scholarly journals Construction of Analytic Solution to Axisymmetric Flow and Heat Transfer on a Moving Cylinder

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1335
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stokes Equations ◽  
Nonlinear Differential Equations ◽  
Axisymmetric Flow ◽  
Control Parameters ◽  
Auxiliary Functions ◽  
Flow And Heat Transfer ◽  
Moving Cylinder ◽  
Convergence Control

Based on a new kind of analytical approach, namely the Optimal Auxiliary Functions Method (OAFM), a new analytical procedure is proposed to solve the problem of the annular axisymmetric stagnation flow and heat transfer on a moving cylinder with finite radius. As a novelty, explicit analytical solutions were obtained for the considered complex problem. First, the Navier–Stokes equations were simplified by means of similarity transformations that depended on different parameters and some combinations of these parameters, and the problem under study was reduced to six nonlinear ordinary differential equations with six unknowns. The OAFM proves to be a powerful tool for finding an accurate analytical solution for nonlinear problems, ensuring a fast convergence after the first iteration, even if the small or large parameters are absent, since the determination of the convergence-control parameters is independent of the magnitude of the coefficients that appear in the nonlinear differential equations. Concerning the main novelties of the proposed approach, it is worth mentioning the presence of some auxiliary functions, the involvement of the convergence-control parameters, the construction of the first iteration and much freedom to select the procedure for determining the optimal values of the convergence-control parameters.

scholarly journals Numerical Study of Axisymmetric Flow and Heat Transfer in a Liquid Film over an Unsteady Radially Stretching Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Azeem Shahzad ◽  
Uzma Gulistan ◽  
Ramzan Ali ◽  
Azhar Iqbal ◽  
Ali Cemal Benim ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Liquid Film ◽  
Magnetic Parameter ◽  
Numerical Study ◽  
Nonlinear Differential Equations ◽  
Axisymmetric Flow ◽  
Stretching Surface ◽  
Flow And Heat Transfer ◽  
Highly Nonlinear

The main emphasis on this paper is to analyze the axisymmetric flow and heat transfer in a liquid film over an unsteady radially stretching surface in the presence of a transverse magnetic field. The similarity transformations are used to reduce the highly nonlinear governing partial differential equations for momentum and energy into a set of ordinary differential equations. A numerical scheme is developed for the reduced nonlinear differential equations for the velocity and temperature fields. The literature survey shows that the present problem of thin film flow over a radially stretching sheet has not been studied before. The features of the flow and heat transfer characteristic for different values of governing parameters such as unsteadiness parameter, Prandtl number, Eckert number, and magnetic parameter are thoroughly examined. This study noticed that, by increasing the magnetic parameter and unsteadiness parameter, film thickness decreases.

Numerical analysis of flow and heat transfer of a viscoelastic fluid over a stretching sheet

2011 ◽  
Vol 21 (2) ◽  
pp. 206-218 ◽  
Author(s):  
Maryam Momeni ◽  
Naghmeh Jamshidi ◽  
Amin Barari ◽  
Ganji Domairry
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stretching Sheet ◽  
Nonlinear Differential Equations ◽  
Second Grade ◽  
Second Grade Fluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Wide Range ◽  
Grade Fluid

PurposeThe purpose of this paper is to study the flow and heat transfer of an incompressible homogeneous second‐grade fluid past a stretching sheet channel and employ the homotopy analysis method (HAM) to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem.Design/methodology/approachIn this paper, a study of the flow and heat transfer of an incompressible homogeneous second‐grade fluid past a stretching sheet channel is presented and the HAM is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide‐range applications of the HAM in comparison with the numerical method in solving this problem.FindingsThe obtained solutions, in comparison with the exact solutions admit a remarkable accuracy.Originality/valueIn this paper, a study of the flow and heat transfer of an incompressible homogeneous second‐grade fluid past a stretching sheet channel is presented and the HAM is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. The paper shows the capabilities and wide‐range applications of the HAM in comparison with the numerical method in solving this problem. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy.

Flow and heat transfer of hydromagnetic Oldroyd-B fluid in a channel with stretching walls

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Ali Nasir ◽  
Sami Ullah Khan ◽  
Muhammad Sajid ◽  
Zaheer Abbas
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Nonlinear Ordinary Differential Equations ◽  
Electrically Conducting ◽  
Flow And Heat Transfer ◽  
Implicit Finite Difference ◽  
Dimensionless Variables

AbstractThe present study investigates the heat transfer in an electrically conducting Oldroyd-B fluid through a channel with stretchingwalls in the presence of an applied magnetic field. The governing partial differential equations are reduced in a set of nonlinear ordinary differential equations using dimensionless variables. An implicit finite difference method is employed to develop a numerical solution at each spatial node for the governing nonlinear differential equations. The obtained results are analyzed and discussed graphically under the influence of controlling pertinent parameters.

scholarly journals Optimal homotopy perturbation method for nonlinear differential equations governing MHD Jeffery-Hamel flow with heat transfer problem

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 42-57 ◽  
Author(s):  
Vasile Marinca ◽  
Remus-Daniel Ene
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Stokes Equations ◽  
Transfer Problem ◽  
Nonlinear Differential Equations ◽  
Heat Transfer Problem ◽  
Navier Stokes ◽  
Homotopy Perturbation

AbstractIn this paper, the Optimal Homotopy Perturbation Method (OHPM) is employed to determine an analytic approximate solution for the nonlinear MHD Jeffery-Hamel flow and heat transfer problem. The Navier-Stokes equations, taking into account Maxwell’s electromagnetism and heat transfer, lead to two nonlinear ordinary differential equations. The results obtained by means of OHPM show very good agreement with numerical results and with Homotopy Perturbation Method (HPM) results.

Numerical exploration of mixed convection heat transfer features within a copper-water nanofluidic medium occupied a square geometrical cavity

2021 ◽  
Vol 8 (4) ◽  
pp. 807-820
Author(s):  
M. Zaydan ◽  
◽  
A. Wakif ◽  
E. Essaghir ◽  
R. Sehaqui ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Nonlinear Differential Equations ◽  
Convection Heat Transfer ◽  
Local Heat Transfer ◽  
Physical Parameters ◽  
Convection Heat ◽  
Linear Temperature ◽  
Mixed Convection Heat Transfer

The phenomenon of mixed convection heat transfer in a homogeneous mixture is deliberated thoroughly in this study for cooper-water nanofluids flowing inside a lid-driven square cavity. By adopting the Oberbeck-Boussinesq approximation and using the single-phase nanofluid model, the governing partial differential equations modeling the present flow are stated mathematically based on the Navier--Stokes and thermal balance formulations, where the important features of the scrutinized medium are presumed to remain constant at the cold temperature. Note here that the density quantity in the buoyancy body force is a linear temperature-dependent function. The characteristic quantities are computed realistically via the commonly used phenomenological laws and the more accurate experimental correlations. A feasible non-dimensionalization procedure has been employed to derive the dimensionless conservation equations. The resulting nonlinear differential equations are solved numerically for realistic boundary conditions by employing the fourth-order compact finite-difference method (FOCFDM). After performing extensive validations with the previously published findings, the dynamical and thermal features of the studied convective nanofluid flow are revealed to be in good agreement for sundry values of the involved physical parameters. Besides, the present numerical outcomes are discussed graphically and tabularly with the help of streamlines, isotherms, velocity fields, temperature distributions, and local heat transfer rate profiles.

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.

Sign in / Sign up

Export Citation Format

Share Document