Heat transfer over an unsteady stretching surface with prescribed heat flux

2008 ◽  
Vol 86 (6) ◽  
pp. 853-855 ◽  
Author(s):  
A Ishak ◽  
R Nazar ◽  
I Pop
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Method Comparison ◽  
Temperature Fields ◽  
Stretching Surface ◽  
Keller Box Method ◽  
Unsteady Stretching Surface ◽  
Layer Flow

The unsteady laminar boundary-layer flow over a continuously stretching surface in a viscous and incompressible quiescent fluid is studied. The unsteadiness in the flow and temperature fields is caused by the time dependence of the stretching velocity and the surface heat flux. The nonlinear partial differential equations of continuity, momentum, and energy, with three independent variables, are reduced to nonlinear ordinary differential equations, before they are solved numerically by the Keller-box method. Comparison with available data from the open literature as well as the exact solution for the steady-state case of the present problem is made, and found to be in good agreement. Effects of the unsteadiness parameter and Prandtl number on the flow and heat transfer characteristics are thoroughly examined.PACS No.: 47.15.Cb

Existence of Dual Solutions and Melting Phenomenon in Unsteady Nanofluid Flow and Heat Transfer over a Stretching Surface

2019 ◽  
Vol 35 (5) ◽  
pp. 705-717
Author(s):  
S. Ghosh ◽  
S. Mukhopadhyay ◽  
K. Vajravelu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Lewis Number ◽  
Skin Friction Coefficient ◽  
Dual Solutions ◽  
Stretching Surface ◽  
Melting Phenomenon ◽  
Runge Kutta Method ◽  
Layer Flow

ABSTRACTThe problem of unsteady boundary layer flow of a nanofluid over a stretching surface is studied. Heat transfer due to melting is analyzed. Using a similarity transformation the governing coupled nonlinear partial differential equations of the model are reduced to a system of nonlinear ordinary differential equations, and then solved numerically by a Runge-Kutta method with a shooting technique. Dual solutions are observed numerically and their characteristics are analyzed. The effects of the pertinent parameters such as the acceleration parameter, the Brownian motion parameter, the thermophoresis parameter, the Prandtl number and the Lewis number on the velocity, temperature and concentration fields are discussed. Also the effects of these parameters on the skin friction coefficient, the Nusselt number and the Sherwood number are analyzed through graphs. It is observed that the melting phenomenon has a significant effect on the flow, heat and mass transfer characteristics.

Heat transfer of three-dimensional micropolar fluid on a Riga plate

2020 ◽  
Vol 98 (1) ◽  
pp. 32-38 ◽  
Author(s):  
S. Nadeem ◽  
M.Y. Malik ◽  
Nadeem Abbas
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Differential Equations ◽  
Surface Temperature ◽  
Ordinary Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Ordinary Differential Equations ◽  
Exponential Order ◽  
Riga Plate

In this article, we deal with prescribed exponential surface temperature and prescribed exponential heat flux due to micropolar fluids flow on a Riga plate. The flow is induced through an exponentially stretching surface within the time-dependent thermal conductivity. Analysis is performed inside the heat transfer. In our study, two cases are discussed here, namely prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). The governing systems of the nonlinear partial differential equations are converted into nonlinear ordinary differential equations using appropriate similarity transformations and boundary layer approach. The reduced systems of nonlinear ordinary differential equations are solved numerically with the help of bvp4c. The significant results are shown in tables and graphs. The variation due to modified Hartman number M is observed in θ (PEST) and [Formula: see text] (PEHF). θ and [Formula: see text] are also reduced for higher values of the radiation parameter Tr. Obtained results are compared with results from the literature.

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.

Convection heat transfer in a Maxwell fluid at a non-isothermal surface

Open Physics ◽  
2011 ◽  
Vol 9 (3) ◽  
Author(s):  
Kuppalapalle Vajravelu ◽  
Kerehalli Prasad ◽  
Ashwatha Sujatha
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Variable Temperature ◽  
Nonlinear Partial Differential Equations ◽  
Convection Heat Transfer ◽  
Maxwell Fluid ◽  
Convection Heat ◽  
Stretching Surface ◽  
Coupled Equations ◽  
Wide Range

AbstractAnalysis is carried out to study the convection heat transfer in an upper convected Maxwell fluid at a non-isothermal stretching surface. This is a generalization of the paper by Sadeghy et al. [21] to study the effects of free convection currents, variable thermal conductivity and the variable temperature at the stretching surface. Unlike in Sadeghy et al., here the governing nonlinear partial differential equations are coupled. These coupled equations are transformed in to a system of nonlinear ordinary differential equations and are solved numerically by a finite difference scheme (known as the Keller-Box method) and the numerical results are presented through graphs and tables for a wide range of governing parameters. The results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study of nonlinear convection heat transfer.

scholarly journals Three-dimensional boundary layer flow of nanofluids due to an unsteady stretching surface

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
A. Mahdy
Keyword(s):  
Differential Equations ◽  
Three Dimensional ◽  
Continuous Phase ◽  
Temperature Fields ◽  
Flow And Heat Transfer ◽  
Dimensional Boundary ◽  
Unsteady Stretching Surface ◽  
Layer Flow ◽  
Solid Liquid ◽  
Stretching Flow

A numerical solution has been obtained for the unsteady three-dimensional stretching flow and heat transfer due to uncertainties of thermal conductivity and dynamic viscosity of nanofluids. The term of nanofluid refers to a solid–liquid mixture with a continuous phase which is a nanometer sized nanoparticle dispersed in conventional base fluids. The unsteadiness in the flow and temperature fields is caused by the time-dependent of the stretching velocity and the surface temperature.  Different water-based nanofluids containing Cu, Ag, and TiO2 are taken into consideration. The governing partial differential equations with the auxiliary conditions are converted to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. Comparison with known results for steady state flow is presented and it found to be in excellent agreement.

Flow Over a Stretching Sheet in a Dusty Fluid With Radiation Effect

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
G. K. Ramesh ◽  
B. J. Gireesha
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Radiation Effect ◽  
Stretching Sheet ◽  
Nonlinear Partial Differential Equations ◽  
Particle Interaction ◽  
Dusty Fluid ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Fifth Order

The radiation effect on a steady two-dimensional boundary layer flow of a dusty fluid over a stretching sheet is analyzed. The governing nonlinear partial differential equations have been transformed by a similarity transformation into a system of nonlinear ordinary differential equations and then solved numerically by applying Runge Kutta Fehlberg fourth-fifth order method (RKF45 method). The effect of fluid particle interaction parameter, Prandtl number, Eckert number, and radiation parameter on heat transfer characteristics in two different general cases, namely (1) the prescribed surface temperature (PST) and (2) the prescribed heat flux (PHF) are presented graphically and discussed. The rate of heat transfer is computed and tabulated for various values of the different parameters. Comparison of the obtained numerical results is made with previously published results.

Rotating Flow of a Micropolar Fluid Induced by a Stretching Surface

2010 ◽  
Vol 65 (10) ◽  
pp. 829-843 ◽  
Author(s):  
Tariq Javed ◽  
Iftikhar Ahmad ◽  
Zaheer Abbas ◽  
Tasawar Hayat
Keyword(s):  
Differential Equations ◽  
Micropolar Fluid ◽  
Nonlinear Partial Differential Equations ◽  
Rotating Flow ◽  
Nonlinear Ordinary Differential Equations ◽  
Series Solutions ◽  
Analysis Method ◽  
Stretching Surface ◽  
Homotopy Analysis ◽  
Layer Flow

This investigation deals with the boundary layer flow of a micropolar fluid over a stretching surface. The flow is considered in a rotating frame of reference. The governing nonlinear partial differential equations are reduced to coupled nonlinear ordinary differential equations. The set of similarity equations has been solved analytically employing the homotopy analysis method (HAM). The series solutions are given for velocity and microrotation, and the convergence of these solutions are explicitly discussed. Attention has been focused to the variations of the emerging parameters on the velocity and microrotation are discussed through graphs.

Nanofluidic Transport over a Curved Surface with Viscous Dissipation and Convective Mass Flux

2017 ◽  
Vol 72 (3) ◽  
pp. 223-229 ◽  
Author(s):  
Zaffar Mehmood ◽  
Z. Iqbal ◽  
Ehtsham Azhar ◽  
E.N. Maraj
Keyword(s):  
Differential Equations ◽  
Viscous Dissipation ◽  
Mass Flux ◽  
Shooting Method ◽  
Nonlinear Partial Differential Equations ◽  
Stretching Surface ◽  
Similarity Transformations ◽  
Curvature Parameter ◽  
Layer Flow ◽  
Convective Mass Flux

AbstractThis article is a numerical investigation of boundary layer flow of nanofluid over a bended stretching surface. The study is carried out by considering convective mass flux condition. Contribution of viscous dissipation is taken into the account along with thermal radiation. Suitable similarity transformations are employed to simplify the system of nonlinear partial differential equations into a system of nonlinear ordinary differential equations. Computational results are extracted by means of a shooting method embedded with a Runge-Kutta Fehlberg technique. Key findings include that velocity is a decreasing function of curvature parameter K. Moreover, Nusselt number decreases with increase in curvature of the stretching surface while skin friction and Sherwood number enhance with increase in K.

scholarly journals Numerical Study on Micropolar Nanofluid Flow over an Inclined Surface by Means of Keller-Box

2019 ◽  
pp. 1-21 ◽  
Author(s):  
Khuram Rafique ◽  
Muhammad Imran Anwar ◽  
Masnita Misiran
Keyword(s):  
Differential Equations ◽  
Numerical Study ◽  
Nonlinear Partial Differential Equations ◽  
Nanofluid Flow ◽  
Heat And Mass Exchange ◽  
Buongiorno’S Model ◽  
Similarity Transformations ◽  
Keller Box Method ◽  
Micropolar Nanofluid ◽  
Layer Flow

In this paper, micropolar nanofluid boundary layer flow over a linear inclined stretching surface with the magnetic effect is investigated. Buongiorno’s model utilized in this study for the thermal efficiencies of the fluid flow in the presence of Brownian motion and thermophoresis properties. The nonlinear problem for micropolar nanofluid flow over an inclined sheet is established to study the heat and mass exchange phenomenon by considering portent flow parameters to strengthen the boundary layers. The governing nonlinear partial differential equations are changed to nonlinear ordinary differential equations by using suitable similarity transformations and then solved numerically by applying the Keller-Box method. A comparison of the setup results in the absence of the incorporated impacts is performed with the accessible results and perceived in a decent settlement. Numerical and graphical outcomes are additionally presented in tables and diagrams.

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