scholarly journals Hybrid Nanofluids Flows Determined by a Permeable Power-Law Stretching/Shrinking Sheet Modulated by Orthogonal Surface Shear

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 813
Author(s):  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Shrinking Sheet ◽  
Surface Shear ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Shrinking Surface ◽  
Orthogonal Surface

The present paper studies the flow and heat transfer of the hybrid nanofluids flows induced by a permeable power-law stretching/shrinking surface modulated orthogonal surface shear. The governing partial differential equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved applying a numerical technique, namely bvp4c solver in MATLAB. Results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that increasing mass flux parameter slows down the velocity and, hence, decreases the temperature. Furthermore, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases. We apply similarity transformation in order to transform the governing model into a system of ODEs (ordinary differential equations). Numerical solutions for particular values of involved parameters are in very good agreement with previous calculations. The most important and interesting result of this paper is that for both the cases of shrinking and stretching sheet flows exhibit dual solutions in some intervals of the shrinking and stretching parameter. In spite of numerous published papers on the flow and heat transfer over a permeable stretching/shrinking surface in nanofluids and hybrid nanofluids, none of the researchers studied the present problem. Therefore, we believe that the results of the present paper are new, and have many industrial applications.

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals Homann Stagnation Point Flow and Heat Transfer of Hybrid Nanofluids Over a Permeable Radially Stretching/Shrinking Sheet

2021 ◽  
Vol 85 (1) ◽  
pp. 101-112
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Mohd Hisyam Ariff ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Nanoparticle Volume Fraction ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Water Base

The steady two-dimensional Homan stagnation point flow and heat transfer of water base hybrid nanofluids (Al2O3 & Cu) over a permeable radially stretching/shrinking sheet have been studied. The similarity variables are introduced to transform the partial differential equations of the model into the ordinary differential equations. Numerical findings and dual solutions have been carried out by implementing the bvp4c code through MATLAB software. The most prominent effect is illustrated in the boundary layer thickness where the velocity profile increases upon the increment of the suction intensity but decreases in the temperature profile. Besides, the reduced Nusselt number also decreases as enlarging the value of copper and alumina nanoparticle volume fraction. The analysis of the first and second solutions are presented graphically with critical values as well as the detail discussions on the effects of the other involving parameters.

scholarly journals Flow and Heat Transfer Past a Stretching/Shrinking Sheet Using Modified Buongiorno Nanoliquid Model

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3047
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Emad H. Aly ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids ◽  
Layer Flow ◽  
Shrinking Surface

This paper studies the boundary layer flow and heat transfer characteristics past a permeable isothermal stretching/shrinking surface using both nanofluid and hybrid nanofluid flows (called modified Buongiorno nonliquid model). Using appropriate similarity variables, the PDEs are transformed into ODEs to be solved numerically using the function bvp4c from MATLAB. It was found that the solutions of the resulting system have two branches, upper and lower branch solutions, in a certain range of the suction, stretching/shrinking and hybrid nanofluids parameters. Both the analytic and numerical results are obtained for the skin friction coefficient, local Nusselt number, and velocity and temperature distributions, for several values of the governing parameters. It results in the governing parameters considerably affecting the flow and heat transfer characteristics.

scholarly journals Magneto-Hydro Dynamic Flow and Heat Transfer of Nonnewtonian Power-Law Fluid Over a Non-Linear Stretching Surface with Viscous Dissipation

2014 ◽  
Vol 19 (2) ◽  
pp. 259-273 ◽  
Author(s):  
N. Kishan ◽  
P. Kavitha
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Power Law ◽  
Transverse Magnetic ◽  
Stretching Surface ◽  
Power Law Fluid ◽  
Flow And Heat Transfer ◽  
Non Linear

Abstract A fluid flow and heat transfer analysis of an electrically conducting non-Newtonian power law fluid flowing over a non-linear stretching surface in the presence of a transverse magnetic field taking into consideration viscous dissipation effects is investigated. The stretching velocity, the temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The flow is induced due to an infinite elastic sheet which is stretched in its own plane. The governing equations are reduced to non-linear ordinary differential equations by means of similarity transformations. By using quasi-linearization techniques first linearize the non linear momentum equation is linearized and then the coupled ordinary differential equations are solved numerically by an implicit finite difference scheme. The numerical solution is found to be dependent on several governing parameters, including the magnetic field parameter, power-law index, Eckert number, velocity exponent parameter, temperature exponent parameter, modified Prandtl number and heat source/sink parameter. A systematic study is carried out to illustrate the effects of these parameters on the fluid velocity and the temperature distribution in the boundary layer. The results for the local skin-friction coefficient and the local Nusselt number are tabulated and discussed.

scholarly journals Numerical Study of (Au-Cu)/Water and (Au-Cu)/Ethylene Glycol Hybrid Nanofluids Flow and Heat Transfer over a Stretching Porous Plate

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8341
Author(s):  
Umair Rashid ◽  
Azhar Iqbal ◽  
Abdullah Alsharif
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ethylene Glycol ◽  
Ordinary Differential Equations ◽  
Porous Plate ◽  
Graphical Form ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Flow And Heat Transfer ◽  
Hybrid Nanofluids

The purpose of the study is to investigate the (Au-Cu)/Water and (Au-Cu)/Ethylene glycol hybrid nanofluids flow and heat transfer through a linear stretching porous plate with the effects of thermal radiation, ohmic heating, and viscous dissipation. Similarity transformations technique is used to transform a governing system of partial differential equations into ordinary differential equations. The NDSolve Mathematica program is used to solve the nonlinear ordinary differential equations. Furthermore, the results are compared with the results of homotopy analysis method. The impacts of relevant physical parameters on velocity, temperature, and the Nusselt number are represented in graphical form. The key points indicate that the temperature of (Au-Cu)/water and (Au-Cu)/Ethylene glycol hybrid nanofluids is increased with the effects of Eckert number and magnetic field. The (Au-Cu)/Ethylene glycol hybrid nanofluid also has a greater rate of heat transfer than (Au-Cu)/Water hybrid nanofluid.

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.

Unsteady separated stagnation-point flow and heat transfer past a stretching/shrinking sheet in a copper-water nanofluid

2019 ◽  
Vol 29 (8) ◽  
pp. 2588-2605 ◽  
Author(s):  
Natalia C. Roşca ◽  
Alin V. Roşca ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stagnation Point ◽  
Design Methodology ◽  
Similarity Transformation ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer

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.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

scholarly journals Unsteady flow and heat transfer over a permeable stretching/shrinking sheet with generalized slip velocity

2018 ◽  
Vol 28 (6) ◽  
pp. 1457-1470 ◽  
Author(s):  
Mohd Ezad Hafidz Hafidzuddin ◽  
Roslinda Nazar ◽  
Norihan M. Arifin ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Unsteady Flow ◽  
Slip Velocity ◽  
Shrinking Sheet ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Polymer Sheets ◽  
Branch Solution ◽  
Layer Flow

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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