Nur Syahirah Wahid, Norihan Md Arifin, Najiyah Safwa Khashi'ie, Ioan Pop, Norfifah Bachok and Ezad Hafidz Hafidzuddin
The purpose of this paper is to numerically investigate the hybrid nanofluid flow with the imposition of magnetohydrodynamic (MHD) and radiation effects alongside the convective…
Abstract
Purpose
The purpose of this paper is to numerically investigate the hybrid nanofluid flow with the imposition of magnetohydrodynamic (MHD) and radiation effects alongside the convective boundary conditions over a permeable stretching/shrinking surface.
Design/methodology/approach
The mathematical model is formulated in the form of partial differential equations (PDEs) and are then transformed into the form of ordinary differential equations (ODEs) by using the similarity variables. The deriving ODEs are solved numerically by using the bvp4c solver in MATLAB software. Stability analysis also has been performed to determine the stable solution among the dual solutions obtain. For method validation purposes, a comparison of numerical results has been made with the previous studies.
Findings
The flow and the heat transfer of the fluid at the boundary layer are described through the plot of the velocity profile, temperature profile, skin friction coefficient and local Nusselt number that are presented graphically. Dual solutions are obtained, but only the first solution is stable. For the realizable solution at the shrinking surface, the proliferation of nanoparticle volume fraction (copper) and magnetic (magnetohydrodynamics) parameters can impede the boundary layer separation. Also, Biot number could enhance the temperature profile and the heat transfer rate at the shrinking surface region. The incrementation of 0.1% of Biot number has enhanced the heat transfer rate by approximately 0.1% and the incrementation of 0.5% volume fraction for copper has reduced the heat transfer rate by approximately 0.17%.
Originality/value
The presented model and numerical results are original and new. It can be used as a future reference for further investigation and related practical application. The main contribution of this investigation includes giving the initial prediction and providing the numerical data for the other researchers for their future reference regarding the impacts of nanoparticles volumetric concentration towards the main physical quantities of interest in the presence of magnetic and radiation parameters with the convective boundary conditions.
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Najiyah Safwa Khashi’ie, Norihan Md Arifin, Ioan Pop, Roslinda Nazar, Ezad Hafidz Hafidzuddin and Nadihah Wahi
This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat…
Abstract
Purpose
This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat plate.
Design/methodology/approach
The similarity transformation which fulfils the continuity equation is opted to transform the coupled momentum and energy equations into the nonlinear ordinary differential equations. Numerical solutions which are elucidated in the tables and graphs are obtained using the bvp4c solver.
Findings
Non-unique solutions (first and second) are feasible for both stretching and shrinking cases within the specific values of the parameters. First solution is the physical/real solution based on the execution of stability analysis. An upsurge of the ratio of the ambient fluid strain rate to the plate strain rate can delay the boundary layer separation, whereas a boost of the ratio of the ambient fluid shear rate to the plate strain rate only accelerates the separation of boundary layer. The heat transfer rate of hybrid nanofluid is greater for the stretching case than the shrinking case. However, for the shrinking case, the heat transfer rate intensifies with the increment of the copper (Cu) nanoparticles volume fraction, whereas a contrary result is found for the stretching case.
Originality/value
The present numerical results are original and new. It can contribute to other researchers on electing the relevant parameters to optimize the heat transfer process in the modern industry, and the right parameters to generate non-unique solution so that no misjudgment on flow and heat transfer features.
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Mohd Ezad Hafidz Hafidzuddin, Roslinda Nazar, Norihan M. Arifin and Ioan Pop
This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized slip…
Abstract
Purpose
This study aims to investigate the unsteady two-dimensional viscous flow and heat transfer over an unsteady permeable stretching/shrinking sheet (surface) with generalized slip velocity condition.
Design/methodology/approach
Similarity transformation is used to reduce the system of partial differential equations into a system of nonlinear ordinary differential equations. The resulting equations are then solved numerically using “bvp4c” function in MATLAB software.
Findings
Dual solutions are found for a certain range of the unsteady, suction and stretching/shrinking parameters. Stability analysis is performed, and it is revealed that the first (upper branch) solution is stable and physically realizable, whereas the second (lower branch) solution is unstable.
Practical implications
The results obtained can be used to explain the characteristics and applications of the generalized slip in boundary layer flow. Such condition is applied for particulate fluids such as foams, emulsions, polymer solutions and suspensions. Furthermore, the phenomenon of stretching/shrinking sheet can be found on the manufacturing of polymer sheets, rising and shrinking balloon or moving and shrinking polymer film.
Originality/value
The present numerical results are original and new for the study of unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity.
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Najiyah Safwa Khashi'ie, Norihan M. Arifin, Ioan Pop, Roslinda Nazar and Ezad Hafidz Hafidzuddin
The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water…
Abstract
Purpose
The purpose of this study is to implement a new class of similarity transformation in analyzing the three-dimensional boundary layer flow of hybrid nanofluid. The Cu-Al2O3/water hybrid nanofluid is formulated using the single-phase nanofluid model with modified thermophysical properties.
Design/methodology/approach
The governing partial differential equations are reduced to the ordinary (similarity) differential equations using the proposed similarity transformation. The resulting equations are programmed in Matlab software through the bvp4c solver to obtain their solutions. The features of the reduced skin frictions and the velocity profiles for different values of the physical parameters are analyzed and discussed.
Findings
The non-uniqueness of the solutions is observed for certain physical parameters. The dual solutions are perceived for both permeable and impermeable cases and being the main agenda of the work. The execution of stability analysis proves that the first solution is undoubtedly stable than the second solution. An increase in the mass transpiration parameter leads to the uniqueness of the solution. Oppositely, as the injection parameter increase, the two solutions remain. However, no separation point is detected in this problem within the considered parameter values. The present results are decisive to the pair of alumina and copper only.
Originality/value
The present findings are original and can benefit other researchers particularly in the field of fluid dynamics. This study can provide a different insight of the transformation that is applicable to reduce the complexity of the boundary layer equations.