Flow and heat transfer with prescribed skin friction in a rotating fluid

2011 ◽  
Vol 68 (7) ◽  
pp. 872-886 ◽  
Author(s):  
Z. Iqbal ◽  
M. Sajid ◽  
T. Hayat ◽  
S. Obaidat
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Rotating Fluid ◽  
Flow And Heat Transfer ◽  
Prescribed Skin Friction

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.

scholarly journals A Stability Analysis of Solutions in Boundary Layer Flow and Heat Transfer of Carbon Nanotubes over a Moving Plate with Slip Effect

Energies ◽  
2018 ◽  
Vol 11 (12) ◽  
pp. 3243 ◽  
Author(s):  
Nur Anuar ◽  
Norfifah Bachok ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Stability Analysis ◽  
Skin Friction ◽  
Single Wall Carbon Nanotubes ◽  
Slip Effect ◽  
Slip Parameter ◽  
Moving Plate ◽  
Multi Wall Carbon Nanotubes ◽  
Flow And Heat Transfer

The flow and heat transfer characteristics of both single-wall and multi-wall carbon nanotubes (CNTs) with water and kerosene as base fluid on a moving plate with slip effect are studied numerically. By employing similarity transformation, governing equations are transformed into a set of nonlinear ordinary equations. These equations are solved numerically using the bvp4c solver in Matlab which is a very efficient finite difference method. The influence of numerous parameters such as nanoparticle volume fraction, velocity ratio parameter and first order slip parameter on velocity, temperature, skin friction and heat transfer rate are further explored and discussed in the form of graphical and tabular forms. The results reveal that dual solutions exist when the plate and free stream move in the opposite direction and slip parameter was found to widen the range of the possible solutions. However, skin friction coefficients decrease, whereas the heat transfer increases in the presence of slip parameter. Single-wall carbon nanotubes (SWCNTs) give higher skin friction and heat transfer compared to multi-wall carbon nanotubes (MWCNTs) due to the fact that they have higher density and thermal conductivity. A stability analysis is carried out to determine the stability of the solutions obtained.

Hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface

2019 ◽  
Vol 29 (9) ◽  
pp. 3110-3127 ◽  
Author(s):  
Iskandar Waini ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Local Nusselt Number ◽  
Skin Friction Coefficient ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

PurposeThis paper aims to investigate the steady flow and heat transfer of a Cu-Al2O3/water hybrid nanofluid over a nonlinear permeable stretching/shrinking surface with radiation effects. The surface velocity condition is assumed to be of the power-law form with an exponent of 1/3. The governing equations of the problem are converted into a system of similarity equations by using a similarity transformation.Design/methodology/approachThe problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The results of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented through graphs and tables for several values of the parameters. The effects of these parameters on the flow and heat transfer characteristics are examined and discussed.FindingsResults found that dual solutions exist for a certain range of the stretching/shrinking and suction parameters. The increment of the skin friction coefficient and reduction of the local Nusselt number on the shrinking sheet is observed with the increasing of copper (Cu) nanoparticle volume fractions for the upper branch. The skin friction coefficient and the local Nusselt number increase when suction parameter is increased for the upper branch. Meanwhile, the temperature increases in the presence of the radiation parameter for both branches.Originality/valueThe problem of Cu-Al2O3/water hybrid nanofluid flow and heat transfer over a nonlinear permeable stretching/shrinking surface with radiation effects is the important originality of the present study where the dual solutions for the flow reversals are obtained.

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Over an Exponentially Stretching/Shrinking Sheet in Ferrofluids

2021 ◽  
Vol 29 (3) ◽  
Author(s):  
Nurfazila Rasli ◽  
Norshafira Ramli
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Friction Coefficient ◽  
Differential Equations ◽  
Skin Friction ◽  
Skin Friction Coefficient ◽  
Magnetohydrodynamic Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Exponentially Stretching

In this research, the problem of magnetohydrodynamic flow and heat transfer over an exponentially stretching/shrinking sheet in ferrofluids is presented. The governing partial differential equations are transformed into nonlinear ordinary differential equations by applying suitable similarity transformations. These equations are then solved numerically using the shooting method for some pertinent parameters. For this research, the water-based ferrofluid is considered with three types of ferroparticles: magnetite, cobalt ferrite, and manganese-zinc ferrite. The numerical solutions on the skin friction coefficient, Nusselt number, velocity and temperature profiles influenced by the magnetic parameter, wall mass transfer parameter, stretching/shrinking parameter, and volume fraction of solid ferroparticle are graphically displayed and discussed in more details. The existences of dual solutions are noticeable for the stretching/shrinking case in a specific range of limit. For the first solution, an increasing number in magnetic and suction will also give an increment of skin friction coefficient and Nusselt number over stretching/shrinking sheet. For the skin friction coefficient only, it is showed a decreasing pattern after the intersection. Besides, the presence of ferroparticles in the fluids causes a high number of the fluid’s thermal conductivity and heat transfer rate.

Analytical Investigation of Nusselt Number and Skin Friction of Fluid Flow Over a Stretching Sheet Using Optimal Homotopy Asymptotic Method

2020 ◽  
Vol 12 (5) ◽  
pp. 657-661
Author(s):  
Zohreh Aliannejadi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Layer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Differential Equations ◽  
Skin Friction ◽  
Flow And Heat Transfer ◽  
Optimal Homotopy Asymptotic Method ◽  
The Magnetic Field

In many cases such as production of metal sheets, the behavior of fluid flow and heat transfer in the neighborhood of a hot plate is very important. The CFD simulation of fluid flow is a widespread study that reveals detail information about the fluid flow in the calculated domain. In this study, the flow and heat transfer of a specific fluid in the above area of a stretching plate is examined analytically to find the variation of skin friction and Nusselt number. For this purpose, the similarity transformations can be employed to achieve the ordinary differential equations from the governing partial differential equations. The optimal homotopy asymptotic method (OHAM) is used to solve the ordinary differential equations which is applicable in solving of nonlinear equations. The effects of magnetic field on the analytical results from solving the equations are evaluated in detail. It is found that the thickness of the flow boundary layer decreases and the thickness of the thermal boundary layer increases by increasing in the magnetic field. Moreover, the Nusselt number is lower and skin friction is higher for the higher values of the magnetic field.

scholarly journals Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

2018 ◽  
Vol 8 (11) ◽  
pp. 2172 ◽  
Author(s):  
Nor Dzulkifli ◽  
Norfifah Bachok ◽  
Nor Yacob ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Skin Friction ◽  
Stagnation Point ◽  
Velocity Slip ◽  
Shrinking Sheet ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Flow And Heat Transfer ◽  
Exponential Stretching

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution.

Flow and Heat Transfer Over a Stretched Microsurface

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Suhil Kiwan ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Transfer ◽  
Friction Coefficient ◽  
Flat Plate ◽  
Skin Friction ◽  
Convection Heat Transfer ◽  
Skin Friction Coefficient ◽  
Slip Parameter ◽  
Heat Transfer Characteristics ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

The convection heat transfer induced by a stretching flat plate has been studied. Similarity conditions are obtained for the boundary layer equations for a flat plate subjected to a power law temperature and velocity variations. It is found that a similarity solution exists only for a linearly stretching plate and only when the plate is isothermal. The analysis shows that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter K1, the temperature slip parameter K2, and the Prandtl number. The effect of these parameters on the flow and heat transfer of the problem has been studied and presented. It is found that the slip velocity parameter affect both the flow and heat transfer characteristics of the problem. It is found that the skin friction coefficient decreases with increasing K1 and most of the changes in the skin friction takes place in the range 0<K1<1. A correlation between the skin friction coefficient and K1 and Rex has been found and presented. It is found that cf=23Rex−0.5(K1+0.64)−0.884 for 0<K1<10 with an error of ±0.8%. Other correlations between Nu and K1 and K2 has been found and presented in Eq. 28.

scholarly journals Slip-Flow and Heat Transfer in a Porous Microchannel Saturated with Power-Law Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Yazan Taamneh ◽  
Reyad Omari
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Skin Friction ◽  
Knudsen Number ◽  
Power Law ◽  
Slip Flow ◽  
Darcy Number ◽  
Power Law Fluid ◽  
Flow And Heat Transfer ◽  
Power Law Index

This study aims to numerically examine the fluid flow and heat transfer in a porous microchannel saturated with power-law fluid. The governing momentum and energy equations are solved by using the finite difference technique. The present study focuses on the slip flow regime, and the flow in porous media is modeled using the modified Darcy-Brinkman-Forchheimer model for power-law fluids. Parametric studies are conducted to examine the effects of Knudsen number, Darcy number, power law index, and inertia parameter. Results are given in terms of skin friction and Nusselt number. It is found that when the Knudsen number and the power law index decrease, the skin friction on the walls decreases. This effect is reduced slowly while the Darcy number decreases until it reaches the Darcy regime. Consequently, with a very low permeability the effect of power law index vanishes. The numerical results indicated also that when the power law index decreases the fully-developed Nusselt number increases considerably especially, in the limit of high permeability, that is, nonDarcy regime. As far as Darcy regime is concerned the effects of the Knudsen number and the power law index of the fully-developed Nusselt number is very little.

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