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1 – 10 of over 3000Najiyah Safwa Khashi'ie, Iskandar Waini, Syazwani Mohd Zokri, Abdul Rahman Mohd Kasim, Norihan Md Arifin and Ioan Pop
This paper aims to accentuate the behavior of second-grade hybrid Al2O3–Cu nanofluid flow and its thermal characteristics driven by a stretching/shrinking Riga plate.
Abstract
Purpose
This paper aims to accentuate the behavior of second-grade hybrid Al2O3–Cu nanofluid flow and its thermal characteristics driven by a stretching/shrinking Riga plate.
Design/methodology/approach
The second-grade fluid is considered with the combination of Cu and Al2O3 nanoparticles. Three base fluids namely water, ethylene glycol (EG) and methanol with different Prandtl number are also examined. The formulation of the mathematical model of second-grade hybrid nanofluid complies with the boundary layer approximations. The complexity of the governing model is reduced into a simpler differential equations using the similarity transformation. The bvp4c solver is fully used to solve the reduced equations. The observation of multiple solutions is conducted for the assisting (stretching) and opposing (shrinking) cases.
Findings
The impact of suction parameter, second-grade parameter, electromagnetohydrodynamics (EMHD) parameter, velocity ratio parameter and the volumetric concentration of the alumina and copper nanoparticles are numerically analyzed on the velocity and temperature profiles, skin friction coefficient and local Nusselt number (thermal rate) of the second-grade Al2O3–Cu/water. The solution is unique when (static and stretching cases) while dual for a specific range of negative in the presence of suction effect. Based on the appearance of the first solution in all cases of, it is physically showed that the first solution is stable. Further examination reveals that the EMHD and suction parameters are the contributing factors for the thermal enhancement of this non-Newtonian working fluid. Meanwhile, the viscosity of the non-Newtonian fluid also plays a significant role in the fluid motion and heat transfer rate based on the finding that the EG base fluid produces the maximum heat transfer rate but the lowest critical value and skin friction coefficient.
Originality/value
The results are novel and contribute to the discovery of the hybrid nanoparticles’ performance in the non-Newtonian second-grade fluid. Besides, this study is beneficial to the researchers in this field and general audience from industries regarding the factors, which contributing to the thermal enhancement of the working fluid.
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Lazhar Bougoffa, Jun-Sheng Duan and Randolph Rach
The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed…
Abstract
Purpose
The purpose of this paper is to first deduce a new form of the exact analytic solution of the well-known nonlinear second-order differential equation subject to a set of mixed nonlinear Robin and Neumann boundary conditions that model the thin film flows of fourth-grade fluids, and second to compare the approximate analytic solutions by the Adomian decomposition method (ADM) with the new exact analytic solution to validate its accuracy for parametric simulations of the thin film fluid flows, even for more complex models of non-Newtonian fluids in industrial applications.
Design/methodology/approach
The approach to calculating a new form of the exact analytic solution of thin film fluid flows rests upon a sequence of transformations including the modification of the classic technique due to Scipione del Ferro and Niccolò Fontana Tartaglia. Next the authors establish a lemma that justifies the new expression of the exact analytic solution for thin film fluid flows of fourth-grade fluids. Second, the authors apply a modification of the systematic ADM to quickly and easily calculate the sequence of analytic approximate solutions for this strongly nonlinear model of thin film flow of fourth-grade fluids. The ADM has been previously demonstrated to be eminently practical with widespread applicability to frontier problems arising in scientific and engineering applications. Herein, the authors seek to establish the relative merits of the ADM in the context of the thin film flows of fourth-grade fluids.
Findings
The ADM is shown to closely agree with the new expression of the exact analytic solution. The authors have calculated the error remainder functions and the maximal error remainder parameters in the error analysis to corroborate the solutions. The error analysis demonstrates the rapid rate of convergence and that we can approximate the exact solution as closely as we please; furthermore the rate of convergence is shown to be approximately exponential, and thus only a low-stage approximation will be adequate for engineering simulations as previously documented in the literature.
Originality/value
This paper presents an accurate work for solving thin film flows of fourth-grade fluids. The authors have compared the approximate analytic solutions by the ADM with the new expression of the exact analytic solution for this strongly nonlinear model. The authors commend this technique for more complex thin film fluid flow models.
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T. Hayat, M. Hussain, M. Awais and S. Obaidat
The boundary layer flow and heat transfer of second grade fluid in a region of the stagnation point over a stretching surface has been examined. Thermal-diffusion (Dufour) and…
Abstract
Purpose
The boundary layer flow and heat transfer of second grade fluid in a region of the stagnation point over a stretching surface has been examined. Thermal-diffusion (Dufour) and diffusion-thermo (Soret) effects combined with melting heat transfer are also considered. Suitable transformations are employed to convert the partial differential equations representing the conservation of mass, momentum, energy and diffusion into the system of ordinary differential equations. The series solutions for the flow quantities of interest are presented. Interpretation to velocity, temperature and concentration is assigned. Numerical values of the local Nusselt and Sherwood numbers have been computed. The paper aims to discuss these issues.
Design/methodology/approach
Analytic approach homotopy analysis method (HAM) is used to find the convergent solution of melting heat transfer in a boundary layer flow of a second grade fluid under Soret and Dufour effects.
Findings
In this article the main findings are as second grade fluid; melting heat transfer; Soret and Dufour effects; mass transfer; stretching sheet. It is noted that melting heat transfer enhances the flow. Moreover, the effects of Soret and Dufour parameters have opposite effects on the temperature and concentration fields.
Originality/value
The performed computations show that the behaviors of Prandtl number Pr and Schmidt number Sc on the dimensionless temperature and concentration fields are similar in a qualitative sense.
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Umair Khan, Aurang Zaib, Anuar Ishak, El-Sayed M. Sherif and Piotr Wróblewski
Ferrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable…
Abstract
Purpose
Ferrofluids are aqueous or non-aqueous solutions with colloidal particles of iron oxide nanoparticles with high magnetic characteristics. Their magnetic characteristics enable them to be controlled and manipulated when ferrofluids are exposed to magnetic fields. This study aims to inspect the features of unsteady stagnation point flow (SPF) and heat flux from the surface by incorporating ferromagnetic particles through a special kind of second-grade fluid (SGF) across a movable sheet with a nonlinear heat source/sink and magnetic field effect. The mass suction/injection and stretching/shrinking boundary conditions are also inspected to calculate the fine points of the features of multiple solutions.
Design/methodology/approach
The leading equations that govern the ferrofluid flow are reduced to a group of ordinary differential equations by applying similarity variables. The converted equations are numerically solved through the bvp4c solver. Afterward, study and discussion are carried out to examine the different physical parameters of the characteristics of nanofluid flow and thermal properties.
Findings
Multiple solutions are revealed to happen for situations of unsteadiness, shrinking as well as stretching sheets. Greater suction slows the separation of the boundary layers and causes the critical values to expand. The region where the multiple solutions appear is observed to expand with increasing values of the magnetic, non-Newtonian and suction parameters. Moreover, the fluid velocity significantly uplifts while the temperature declines due to the suction parameter.
Originality/value
The novelty of the work is to deliberate the impact of mass suction/injection on the unsteady SPF through the special second-grade ferrofluids across a movable sheet with an erratic heat source/sink. The confirmed results provide a very good consistency with the accepted papers. Previous studies have not yet fully explored the entire analysis of the proposed model.
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Taimoor Salahuddin, Ali Haider and Metib Alghamdi
The current investigation is communicated to analyze the characteristics of squeezed second grade nanofluid flow enclosed by infinite channel in the existence of both heat…
Abstract
Purpose
The current investigation is communicated to analyze the characteristics of squeezed second grade nanofluid flow enclosed by infinite channel in the existence of both heat generation and variable viscosity. The leading non-linear energy and momentum PDEs are converted into non-linear ODEs by using suitable analogous approach.
Design/methodology/approach
Then the acquired non-linear problem is numerically calculated by using Bvp4c (built in) technique in MATLAB.
Findings
The influence of certain appropriate physical parameters, namely, squeezed number, fluid parameter, Brownian motion, heat generation, thermophoresis parameter, Prandtl number, Schmidt number and variable viscosity parameter on temperature, velocity and concentration distributions are studied and deliberated in detail. Numerical calculations of Sherwood number, Nusselt number and skin friction for distinct estimations of appearing parameters are analyzed through graphs and tables. It is examined that for large values of squeezing parameter, the velocity profile increases, whereas opposite behavior is noticed for large values of variable viscosity and fluid parameter. Moreover, temperature profile increases for large values of Brownian motion, thermophoresis parameter and squeezed parameter and decreases by increases Prandtl number and heat generation. Moreover, concentration profile increases for large values of Brownian motion parameter and decreases by increases thermophoresis parameter, squeezed parameter and Schmidt number.
Originality/value
No one has ever taken infinite squeezed channel having second grade fluid model with variable viscosity and heat generation.
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T. Hayat, R. Naz, S. Asghar and A. Alsaedi
The purpose of this paper is to study the heat and mass transfer with Soret-Dufour effects for the magnetohydrodynamic three-dimensional flow of second grade fluid in the rotating…
Abstract
Purpose
The purpose of this paper is to study the heat and mass transfer with Soret-Dufour effects for the magnetohydrodynamic three-dimensional flow of second grade fluid in the rotating frame of reference.
Design/methodology/approach
Series solution is obtained by homotopy analysis method.
Findings
Increase in Soret number, Schmidt number and Dufour number, the heat transfer increases and mass transfer decreases. Effects of Prandtl and Eckert numbers are qualitatively similar as they assist the temperature profile and reduce the concentration of species. Increase in the length of the channel versus height increases the temperature profile but decreases the concentration field. Increase in the second grade fluid parameter causes reduction in both the temperature and concentration fields. The heat flux values at the lower plate are smaller than the values at the upper plate, whereas the situation is opposite in the case of mass transfer.
Originality/value
These findings will be useful for the fluid flow in porous channel.
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The purpose of this paper is to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third…
Abstract
Purpose
The purpose of this paper is to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. The principal question the authors address in this paper is in regard to the applicability of the no‐slip condition at a solid‐liquid boundary. The authors present the effects of slip, magnetohydrodynamics (MHD) and heat transfer for the plane Couette, plane Poiseuille and plane Couette‐Poiseuille flows in a homogeneous and thermodynamically compatible third grade fluid. The problem of a non‐Newtonian plane Couette flow, fully developed plane Poiseuille flow and Couette‐Poiseuille flow are investigated.
Design/methodology/approach
The present investigation is an attempt to study the effects of nonlinear partial slip on the walls for steady flow and heat transfer of an incompressible, thermodynamically compatible third grade fluid in a channel. A very effective and higher order numerical scheme is used to solve the resulting system of nonlinear differential equations with nonlinear boundary conditions. Numerical solutions are obtained by solving nonlinear ordinary differential equations using Chebyshev spectral method.
Findings
Due to the nonlinear and highly complicated nature of the governing equations and boundary conditions, finding an analytical or numerical solution is not easy. The authors obtained numerical solutions of the coupled nonlinear ordinary differential equations with nonlinear boundary conditions using higher order Chebyshev spectral collocation method. Spectral methods are proven to offer a superior intrinsic accuracy for derivative calculations.
Originality/value
To the best of the authors' knowledge, no such analysis is available in the literature which can describe the heat transfer, MHD and slip effects simultaneously on the flows of the non‐Newtonian fluids.
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This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM).
Abstract
Purpose
This paper aims to study the two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the homotopy perturbation method (HPM).
Design/methodology/approach
The governing Navier–Stokes equations of the flow are reduced to a third-order nonlinear ordinary differential equation by a suitable similarity transformation. Analytic solution of the resulting differential equation is obtained using the HPM. Mathematica software is used to visualize the flow behavior. The effects of the various parameters on velocity field are analyzed through appropriate graphs.
Findings
It is found that x component of the velocity increases with the increase of the Hartman number when the transverse direction variable ranges from 0 to 0.2 and the reverse behavior is observed when transverse direction variable takes values between 0.2 and 0.5. It is noted that the y component of the velocity increases rapidly with the increase of the transverse direction variable. The y component of the velocity increases marginally with the increase of the Hartman number M. The effect of the Reynolds number R on the x and y components of the velocity is quite opposite to the effect of the Hartman number on the x and y components of the velocity and the effect of the parameter on the x and y components of the velocity is similar to that of the Reynolds number.
Originality/value
To the best of the author’s knowledge, nobody had tried before two-dimensional steady magneto-hydrodynamic flow of a second-grade fluid in a porous channel using the HPM.
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E. Momoniat and C. Harley
The purpose of this paper is to obtain numerical solutions of a two‐dimensional mixed space‐time PDE modelling the flow of a second‐grade.
Abstract
Purpose
The purpose of this paper is to obtain numerical solutions of a two‐dimensional mixed space‐time PDE modelling the flow of a second‐grade.
Design/methodology/approach
The paper derives conditionally stable Crank‐Nicolson schemes to solve both the one and two dimensional mixed‐space time PDE. For the two‐dimensional case we implement the Crank‐Nicolson scheme using a Peaceman‐Rachford ADI scheme.
Findings
For zero‐shear boundaries the Cattanneo representation of the model equation blows up whilst the representation derived by Rajagopal is stable and produces solutions which decay over time.
Originality/value
The use of a Peaceman‐Rachford ADI scheme to solve a mixed space‐time PDE is both novel and new.
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Mohamed Kezzar, Nabil Talbi, Saeed Dinarvand, Sanatan Das, Mohamed Rafik Sari, Samia Nasr and Ali Akhlaghi Mozaffar
This paper aims to model and analyze Jeffery Hamel’s channel flow with the magnetohydrodynamics second-grade hybrid nanofluid. Considering the importance of studying the velocity…
Abstract
Purpose
This paper aims to model and analyze Jeffery Hamel’s channel flow with the magnetohydrodynamics second-grade hybrid nanofluid. Considering the importance of studying the velocity slip and temperature jump in the boundary conditions of the flow, which leads to results close to reality, this paper intends to analyze the mentioned topic in the convergent and divergent channels that have significant applications.
Design/methodology/approach
The examination is conducted on a EG-H_2 O <30%–70%> base fluid that contains hybrid nanoparticles (i.e. SWCNT-MWCNT). To ensure comprehensive results, this study also considers the effects of thermal radiation, thermal sink/source, rotating convergent-divergent channels and magnetic fields. Initially, the governing equations are formulated in cylindrical coordinates and then simplified to ordinary differential equations through appropriate transformations. These equations are solved using the Explicit Runge–Kutta numerical method, and the results are compared with previous studies for validation.
Findings
After the validation, the effect of the governing parameters on the temperature and velocity of the second-grade hybrid nanofluid has been investigated by means of various and comprehensive contours. In the following, the issue of entropy generation and its related graphical results for this problem is presented. The mentioned contours and graphs accurately display the influence of problem parameters, including velocity slip and temperature jump. Besides, when thermal radiation is introduced (Rd = +0.1 and Rd = +0.2), entropy generation in convergent-divergent channels decreases by 7% and 14%, respectively, compared to conditions without thermal radiation (Rd = 0). Conversely, increasing the thermal sink/source from 0 to 4 leads to an 8% increase in entropy generation at Q = 2 and a 17% increase at Q = 4 in both types of channels. The details of the analysis of contours and the entropy generation results are fully mentioned in the body of the paper.
Originality/value
There are many studies on convergent and divergent channels, but this study comprehensively investigates the effects of velocity slip and temperature jump and certainly, this geometry with the specifications presented in this paper has not been explored before. Among the other distinctive features of this paper compared to previous works, the authors can mention the presentation of velocity and temperature results in the form of contours, which makes the physical analysis of the problem simpler.
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