fluid masses instead of volume fraction of first and second nanoparticles as inputs. After substituting pertinent similarity variables into the basic partial differential equations governing on the problem, the authors obtain a complicated system of nondimensional ordinary differential equations, which has non-unique solution in a certain range of the buoyancy parameter. It is worth mentioning that, the stability analysis of the solutions is also presented and it is shown that always the first solutions are stable and physically realizable.

Findings

It is proved that the magnetic parameter and the wall permeability parameter widen the range of the buoyancy parameter for which the solution exists; however, the opposite trend is valid for second nanoparticle mass. Besides, mass suction at the surface of the plate as well as magnetic parameter leads to reduce both hydrodynamic and thermal boundary layer thicknesses. Moreover, the assisting flow regime always has higher values of similarity skin friction and Nusselt number relative to opposing flow regime.

Originality/value

A novel mass-based model of the hybridity in nanofluids has been used to study the foregoing problem with focus on dual similarity solutions. The results of this paper are completely original and, to the best of the authors’ knowledge, the numerical results of the present paper were never published by any researcher.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 6 December 2018

Davood Aliakbarzadeh Kashani, Saeed Dinarvand, Ioan Pop and Tasawar Hayat

The purpose of this paper is to numerically study the unsteady double-diffusive mixed convective stagnation-point flow of a water-based nanofluid accompanied with one salt past a…

129

Abstract

Purpose

The purpose of this paper is to numerically study the unsteady double-diffusive mixed convective stagnation-point flow of a water-based nanofluid accompanied with one salt past a vertical flat plate. The effects of Brownian motion and thermophoresis parameters are also introduced through Buongiorno’s two-component nonhomogeneous equilibrium model in the governing equations.

Design/methodology/approach

In the present explanation of double-diffusive mixed convective model, there are four boundary layers entitled: velocity, thermal, solutal concentration and nanoparticle concentration. The resulting basic equations are solved numerically via an efficient Runge–Kutta fourth-order method with shooting technique after the governing nonlinear partial differential equations are converted into a system of nonlinear ordinary differential equations by the use of similarity transformations.

Findings

To avail the physical insight of problem, the effects of the mixed convection parameter, unsteadiness parameter and salt/nanoparticle parameters on the boundary layers behavior are investigated. Moreover, four possible types of diffusion problems entitled: double-diffusive nanofluid (DDNF), double-diffusive regular fluid (DDRF), mono-diffusive nanofluid (MDNF) and mono-diffusive regular fluid (MDRF) are considered to analyze and compare them in concepts of heat and mass transfer.

Originality/value

The results demonstrate that, for a regular fluid, without nanoparticle and salt (MDRF), the dimensionless heat transfer rate is smaller than other diffusion cases. As we include nanoparticle and salt (DDNF), the rate of heat transfer increases due to an increase in thermal conductivity and rate of diffusion of salt. Moreover, it is observed that the highest heat transfer rate is obtained for the situation that the thermophoretic effect of nanoparticles is negligible. Besides, the heat transfer rate enhances with the increase in the regular double-diffusive buoyancy parameter of salt.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Access Restricted. View access options
Article
Publication date: 19 March 2021

Najiyah Safwa Khashi'ie, Norihan M. Arifin, John H. Merkin, Rusya Iryanti Yahaya and Ioan Pop

The purpose of this paper is to numerically analyze the stagnation point flow of Cu-Al2O3/water hybrid nanofluid with mixed convection past a flat plate and circular cylinder.

241

Abstract

Purpose

The purpose of this paper is to numerically analyze the stagnation point flow of Cu-Al2O3/water hybrid nanofluid with mixed convection past a flat plate and circular cylinder.

Design/methodology/approach

The similarity equations that reduced from the boundary layer and energy equations are solved using the bvp4c solver. The duality of solutions is observed within the specific range of the control parameters, namely, mixed convection parameter λ, curvature parameter γ and nanoparticles volumetric concentration ϕ1 for alumina, while for copper ϕ2. The stability analysis is also designed to justify the particular solutions’ stability. Additionally, the idea to obtain the solution for large value of λ and γ is also presented in this paper.

Findings

Two solutions exist in opposing and assisting flows up to a critical value λc where λc lies in the opposing region. An upsurge of the curvature parameter tends to extend the critical value (delay the separation process), whilst increase the heat transfer performance of the working fluid. Meanwhile, the application of hybrid Cu-Al2O3/water nanofluid also can decelerate the separation of laminar boundary layer flow and produce higher heat transfer rate than the Cu–water nanofluid and pure water.

Originality/value

The results are new and original. This study benefits to the other researchers, specifically in the observation of the fluid flow characteristics and heat transfer rate of the hybrid nanofluid. Also, this paper features with the mathematical formulation for the solution with large values of λ and γ.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 12
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of 933
Per page
102050