scholarly journals Convective Heat Transfer of a Hybrid Nanofluid over a Nonlinearly Stretching Surface with Radiation Effect

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2220
Author(s):  
Emad H. Aly ◽  
Alin V. Roşca ◽  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Radiation Effect ◽  
Numerical Technique ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Temperature Parameter ◽  
Nonlinearly Stretching Surface

The flow of the hybrid nanofluid (copper–titanium dioxide/water) over a nonlinearly stretching surface was studied with suction and radiation effect. The governing partial differential equations were then converted into non-linear ordinary differential equations by using proper similarity transformations. Therefore, these equations were solved by applying a numerical technique, namely Chebyshev pseudo spectral differentiation matrix. The results of the flow field, temperature distribution, reduced skin friction coefficient and reduced Nusselt number were deduced. It was found that the rising of the mass flux parameter slows down the velocity and, hence, decreases the temperature. Further, on enlarging the stretching parameter, the velocity and temperature increases and decreases, respectively. In addition, it was mentioned that the radiation parameter can effectively control the thermal boundary layer. Finally, the temperature decreases when the values of the temperature parameter increases.

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.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

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.

Radiative and Viscous Ohmic Dissipation on MHD Tangent Hyperbolic Fluid over a Convectively Heated Sheet in a Suspension of Dust Particles

2018 ◽  
Vol 16 ◽  
pp. 177-190 ◽  
Author(s):  
S.U. Mamatha ◽  
Chakravarthula S.K. Raju ◽  
Mahesha ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Ohmic Heating ◽  
Skin Friction Coefficient ◽  
Dust Particles ◽  
Stretching Surface ◽  
Ohmic Dissipation ◽  
Transfer Rates ◽  
Similarity Transformations ◽  
Tangent Hyperbolic Fluid

The present study deals with steady incompressible magneto hydrodynamic hyperbolic tangent fluid flow induced by a convectively heated stretching surface with the suspension of dust particles, Darcy-Forchheimer, thermal radiation, viscous dissipation and Ohmic heating. Similarity transformations were used to convert partial differential equations (PDEs) to a system of nonlinear ordinary differential equations (NODEs) which are solved numerically by Runge-Kutta Fehlberg method. The effect of pertinent parameters on velocity and temperature profiles of both fluid and dust phase within the boundary layer has been studied by considering various values of controlling parameters. Additionally, the skin friction coefficient and reduced heat transfer coefficient have been examined for various values of the governing parameters. It is found that Hartmann number and Forchheimer parameter reduce friction factor and heat transfer rates.

Scrutinization of Chemical Reaction Effect on Flow and Mass Transfer of Prandtl Liquid over a Riga Plate in the Presence of Solutal Slip Effect

2018 ◽  
Vol 16 (8) ◽  
Author(s):  
B.J. Gireesha ◽  
K. Ganesh Kumar ◽  
B.C. Prasannakumar
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Layer Thickness ◽  
Chemical Reaction ◽  
Boundary Layer Thickness ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Riga Plate

AbstractIn the present paper focused on flow and mass transfer of Prandtl fluid over a Riga plate. The effects of chemical reaction and solutal slip are taken into the account. The governing partial differential equations are reduced into a set of coupled non linear ordinary differential equations using suitable similarity transformations. These equations are then solved using Runge-Kutta-Fehlberg-45 method. Behaviour of emerging parameters are presented graphically and discussed for velocity and concentration distribution. Numerical values of reduced skin friction coefficient and Sherwood number are shown in table and are discussed. From the plotted results it can be observed that the solutal boundary layer thickness decreases for larger values of chemical reaction parameter and Schmidt number. Also, momentum boundary layer thickness rise with stronger modified Hartman number.

Slip Effects on Flow and Heat Transfer of a Non-Newtonian Fluid on a Stretching Surface with Thermal Radiation

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Mostafa Abd El-Hameed Mahmoud
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction Coefficient ◽  
Local Similarity ◽  
Radiation Parameter ◽  
Slip Parameter ◽  
Stretching Surface ◽  
Local Skin ◽  
Linear Ordinary Differential Equations ◽  
Flow And Heat Transfer

An analysis is carried out to study the flow and heat transfer characteristics of a non-Newtonian power-law fluid over a stretching surface in the presence of radiation and slip condition at the surface. The local similarity solution is used to transform the system of partial differential equations, describing the problem, into a system of highly coupled non-linear ordinary differential equations. The transformed system of equations is solved numerically using the fourth order Runge-Kutta method coupled with the shooting technique. The effects of the radiation parameter and the slip parameter on both the flow and the heat transfer are investigated and discussed. Also, it is found that the local skin-friction coefficient decreases as the slip parameter increases. However, it is found that increasing the slip parameter or the radiation parameter has the effect of decreasing the local Nusselt number.

scholarly journals Viscous Dissipation and Suction characteristics of Heat and Mass Transfer past a Stretching Sheet.

2021 ◽  
Vol 12 (1S) ◽  
pp. 623-630
Author(s):  
AlfunsaPrathiba, Et. al.
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Viscous Dissipation ◽  
Schmidt Number ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Skin Friction Coefficient ◽  
Linear Ordinary Differential Equations ◽  
Similarity Transformations

in this paper, we analyzed the effect of a suction and Soret number on heat and mass transfer Magneto Hydrodynamics (MHD) flow past an exponentially stretching sheet with the heat source/sink. Appropriate similarity transformations were employed to convert the governing partial differential equations to a set of highly non-linear ordinary differential equations, which was then solved numerically by Runga kutta sixth order method together with shooting technique. The Numerical results are obtained for the skin friction coefficient, Nusselt and Sherwood numbers for selected values of the governing parameters, such as the suction, magnetic field parameter  , viscous dissipation parameter  , heat generation parameter  , Schmidt number  , and the chemical reaction rate parameter  . Besides, it is obtained that the concentration profile decreases with an increment of the Schmidt number. A comparison was made with a previous study available in the literature and we found that it is in a good agreement.

scholarly journals Approximate Analytical Analysis of Unsteady MHD Mixed Flow of Non-Newtonian Hybrid Nanofluid over a Stretching Surface

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 138
Author(s):  
Ali Rehman ◽  
Zabidin Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Base Fluid ◽  
Research Work ◽  
Hybrid Nanofluid ◽  
Stretching Surface ◽  
Optimal Homotopy Analysis Method ◽  
Analytical Analysis ◽  
Transfer Ratio ◽  
The Impact

This paper analyses the two-dimensional unsteady and incompressible flow of a non-Newtonian hybrid nanofluid over a stretching surface. The nanofluid formulated in the present study is TiO2 + Ag + blood, and TiO2 + blood, where in this combination TiO2 + blood is the base fluid and TiO2 + Ag + blood represents the hybrid nanofluid. The aim of the present research work is to improve the heat transfer ratio because the heat transfer ratio of the hybrid nanofluid is higher than that of the base fluid. The novelty of the recent work is the approximate analytical analysis of the magnetohydrodynamics mixed non-Newtonian hybrid nanofluid over a stretching surface. This type of combination, where TiO2+blood is the base fluid and TiO2 + Ag + blood is the hybrid nanofluid, is studied for the first time in the literature. The fundamental partial differential equations are transformed to a set of nonlinear ordinary differential equations with the guide of some appropriate similarity transformations. The analytical approximate method, namely the optimal homotopy analysis method (OHAM), is used for the approximate analytical solution. The convergence of the OHAM for particular problems is also discussed. The impact of the magnetic parameter, dynamic viscosity parameter, stretching surface parameter and Prandtl number is interpreted through graphs. The skin friction coefficient and Nusselt number are explained in table form. The present work is found to be in very good agreement with those published earlier.

Slip flow over a non-Newtonian fluid through a Darcy–Forchheimer medium: Numerical approach

2019 ◽  
Vol 33 (35) ◽  
pp. 1950448
Author(s):  
K. Ganesh Kumar ◽  
M. N. Khan ◽  
M. Osman ◽  
Abdulaziz R. Alharbi ◽  
Mohammad Rahimi-Gorji ◽  
...  
Keyword(s):  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Slip Flow ◽  
Convective Boundary Condition ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Convective Boundary ◽  
Nusselt Numbers ◽  
Similarity Transformations ◽  
Liquid Suspension

This work focused on slip flow over a non-Newtonian nanofluid fluid flow past a stretching sheet with particles–liquid suspension. The convective boundary condition is taken into account. Similarity transformations are utilized to reduce the nonlinear partial differential equations into a set of nonlinear ordinary differential equations. Runge–Kutta–Fehlberg scheme is used to get the numerical solution. Important parameters are analyzed through graphs and skin friction coefficient. Nusselt numbers are presented in tables. Investigation reveals that slip parameter decreases the velocity field and Biot number increases the temperature field.

scholarly journals Heat Transfer Enhancement by Coupling of Carbon Nanotubes and SiO2 Nanofluids: A Numerical Approach

Processes ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 937 ◽  
Author(s):  
Fitnat Saba ◽  
Saima Noor ◽  
Naveed Ahmed ◽  
Umar Khan ◽  
Syed Tauseef Mohyud-Din ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Three Dimensional ◽  
Numerical Approach ◽  
Skin Friction Coefficient ◽  
Squeezing Flow ◽  
Hybrid Nanofluid ◽  
Governing Equations ◽  
Similarity Transformations ◽  
Rotating Channel

This article comprises the study of three-dimensional squeezing flow of (CNT-SiO2/H2O) hybrid nanofluid. The flow is confined inside a rotating channel whose lower wall is stretchable as well as permeable. Heat transfer with viscous dissipation is a main subject of interest. We have analyzed mathematically the benefits of hybridizing SiO 2 -based nanofluid with carbon nanotubes ( CNTs ) nanoparticles. To describe the effective thermal conductivity of the CNTs -based nanofluid, a renovated Hamilton–Crosser model (RHCM) has been employed. This model is an extension of Hamilton and Crosser’s model because it also incorporates the effect of the interfacial layer. For the present flow scenario, the governing equations (after the implementation of similarity transformations) results in a set of ordinary differential equations (ODEs). We have solved that system of ODEs, coupled with suitable boundary conditions (BCs), by implementing a newly proposed modified Hermite wavelet method (MHWM). The credibility of the proposed algorithm has been ensured by comparing the procured results with the result obtained by the Runge-Kutta-Fehlberg solution. Moreover, graphical assistance has also been provided to inspect the significance of various embedded parameters on the temperature and velocity profile. The expression for the local Nusselt number and the skin friction coefficient were also derived, and their influential behavior has been briefly discussed.

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