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.

scholarly journals Stagnation Point Flow and Heat Transfer over an Exponentially Stretching/Shrinking Sheet in CNT with Homogeneous–Heterogeneous Reaction: Stability Analysis

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 522 ◽  
Author(s):  
Nur Syazana Anuar ◽  
Norfifah Bachok ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Stability Analysis ◽  
Differential Equations ◽  
Skin Friction ◽  
Heterogeneous Reaction ◽  
Shrinking Sheet ◽  
Multi Wall Carbon Nanotubes ◽  
Exponentially Stretching ◽  
The Impact

This study focuses on the flow of stagnation region and heat transfer of carbon nanotubes (CNTs) over an exponentially stretching/shrinked sheet in the presence of homogeneous–heterogeneous reactions. Kerosene and water are considered base fluids in both single-wall and multi-wall carbon nanotubes. After employing the appropriate similarity variables, the system of partial differential equations is transformed to a system of nonlinear ordinary differential equations. Solution of the problems is obtained numerically using the bvp4c solver in MATLAB software. The impact of physical parameters, such as solid volume fraction, stretching/shrinking parameter, homogeneous and heterogeneous reaction rate, Schmidt number on the velocity, temperature and concentration profiles, skin friction, and heat transfer rate are discussed graphically and interpreted physically. The results indicate that for an exponentially shrinking sheet, dual solutions exist for a certain range. It is clear from figures that the concentration profile increases for increasing values of heterogeneous parameter and decreasing values of homogeneous parameter. Heat transfer and skin friction were observed to have a greater impact for single-wall carbon nanotubes (SWCNTs) compared to multi-wall carbon nanotubes (MWCNTs). A stability analysis has been performed to show which solutions are linearly stable.

scholarly journals A Weibull Distribution: Flow and Heat Transfer of Nanofluids Containing Carbon Nanotubes with Radiation and Velocity Slip Effects

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Izamarlina Asshaari ◽  
Alias Jedi ◽  
Kafi Dano Pati
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Thermal Radiation ◽  
Weibull Distribution ◽  
Skin Friction ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Moving Plate ◽  
Flow And Heat Transfer

In this study, the Tiwari and Das model is numerically studied, in case of a moving plate containing both single-walled and multiwalled carbon nanotubes (SWCNTs and MWCNTs, respectively), in the presence of thermal radiation and the slip effect. Employing the similarity transformation, a set of 2nd-order partial differential equations (which are used to model the flow and heat transfer) are solved numerically using the boundary value problem with 4th-order accuracy (BVP4C) method. The effects of related parameters, such as the volume fraction of nanoparticles, moving, slip, and radiation parameter on the heat transfer performance are analysed and discussed. Results indicate that a unique solution was placed when the plate travels in assisting flow conditions. Additionally, as the nanoparticle volume fraction (φ) rises at φ = 0.2, the skin friction and heat transfer rate decrease. It is also observed that when the slip parameter (β) increases at β = 0.4, the skin friction decreases, whereas the heat transfer rate increases. Meanwhile, the heat transfer rate decreases when the thermal radiation (NR) increases to 0.7. Moreover, it is found that the SWCNTs are more efficient when the skin friction coefficient and the Nusselt number are considered. It is found that the Weibull distribution is more suitable in fitting the skin friction data.

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 Application of Fractional Derivative Without Singular and Local Kernel to Enhanced Heat Transfer in CNTs Nanofluid Over an Inclined Plate

2020 ◽  
Author(s):  
Muhammad Saqib ◽  
Abdul Rahman Mohd Kasim ◽  
Nurul Farahain Mohammad ◽  
Dennis Ling Chuan Ching ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Fractional Derivatives ◽  
Saturated Porous Medium ◽  
Convection Heat Transfer ◽  
Heat Transfer Fluid ◽  
Single Wall Carbon Nanotubes ◽  
Inclined Plate ◽  
Multi Wall Carbon Nanotubes ◽  
Laplace Transform Technique

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana-Baleanu fractional derivatives without singular and local kernel having strong memory. The human blood is considered as base fluid dispersing carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes(MWCNTs )) into it to form blood-CNTs nanofluid. The nanofluids are considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood-SWCNTs by reason of higher thermal conductivity whereas, this trend is opposite in case of velocity profile due densities difference.

scholarly journals Application of Fractional Derivative Without Singular and Local Kernel to Enhanced Heat Transfer in CNTs Nanofluid Over an Inclined Plate

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 768 ◽  
Author(s):  
Muhammad Saqib ◽  
Abdul Rahman Mohd Kasim ◽  
Nurul Farahain Mohammad ◽  
Dennis Ling Chuan Ching ◽  
Sharidan Shafie
Keyword(s):  
Heat Transfer ◽  
Carbon Nanotubes ◽  
Fractional Derivatives ◽  
Saturated Porous Medium ◽  
Convection Heat Transfer ◽  
Heat Transfer Fluid ◽  
Single Wall Carbon Nanotubes ◽  
Inclined Plate ◽  
Multi Wall Carbon Nanotubes ◽  
Laplace Transform Technique

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana–Baleanu fractional derivatives without singular and local kernel with a strong memory. Human blood is considered as base fluid and carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs)) are dispersed into it to form blood-CNTs nanofluid. The nanofluid is considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood SWCNTs because of higher thermal conductivity whereas this trend is found opposite in the case of velocity profile due to densities difference.

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.

Viscous Dissipation Effects in Water Driven Carbon Nanotubes along a Stream Wise and Cross Flow Direction

2017 ◽  
Vol 15 (1) ◽  
Author(s):  
Rizwan Ul Haq ◽  
Z. H. Khan ◽  
W. A. Khan ◽  
Inayat Ali Shah
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Carbon Nanotubes ◽  
Skin Friction ◽  
Viscous Dissipation ◽  
Flow Direction ◽  
Flow Behavior ◽  
Principal Component ◽  
Physical Models ◽  
Single Wall Carbon Nanotubes

Abstract Important physical models involving boundary layer occur in almost all internal and external aerodynamic formations. For many of these, the flow outside the boundary layer region may be determined into a large principal component and a small crosswise velocity. In this article, three-dimensional boundary-layer flow over a curved surface is treated for nanofluid under such a simplification. Based on strong thermal conductivity we have considered two same kinds but different shaped nanoparticle namely: Single Wall Carbon Nanotubes (SWCNT) and Multiple Wall Carbon Nanotubes (MWCNT) which are incorporated within the base fluid water. Mathematical model is constructed under the constraint of defined geometry and then transformed into the system of ordinary differential equations. These equations are solved numerically with the help of Runge Kutta (R-K) method with shooting technique. Influences of each physical parameter on velocity and temperature distribution are described through graphs. To analyze the drag and heat transfer at the surface we have plotted the skin friction coefficient and local Nusselt number. Flow behavior along the stream wise and cross direction is visualized through stream lines. It is found that viscous dissipation has same increasing effects along both x- and z-directions for temperature profile however, SWCNTs have comparatively higher skin friction and heat transfer rate at the surface as compare to the MWNTs.

Transient Free Convective Flow of CNT Water Nanofluid with Heat Transfer from a Moving Cylinder

2020 ◽  
Vol 10 ◽  
Author(s):  
C. Sridevi ◽  
A. Sailakumari
Keyword(s):  
Carbon Nanotubes ◽  
Heat Generation ◽  
Convective Flow ◽  
Volume Fraction ◽  
Vertical Cylinder ◽  
Single Wall Carbon Nanotubes ◽  
Free Convective Flow ◽  
Multi Wall Carbon Nanotubes ◽  
Moving Cylinder ◽  
Variable Surface

Background: In this paper, transient two-dimensional laminar boundary layer viscous incompressible free convective flow of water based nanofluid with carbon nanotubes (CNTs) past a moving vertical cylinder with variable surface temperature is studied numerically in the presence of thermal radiation and heat generation. Methods: The prevailing partial differential equations which model the flow with initial and boundary conditions are solved by implicit finite difference method of Crank Nicolson type which is unconditionally stable and convergent. Results: Influence of Grashof number (Gr), nanoparticle volume fraction ( ), heat generation parameter (Q), temperature exponent (m), radiation parameter (N) and time (t) on velocity and temperature profiles are sketched graphically and elaborated comprehensively. Conclusion: Analysis of Nusselt number and Skin friction coefficient are also discussed numerically for both single wall carbon nanotubes (SWCNTs) and multi wall carbon nanotubes (MWCNTs).

Sign in / Sign up

Export Citation Format

Share Document