scholarly journals Heat Transfer Analysis on the Hiemenz Flow of a Non-Newtonian Fluid: A Homotopy Method Solution

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yasir Khan ◽  
Zdeněk Šmarda
Keyword(s):  
Heat Transfer ◽  
Linear Operator ◽  
Stagnation Point ◽  
Newtonian Fluid ◽  
Fluid Flows ◽  
Heat Transfer Analysis ◽  
Shrinking Sheet ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Homotopy Perturbation

The mathematical model for the incompressible two-dimensional/axisymmetric non-Newtonian fluid flows and heat transfer analysis in the region of stagnation point over a stretching/shrinking sheet and axisymmetric shrinking sheet is presented. The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely, the homotopy perturbation method (HPM) with general form of linear operator is used to solve dimensionless nonlinear ordinary differential equations. The series solution is obtained without using the diagonal Padé approximants to handle the boundary condition at infinity which can be considered as a clear advantage of homotopy perturbation technique over the decomposition method. The effects of the pertinent parameters on the velocity and temperature field are discussed through graphs. To the best of authors’ knowledge, HPM solution with general form of linear operator for two-dimensional/axisymmetric non-Newtonian fluid flows and heat transfer analysis in the region of stagnation point is presented for the first time in the literature.

Heat Transfer Analysis on Squeezing Unsteady MHD Nanofluid Flow Between Two Parallel Plates Considering Thermal Radiation, Magnetic and Viscous Dissipations Effects a Solution by Using Homotopy Perturbation Method

2020 ◽  
Vol 18 (2) ◽  
pp. 113-121
Author(s):  
A. El Harfouf ◽  
A. Wakif ◽  
S. Hayani Mounir
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Perturbation Method ◽  
Ordinary Differential Equations ◽  
Homotopy Perturbation Method ◽  
Heat Transfer Analysis ◽  
Nonlinear Ordinary Differential Equations ◽  
Parallel Plates ◽  
Homotopy Perturbation

In this current work, the heat transfer analysis for the unsteady squeezing magnetohydrodynamic flow of a viscous nanofluid between two parallel plates in the presence of thermal radiation, viscous and magnetic dissipations impacts, considering Fourier heat flux model have been explored. The partial differential equations representing flow model are reduced to nonlinear ordinary differential equations by introducing a similarity transformation. The dimensionless and nonlinear ordinary differential equations of the velocity and temperatures functions obtained are solved by employing the homotopy perturbation method. The effects of different parameters on the velocity and temperature profiles are examined graphically, and numerical calculations for the skin friction coefficient and local Nusselt number are tabulated. It is found an excellent agreement in the comparative study with literature results. This present numerical exploration has great relevance, consequently a better understanding of the squeezing flow phenomena in the hydraulic lifts, power transmission, nano gastric tubes, reactor fluidization areas.

Radiative MHD Stagnation-Point Flow with Heat Transfer Past a Permeable Stretching/Shrinking Sheet in a Porous Medium

2017 ◽  
Vol 11 ◽  
pp. 110-128
Author(s):  
Shoeb R. Sayyed ◽  
B.B. Singh ◽  
Nasreen Bano
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Nonlinear Ordinary Differential Equations ◽  
Similarity Transformations ◽  
Energy Equations

In the present study, an analytical analysis has been carried out to investigate the MHD stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in a porous medium in the presence of thermal radiation. Similarity transformations have been employed to simplify the momentum and energy equations into coupled nonlinear ordinary differential equations. The resulting nonlinear ordinary differential equations are then solved analytically through BVPh 2.0 Mathematica package based on homotopy analysis method (HAM). Effects of various parameters such as Prandtl number, permeability parameter, magnetic parameter, suction/blowing parameter, stretching/shrinking parameter, radiation parameter and wall temperature exponent on velocity and/or temperature profiles are explored and discussed graphically. Our results have been compared with the available literature and have been found in excellent agreement. This study may have applications in metallurgy industry and aerodynamic extrusion of plastic sheet.

Heat Transfer Analysis on the Magnetohydrodynamic Flow of a Non- Newtonian Fluid in the Presence of Thermal Radiation: An Analytic Solution

2012 ◽  
Vol 67 (3-4) ◽  
pp. 147-152 ◽  
Author(s):  
Yasir Khan ◽  
Qingbiao Wu ◽  
Naeem Faraz ◽  
Ahmet Yıldırım ◽  
Syed Tauseef Mohyud-Din
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Newtonian Fluid ◽  
Stokes Equations ◽  
Magnetohydrodynamic Flow ◽  
Heat Transfer Analysis ◽  
Nonlinear Ordinary Differential Equations ◽  
Constant Wall Temperature

In this paper, a two-dimensional, steady magnetohydrodynamic flow and heat transfer analysis of a non-Newtonian fluid in a channel with a constant wall temperature are considered in the presence of thermal radiation. The steady Navier-Stokes equations are reduced to nonlinear ordinary differential equations by using similarity variables. The homotopy perturbation method is used to solve the nonlinear ordinary differential equations. The effects of the pertinent parameters on the velocity and temperature field are discussed

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

2018 ◽  
Vol 28 (11) ◽  
pp. 2650-2663 ◽  
Author(s):  
Fatinnabila Kamal ◽  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Heat Source ◽  
Skin Friction ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Source Effect ◽  
Flow And Heat Transfer

PurposeThis paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.Design/methodology/approachThe governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.FindingsThe analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.Practical implicationsIn practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.Originality/valueAlthough many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

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