scholarly journals A Non-Newtonian Magnetohydrodynamics (MHD) Nanofluid Flow and Heat Transfer with Nonlinear Slip and Temperature Jump

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1199 ◽  
Author(s):  
Jing Zhu ◽  
Yaxin Xu ◽  
Xiang Han
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Jump ◽  
Thin Sheet ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Slip Condition ◽  
Physical Parameters ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

The velocity and thermal slip impacts on the magnetohydrodynamics (MHD) nanofluid flow and heat transfer through a stretched thin sheet are discussed in the paper. The no slip condition is substituted for a new slip condition consisting of higher-order slip and constitutive equation. Similarity transformation and Lie point symmetry are adopted to convert the derived governed equations to ordinary differential equations. An approximate analytical solution is gained through the homotopy analysis method. The impacts of velocity slip, temperature jump, and other physical parameters on flow and heat transfer are illustrated. Results indicate that the first-order slip and nonlinear slip parameters reduce the velocity boundary layer thickness and Nusselt number, whereas the effect on shear stress is converse. The temperature jump parameter causes a rise in the temperature, but a decline in the Nusselt number. With the increase of the order, we can get that the error reaches 10 − 6 from residual error curve. In addition, the velocity contours and the change of skin friction coefficient are computed through Ansys Fluent.

scholarly journals Effect of Velocity Slip Boundary Condition on the Flow and Heat Transfer of Cu-Water and TiO2-Water Nanofluids in the Presence of a Magnetic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Fahd Al Mutairi ◽  
S. M. Khaled
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Fluid Velocity ◽  
Velocity Slip ◽  
Slip Boundary Condition ◽  
Dual Solutions ◽  
Slip Condition ◽  
Shrinking Sheet ◽  
Physical Parameters ◽  
Flow And Heat Transfer

In nanofluid mechanics, it has been proven recently that the no slip condition at the boundary is no longer valid which is the reason that we consider the effect of such slip condition on the flow and heat transfer of two types of nanofluids. The present paper considers the effect of the velocity slip condition on the flow and heat transfer of the Cu-water and the TiO2-water nanofluids over stretching/shrinking sheets in the presence of a magnetic field. The exact expression for the fluid velocity is obtained in terms of the exponential function, while an effective analytical procedure is suggested and successfully applied to obtain the exact temperature in terms of the generalized incomplete gamma function. It is found in this paper that the Cu-water nanofluid is slower than the TiO2-water nanofluid for both cases of the stretching/shrinking sheets. However, the temperature of the Cu-water nanofluid is always higher than the temperature of the TiO2-water nanofluid. In the case of shrinking sheet the dual solutions have been obtained at particular values of the physical parameters. In addition, the effect of various physical parameters on such dual solutions is discussed through the graphs.

Hydromagnetic flow and heat transfer with various nanoparticle additives past a wedge with high order velocity slip and temperature jump

2017 ◽  
Vol 95 (5) ◽  
pp. 440-449 ◽  
Author(s):  
Qianfang Liu ◽  
Jing Zhu ◽  
Bandar Bin-Mohsin ◽  
Liancun Zheng
Keyword(s):  
Heat Transfer ◽  
Temperature Jump ◽  
Slip Flow ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
High Order ◽  
Solid Particles ◽  
Flow And Heat Transfer ◽  
Homotopy Analysis ◽  
Fundamental Equations

Nanofluid slip flow with distinct solid particles past a wedge with convective surface and high order slip is discussed in this paper. The wedge model is modified by considering the effects of Brownian motion and thermophphoresis together with the high order velocity slip and temperature jump. In this study, the governing fundamental equations are first transformed into third-order ordinary differential equations and solved by using the homotopy analysis method (HAM). Through error analysis and comparison with previous research, the effectiveness of HAM is ascertained, and the crucial influence of nanoparticles and high-order slip on the fluid skin-friction coefficient and heat transfer coefficient is analyed. Thermophphoresis parameter and suction/injection parameter are found to cause an increase in velocity and temperature. The rate of heat transfer in the Cu–water nanofluid is found to be higher than the others.

Investigation Into the Similarity Solution for Boundary Layer Flows in Microsystems

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Suhil Kiwan ◽  
M. A. Al-Nimr
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Friction Coefficient ◽  
Skin Friction ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Heat Transfer Characteristics ◽  
Boundary Layer Flows ◽  
Flow And Heat Transfer

An investigation toward the existence of a complete similarity solution for boundary layer flows under the velocity slip and temperature jump conditions is carried out. The study is limited to the boundary layer flows resulting from an arbitrary freestream velocity U(x)=Uoxm and wall temperature given by Tw−T∞=Cxn. It is found that a similar solution exists only for m=1 and n=0, which represents stagnation flow on isothermal surface. This case has been thoroughly investigated. The analysis showed that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter K1, the temperature jump parameter K2, and 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 affects 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 changes in the skin friction takes place in the range 0<K1<1. The skin friction coefficient is found to be related to K1 and Rex according to the relation: Cf=3.38Rex−0.5(K1+1.279)−0.8 for 0<K1<5 with an error of ±4%. On the other hand, the correlation between Nu, K1, K2, and Pr has been found by the equation Nu=[(0.449+1.142K11.06)∕(0.515+K11.06)](K2+1.489Pr−0.44)−1, for 0<K1, K2<5, 0.7≤Pr≤5 within a maximum error of ±3%.

scholarly journals Analytical Study of Heat Transfer of a Unsteady Newtonian Nanofluid Flow Problem

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Heat Transfer ◽  
Volume Fraction ◽  
Skin Friction Coefficient ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Shooting Technique ◽  
Flow And Heat Transfer ◽  
Transfer Behavior ◽  
Basic Equations ◽  
Squeeze Number

Heat transfer behavior of unsteady flow of squeezing nanofluid (Copper+water) between two parallel plates is investigated. By using the appropriate transformation for the velocity and temperature, the basic equations governing the flow and heat transfer were reduced to a set of ordinary differential equations. These equations subjected to the associated boundary conditions were solved analytically using Homotopy Perturbation Method and numerically using Runge-Kutta-Fehlberg method with shooting technique. Effects on the behavior of velocity and temperature for various values of relevant parameters are illustrated graphically. The skin-friction coefficient, heat transfer and Nusselt number rate are also tabulated for various governing parameters. The results indicate that, for nanofluid flow, the rates of heat transfer and velocity had direct relationship with squeeze number and nanoparticle volume fraction they are also a decreasing function of those parameters

Slip Gas Flow and Heat Transfer in Confined Porous Media With Different Shape Cylinders

2021 ◽  
Author(s):  
Ammar Tariq ◽  
Zhenyu Liu
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Gas Flow ◽  
Velocity Slip ◽  
Heat Transfer Analysis ◽  
Variable Boundary ◽  
Flow And Heat Transfer ◽  
Multiple Relaxation Time ◽  
Permeability Increase ◽  
Boltzmann Method

Abstract With the recent advances in micro devices, an accurate gas flow and heat transfer analysis become more relevant considering the slip effect. A micro-scale, multiple-relaxation-time (MRT) lattice Boltzmann method with double distribution function approach is used to simulate flow and heat transfer through circular- and diamond-shaped cylinders at the porescale level. The velocity slip and temperature jump are captured at the boundaries using a non-equilibrium extrapolation scheme with the counter-extrapolation method. A pore-scale domain of micro-cylinders comprised of circle and diamond shape are studied. It is found that the permeability increases linearly with an increase in Knudsen number for both circular- and diamond-shaped cylinders. However, the permeability increase for circular obstacle is larger than that of the diamond one. A larger surface area for diamond cylinder will offer more resistance to flow, hence resulting in lower values. For heat transfer, the Nusselt number shows an increase with increasing Reynolds number, however, it decreases with the increase in porosity. Nusselt number values are found to be higher for a circular obstacle. A variable boundary gradient for circular obstacle could be a possible explanation for this difference.

Three-Dimensional Hybrid Nanofluid Flow and Heat Transfer past a Permeable Stretching/Shrinking Sheet with Velocity Slip and Convective Condition

2020 ◽  
Vol 66 ◽  
pp. 157-171 ◽  
Author(s):  
Najiyah Safwa Khashi'ie ◽  
Norihan Md Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Convective Condition ◽  
Nanofluid Flow ◽  
Flow And Heat Transfer

scholarly journals Magnetohydrodynamic Flow and Heat Transfer Induced by a Shrinking Sheet

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1175
Author(s):  
Nor Ain Azeany Mohd Nasir ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Differential Equations ◽  
Prandtl Number ◽  
Heat Generation ◽  
Local Nusselt Number ◽  
Magnetic Parameter ◽  
Skin Friction Coefficient ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer

The magnetohydrodynamic (MHD) stagnation point flow over a shrinking or stretching flat sheet is investigated. The governing partial differential equations (PDEs) are reduced into a set of ordinary differential equations (ODEs) by a similarity transformation and are solved numerically with the help of MATLAB software. The numerical results obtained are for different values of the magnetic parameter M, heat generation parameter Q, Prandtl number Pr and reciprocal of magnetic Prandtl number ε. The influences of these parameters on the flow and heat transfer characteristics are investigated and shown in tables and graphs. Two solutions are found for a certain rate of the shrinking strength. The stability of the solutions in the long run is determined, and shows that only one of them is stable. It is found that the skin friction coefficient f ″ ( 0 ) and the local Nusselt number − θ ′ ( 0 ) decrease as the magnetic parameter M increases. Further, the local Nusselt number increases as the heat generation increases.

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.

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