scholarly journals Unsteady Transport Phenomena of Hybrid Al2O3-Cu/H2O Nanofluid Past a Shrinking Slender Cylinder

2021 ◽  
Vol 50 (12) ◽  
pp. 3753-3764
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Theoretical Investigations ◽  
Suitable Form ◽  
Layer Flow

Theoretical investigations of unsteady boundary layer flow gain interest due to its relatability to practical settings. Thus, this study proposes a unique mathematical model of the unsteady flow and heat transfer in hybrid nanofluid past a permeable shrinking slender cylinder. The suitable form of similarity transformations is adapted to simplify the complex partial differential equations into a solvable form of ordinary differential equations. A built-in bvp4c function in MATLAB software is exercised to elucidate the numerical analysis for certain concerning parameters, including the unsteadiness and curvature parameters. The bvp4c procedure is excellent in providing more than one solution once sufficient predictions are visible. The present analysis further observed dual solutions that exist in the system of equations. Notable findings showed that by increasing the nanoparticles volume fraction, the skin friction coefficient increases in accordance with the heat transfer rate. In contrast, the decline of the unsteadiness parameter demonstrates a downward trend toward the heat transfer performance.

scholarly journals Inclusion of Viscous Dissipation on the Boundary Layer Flow of Cu-TiO2 Hybrid Nanofluid over Stretching/Shrinking Sheet

2021 ◽  
Vol 88 (2) ◽  
pp. 64-79
Author(s):  
Yap Bing Kho ◽  
Rahimah Jusoh ◽  
Mohd Zuki Salleh ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Boundary Layer Flow ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Suction Parameter ◽  
Similarity Transformations ◽  
Layer Flow

The effects of viscous dissipation on the boundary layer flow of hybrid nanofluids have been investigated. This study presents the mathematical modelling of steady two dimensional boundary layer flow of Cu-TiO2 hybrid nanofluid. In this research, the surface of the model is stretched and shrunk at the specific values of stretching/shrinking parameter. The governing partial differential equations of the hybrid nanofluid are reduced to the ordinary differential equations with the employment of the appropriate similarity transformations. Then, Matlab software is used to generate the numerical and graphical results by implementing the bvp4c function. Subsequently, dual solutions are acquired through the exact guessing values. It is observed that the second solution adhere to less stableness than first solution after performing the stability analysis test. The existence of viscous dissipation in this model is dramatically brought down the rate of heat transfer. Besides, the effects of the suction and nanoparticles concentration also have been highlighted. An increment in the suction parameter enhances the magnitude of the reduced skin friction coefficient while the augmentation of concentration of copper and titanium oxide nanoparticles show different modes.

scholarly journals Magnetohydrodynamic Flow Past a Nonlinear Stretching or Shrinking Cylinder in Nanofluid with Viscous Dissipation and Heat Generation Effect

2021 ◽  
Vol 90 (1) ◽  
pp. 102-114
Author(s):  
Mahani Ahmad Kardri ◽  
Norfifah Bachok ◽  
Norihan Md. Arifin ◽  
Fadzilah Md. Ali ◽  
Yong Faezah Rahim
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Flow And Heat Transfer ◽  
Controlling Parameter ◽  
Numerical Computing ◽  
Nonlinear Stretching

The Tiwari-Das model is used to investigate magnetohydrodynamic stagnation point flow and heat transfer past a nonlinear stretching or shrinking cylinder in nanofluid with viscous dissipation and heat generation using. The partial differential equations, also known as governing equations, were reduced to nonlinear ordinary differential equations using similarity transformation. MATLAB with the bvp4c solver is used for numerical computing. The controlling parameter, such as nanoparticle volume fraction, magnetic, curvature, nonlinear, radiation, and heat generation parameters, as well as Eckert and Grashof numbers, influence the skin friction coefficient, heat transfer rate, velocity, and temperature profiles. The results are presented as graphs to show the influence of the variables studied. In some circumstances of stretching and shrinking cases, dual solutions can be obtained.

scholarly journals The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
D. R. V. S. R. K. Sastry ◽  
A. S. N. Murti ◽  
T. Poorna Kantha
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Boundary Layer ◽  
Similarity Transformations ◽  
Layer Flow

The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.

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.

Melting heat transfer in boundary layer stagnation-point flow of a nanofluid towards a stretching–shrinking sheet

2014 ◽  
Vol 92 (12) ◽  
pp. 1703-1708 ◽  
Author(s):  
Kishore Kumar Ch. ◽  
Shankar Bandari
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Skin Friction Coefficient ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Shooting Technique ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Fourth Order Method

The present analysis deals with the study of two-dimensional stagnation-point flow and heat transfer from a warm, laminar liquid flow of a nanofluid towards a melting stretching sheet. Using similarity transformations, the governing differential equations were transformed into coupled, nonlinear ordinary differential equations, which were then solved numerically by using the Runge–Kutta fourth-order method along with the shooting technique for two types of nanoparticles namely copper (Cu) and silver (Ag) in the water-based fluid with Prandtl number Pr = 6.2, the skin friction coefficient, the local Nusselt number, the velocity and the temperature profiles are presented graphically and discussed.

scholarly journals MHD boundary layer flow and heat transfer characteristics of a nanofluid over a stretching sheet

2017 ◽  
Vol 9 (1) ◽  
pp. 140-161 ◽  
Author(s):  
M. Ferdows ◽  
Md. Shakhaoath Khan ◽  
Md. Mahmud Alam ◽  
A. A. Afify
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Iteration Scheme ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Mhd Boundary Layer ◽  
Layer Flow ◽  
Mhd Boundary Layer Flow

AbstractThe study of radiative heat transfer in a nanofluid with the influence of magnetic field over a stretching surface is investigated numerically. Physical mechanisms responsible for magnetic parameter, radiation parameter between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. The parameters for Prandtl numberPr, Eckert numberEc, Lewis numberLe, stretching parameterb/aand constant parametermare examined. The governing partial differential equations were converted into nonlinear ordinary differential equations by using a suitable similarity transformation, which are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration scheme. The accuracy of the numerical method is tested by performing various comparisons with previously published work and the results are found to be in excellent agreement. Numerical results for velocity, temperature and concentration distributions as well as skin-friction coefficient, Nusselt number and Sherwood number are discussed at the sheet for various values of physical parameters.

scholarly journals Similarity Solution of Marangoni Convection Boundary Layer Flow over a Flat Surface in a Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Norihan Md. Arifin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Convection Boundary Layer ◽  
Flow And Heat Transfer ◽  
Different Types ◽  
Layer Flow

The problem of steady Marangoni boundary layer flow and heat transfer over a flat plate in a nanofluid is studied using different types of nanoparticles. The general governing partial differential equations are transformed into a set of two nonlinear ordinary differential equations using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta-Fehlberg (RKF) method. Three different types of nanoparticles are considered, namely, Cu, Al2O3, and TiO2, by using water as a base fluid with Prandtl numberPr=6.2. The effects of the nanoparticle volume fractionϕand the constant exponentmon the flow and heat transfer characteristics are obtained and discussed.

Buoyancy Effect on MHD Slip Flow and Heat Transfer of a Nanofluid Flow Over a Vertical Porous Plate

2020 ◽  
Vol 4 (1) ◽  
pp. 1-16
Author(s):  
Fayyaz Hussain ◽  
Sohaib Abdal ◽  
Zameer Abbas ◽  
Nasir Hussain ◽  
Muhammad Adnan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Slip Flow ◽  
Porous Plate ◽  
Lewis Number ◽  
Similarity Transformations ◽  
Flow And Heat Transfer ◽  
Layer Flow ◽  
Blowing Parameter ◽  
Convection Parameter

This study investigated the boundary layer flow and heat transfer aspects of a nanofluid over a porous plate with thermal radiation.Using suitable similarity transformations,partial differential equations were converted into ordinary differential equations and then solved numerically with the help of the Runge-Kutta scheme. The effects of various parameters were analyzed such as Prandtl number 𝑃𝑟, Lewis number 𝐿𝑒, Thermophoresis 𝑁𝑡, Mixed convection parameter λ,Brownianmotion 𝑁𝑏, Magnetic parameter M, and Suction/Blowing parameter S. The results were depicted with the help of graphs.

scholarly journals Flow and heat transfer past a permeable stretching/shrinking sheet in Cu−Al2O3/water hybrid nanofluid

2019 ◽  
Vol 30 (3) ◽  
pp. 1197-1222 ◽  
Author(s):  
Rusya Iryanti Yahaya ◽  
Norihan M. Arifin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
The Other ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to study the flow and heat transfer of a hybrid nanofluid, Cu–Al2O3/water, past a permeable stretching/shrinking sheet. The effects of Brownian motion and thermophoresis are considered here. Design/methodology/approach Similarity transformations are used to reduce the governing partial differential equations to a system of ordinary (similarity) differential equations. A MATLAB solver called the bvp4c is then used to compute the numerical solutions of equations (12) to (14) subject to the boundary conditions of equation (15). Then, the effects of various physical parameters on the flow and thermal fields of the hybrid nanofluid are analyzed. Findings Multiple (dual) solutions are found for the basic boundary layer equations. A stability analysis is performed to see which solutions are stable and, therefore, applicable in practice and which are not stable. Besides that, a comparison is made between the hybrid nanofluid and a traditional nanofluid, Cu/water. The skin friction coefficient and Nusselt number of the hybrid nanofluid are found to be greater than that of the other nanofluid. Thus, the hybrid nanofluid has a higher heat transfer rate than the other nanofluid. However, the increase in the shrinking parameter reduces the velocity of the hybrid nanofluid. Originality/value The present results are original and new for the study of the flow and heat transfer past a permeable stretching/shrinking sheet in Cu–Al2O3/water hybrid nanofluid.

scholarly journals Analytical Study of Heat Transfer of a Unsteady Newtonian Nanofluid Flow Problem

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Shooting Technique ◽  
Flow And Heat Transfer ◽  
Transfer Behavior ◽  
Basic Equations ◽  
Squeeze Number

Heat transfer behavior of unsteady flow of squeezing nanofluid (Copper+water) between two parallel plates is investigated. By using the appropriate transformation for the velocity and temperature, the basic equations governing the flow and heat transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy Perturbation Method and numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity and temperature for various values of relevant parameters are illustrated graphically. The skin-friction coefficient, heat transfer and Nusselt number rate are also tabulated for various governing parameters. The results indicate that, for nanofluid flow, the rates of heat transfer and velocity had direct relationship with squeeze number and nanoparticle volume fraction they are also a decreasing function of those parameters

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