scholarly journals Unsteady flow and heat transfer of Jeffrey fluid over a stretching sheet

2014 ◽  
Vol 18 (4) ◽  
pp. 1069-1078 ◽  
Author(s):  
Tasawar Hayat ◽  
Zahid Iqbal ◽  
Meraj Mustafa ◽  
Ahmed Alsaedi
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Analytic Solutions ◽  
Momentum Equation ◽  
Elastic Parameter ◽  
Deborah Number ◽  
Jeffrey Fluid ◽  
Dimensionless Energy ◽  
Flow And Heat Transfer

The boundary layer flow and heat transfer of an incompressible Jeffrey fluid have been investigated. The analytic solutions of the arising differential system have been computed by homotopy analysis method (HAM). The dimensionless expressions for wall shear stress and surface heat transfer are also derived. Exact solutions of the momentum equation and numerical solutions of the dimensionless energy equations have been obtained for the steady-state case. The results indicate an increase in the velocity and the boundary layer thickness by increasing the elastic parameter (Deborah number) for a Jeffrey fluid.

Flow and Heat Transfer of Jeffrey Fluid Over a Continuously Moving Surface With a Parallel Free Stream

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
T. Hayat ◽  
Z. Iqbal ◽  
M. Mustafa ◽  
S. Obaidat
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Layer Thickness ◽  
Boundary Layer Thickness ◽  
Free Stream ◽  
Deborah Number ◽  
Jeffrey Fluid ◽  
Stream Velocity ◽  
Moving Surface ◽  
Flow And Heat Transfer

This communication studies the flow and heat transfer characteristics over a continuously moving surface in the presence of a free stream velocity. The Jeffrey fluid is treated as a rheological model. The series expressions of velocity and temperature fields are constructed by applying the homotopy analysis method (HAM). The influence of emerging parameters such as local Deborah number (β), the ratio of relaxation and retardation times (λ2), the Prandtl number (Pr), and the Eckert number (Ec) on the velocity and temperature profiles are presented in the form of graphical and tabulated results for different values of λ. It is found that the boundary layer thickness is an increasing function of local Deborah number (β). However, the temperature and thermal boundary layer thickness decreases with the increasing values of local Deborah number (β).

scholarly journals UNSTEADY BOUNDARY LAYERS: CONVECTIVE HEAT TRANSFER OVER A VERTICAL FLAT PLATE

2009 ◽  
Vol 50 (4) ◽  
pp. 541-549 ◽  
Author(s):  
ROBERT A. VAN GORDER ◽  
K. VAJRAVELU
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Approximate Solutions ◽  
Shear Thinning ◽  
Momentum Equation ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Special Cases ◽  
Layer Flow

AbstractIn this paper, we extend the results in the literature for boundary layer flow over a horizontal plate, by considering the buoyancy force term in the momentum equation. Using a similarity transformation, we transform the partial differential equations of the problem into coupled nonlinear ordinary differential equations. We first analyse several special cases dealing with the properties of the exact and approximate solutions. Then, for the general problem, we construct series solutions for arbitrary values of the physical parameters. Furthermore, we obtain numerical solutions for several sets of values of the parameters. The numerical results thus obtained are presented through graphs and tables and the effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results obtained reveal many interesting behaviours that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress.

scholarly journals Dual Solutions in the Boundary Layer Flow and Heat Transfer in the Presence of Thermal Radiation with Suction Effect

2018 ◽  
Vol 7 (4.33) ◽  
pp. 17
Author(s):  
Siti Nur Aisyah Azeman ◽  
. .
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Boundary Layer Flow ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Shooting Technique ◽  
Flow And Heat Transfer ◽  
Layer Flow

The dual solutions in the boundary layer flow and heat transfer in the presence of thermal radiation is quantitatively studied. The governing partial differential equations are derived into a system of ordinary differential equations using a similarity transformation, and afterward numerical solution obtained by a shooting technique. Dual solutions execute within a certain range of opposing and assisting flow which related to these numerical solutions. The similarity equations have two branches, upper or lower branch solutions, within a certain range of the mixed convection parameters. Further numerical results exist in our observations which enable to discuss the features of the respective solutions.  

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.

scholarly journals Flow and heat transfer of aligned magnetic field with Newtonian heating boundary condition

2018 ◽  
Vol 189 ◽  
pp. 01005
Author(s):  
A R M Kasim ◽  
N S Arifin ◽  
S M Zokri ◽  
M Z Salleh
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Condition ◽  
Numerical Solutions ◽  
Newtonian Heating ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Flow And Heat Transfer ◽  
Aligned Magnetic Field

Influence of aligned magnetic field on the steady boundary layer flow and heat transfer over a stretching sheet with Newtonian heating boundary condition is considered. The transformed governing nonlinear boundary layer equations in the form of ordinary differential equations are solved numerically by Keller box method. The details on computation have been presented and elaborated. The obtained numerical solutions have been captured graphically in the form of velocity and temperature distributions for different values of aligned angle, magnetic field parameter, Prandtl number and conjugate parameter. It is found that, increases in aligned angle associated with magnetic field delayed the velocity profile of the flow and enhances the temperature profile.

scholarly journals Partial Slip Flow and Heat Transfer over a Stretching Sheet in a Nanofluid

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Rajesh Sharma ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Slip Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Partial Slip ◽  
Flow And Heat Transfer

The boundary layer flow and heat transfer of a nanofluid over a stretching sheet are numerically studied. Velocity slip is considered instead of no-slip condition at the boundary as is usually appears in the literature. The governing partial differential equations are transformed into ordinary ones using a similarity transformation, before being solved numerically. Numerical solutions of these equations are obtained using finite element method (FEM). The variations of velocity and temperature inside the boundary layer as well as the skin friction coefficient and the heat transfer rate at the surface for some values of the governing parameters, namely, the nanoparticle volume fraction and the slip parameter are presented graphically and discussed. Comparison with published results for the regular fluid is presented and it is found to be in excellent agreement.

scholarly journals Heat Transfer in Boundary Layer Magneto-Micropolar Fluids with Temperature-Dependent Material Properties over a Stretching Sheet

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Ephesus O. Fatunmbi ◽  
Samuel S. Okoya
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Material Properties ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Viscous Drag ◽  
Integration Scheme ◽  
Temperature Dependent ◽  
Flow And Heat Transfer ◽  
Reported Data

The process of heat transfer in boundary layer magneto-micropolar fluid with temperature-dependent material properties past a flat stretching sheet in a porous medium is investigated in this study. Two distinct cases of boundary heating conditions are analyzed for the heat transfer in this work, viz., prescribed surface temperature (PST) and prescribed heat flux (PHF). With the aid of similarity conversion analysis, the formulated equations of the flow and heat transfer have been translated into a system of nonlinear ordinary differential equations. Subsequently, Runge–Kutta–Fehlberg integration scheme in company of shooting techniques employed to obtain numerical solutions to the reduced equations. The findings are graphically illustrated and discussed in view of the two cases of boundary heating, while the results for the physical quantities of engineering concern are tabulated for various controlling parameters. In the limiting situations, the results generated are compared favourably with the earlier reported data in the literature, while the numerical solutions demonstrate a reduction in the rate of heat transfer Nux⋆ and the viscous drag Cf⋆ for both PST and PHF conditions with growth in the magnitude of material parameter K.

scholarly journals Marangoni Boundary Layer Flow and Heat Transfer of Graphene–Water Nanofluid with Particle Shape Effects

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1120
Author(s):  
Umair Rashid ◽  
Dumitru Baleanu ◽  
Haiyi Liang ◽  
Muhammad Abbas ◽  
Azhar Iqbal ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Numerical Solutions ◽  
Nanofluid Flow ◽  
Suction Parameter ◽  
Flow And Heat Transfer ◽  
Shaped Nanoparticles ◽  
Analytical Results ◽  
Shape Effects ◽  
Marangoni Boundary Layer

Graphene nanofluids have attracted the attention of many researchers because of a variety of remarkable properties such as extraordinary electronic transport properties, high thermal conductivity, and large specific surface areas. This paper investigates the shape effects of nanoparticles on the Marangoni boundary layer of graphene–water nanofluid flow and heat transfer over a porous medium under the influences of the suction parameter. The graphene–water nanofluid flow was contained with various shapes of nanoparticles, namely sphere, column, platelet, and lamina. The problem is modeled in form of partial differential equations (PDES) with boundary conditions. The governing transport equations are converted into dimensionless form with the help of some suitable nondimensional variables. The solution of the problem was found numerically using the NDSolve technique of Mathematica 10.3 software. In addition, the numerical solutions were also compared with analytical results. The homotopy analysis method (HAM) is used to calculate the analytical results. The results show that lamina-shaped nanoparticles have better performance on temperature distribution while sphere-shaped nanoparticles are more efficient for heat transfer than other shapes of nanoparticles.

scholarly journals Numerical Solutions for Convective Boundary Layer Flow of Micropolar Jeffrey Fluid with Prescribe Wall Temperature

2020 ◽  
Vol 26 (3) ◽  
pp. 286-298
Author(s):  
Noraihan Afiqah Rawi ◽  
Nor Athirah Mohd Zin ◽  
Asma Khalid ◽  
Abdul Rahman Mohd Kasim ◽  
Zaiton Mat Isa ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Differential Equations ◽  
Skin Friction ◽  
Convective Boundary Layer ◽  
Boundary Layer Flow ◽  
Deborah Number ◽  
Jeffrey Fluid ◽  
Convective Boundary ◽  
Layer Flow

The steady two dimensional convective boundary layer flow of micropolar Jeffrey fluid past a permeable stretching sheet is studied in this paper. The governing boundary layer equation in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. The effects of Prandtl number, Deborah number, and material parameter with the boundary condition for microrotation, n = 0 (strong concentration of microelements) on the velocity, microrotation, temperature profiles as well as the skin friction and heat transfer coefficients are presented and discussed. An excellent agreement is observed between the present and earlier published results for some special cases. The results revealed that, the effect of Deborah number and stretching parameter are increased the heat transfer coefficient while the opposite trend is observed for the effects of material and velocity slip parameters. It was also observed that, the values of skin friction increased with the increment on the values of all studied parameters.

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