Applications of fractional derivatives to nanofluids: exact and numerical solutions

2018 ◽  
Vol 13 (1) ◽  
pp. 2 ◽  
Author(s):  
Sidra Aman ◽  
Ilyas Khan ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh
Keyword(s):  
Nusselt Number ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Physical Processes ◽  
Carrier Fluid ◽  
Laplace Transform Technique ◽  
Classical Models ◽  
Nanoparticles Volume Fraction ◽  
Graphene Nanoparticles

In this article the idea of time fractional derivatives in Caputo sense is used to study memory effects on the behavior of nanofluids because some physical processes complex visco-elasticity, behavior of mechatronic and rheology are impossible to described by classical models. In present attempt heat and mass transfer of nanofluids (sodium alginate (SA) carrier fluid with graphene nanoparticles) are tackled using fractional derivative approach. Exact solutions are determined for temperature, concentration and velocity field, and Nusselt number via Laplace transform technique. The obtained solutions are then expressed in terms of wright function or its fractional derivatives. Numerical solutions for velocity, temperature, concentration and Nusselt number are obtained using finite difference scheme. It is found that these solutions are significantly controlled by the variations of parameters including thermal Grashof number, fractional parameter and nanoparticles volume fraction. It is observed that rate of heat transfer increases with increasing nanoparticles volume fraction and Caputo time fractional parameters.

scholarly journals Mixed convection of functionalized DWCNT-water nanofluid in baffled lid-driven cavities

2018 ◽  
Vol 22 (6 Part A) ◽  
pp. 2503-2514 ◽  
Author(s):  
Esfe Hemmat ◽  
Arani Abbasian ◽  
Wei-Mon Yan ◽  
Alireza Aghaie ◽  
Masoud Afrand ◽  
...  
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Richardson Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Minimum Length ◽  
Convection Flow ◽  
Flow And Heat Transfer ◽  
Inclination Angles ◽  
Nanoparticles Volume Fraction

The present study aims to evaluate the mixed convection flow and heat transfer of functionalized DWCNT/water nanofluids with variable properties in a cavity having hot baffles. The investigation is performed at different nanoparticles volume fraction including 0, 0.0002, 0.001, 0.002, and 0.004, Richardson numbers ranging from 0.01 to 100, inclination angles ranging from 0 to 60? and at constant Grashof number of 104. The results presented as streamlines and isotherms plot and Nusselt number diagrams. According to the finding with increasing nanoparticles volume fraction and distance between the left hot baffles of nanoparticles average Nusselt number enhances for all considered Richardson numbers and cavity inclination angles. Also with increasing Richardson number, the rate of changes of average Nusselt number increase with increasing distance between the left hot baffles. For example, at Richardson number of 0.01, by increasing L1 from 0.4 to 0.6, the average Nusselt number increases 7%; while for similar situation at Richardson number of 0.1, 1.0, and 10, the average Nusselt number increases, respectively, 17%, 24%, and 26%. At all Richardson numbers, the maximum value of average Nusselt number is achieved for a minimum length of left baffles. <br><br><font color="red"><b> This article has been corrected. Link to the correction <u><a href="http://dx.doi.org/10.2298/TSCI190203032E">10.2298/TSCI190203032E</a><u></b></font>

scholarly journals Mixed Convection and Entropy Generation of an Ag-Water Nanofluid in an Inclined L-Shaped Channel

Energies ◽  
2019 ◽  
Vol 12 (6) ◽  
pp. 1150 ◽  
Author(s):  
Taher Armaghani ◽  
Muneer Ismael ◽  
Ali Chamkha ◽  
Ioan Pop
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Richardson Number ◽  
Volume Fraction ◽  
Governing Equations ◽  
Nanoparticles Volume Fraction ◽  
The Mean ◽  
The Right ◽  
Volume Method

This paper investigates the mixed convection and entropy generation of an Ag-water nanofluid in an L-shaped channel fixed at an inclination angle of 30° to the horizontal axis. An isothermal heat source was positioned in the middle of the right inclined wall of the channel while the other walls were kept adiabatic. The finite volume method was used for solving the problem’s governing equations. The numerical results were obtained for a range of pertinent parameters: Reynolds number, Richardson number, aspect ratio, and the nanoparticles volume fraction. These results were Re = 50–200; Ri = 0.1, 1, 10; AR = 0.5–0.8; and φ = 0.0–0.06, respectively. The results showed that both the Reynolds and the Richardson numbers enhanced the mean Nusselt number and minimized the rate of entropy generation. It was also found that when AR. increased, the mean Nusselt number was enhanced, and the rate of entropy generation decreased. The nanoparticles volume fraction was predicted to contribute to increasing both the mean Nusselt number and the rate of entropy generation.

A comparative study of heat transfer analysis of fractional Maxwell fluid by using Caputo and Caputo–Fabrizio derivatives

2020 ◽  
Vol 98 (1) ◽  
pp. 89-101 ◽  
Author(s):  
Nauman Raza ◽  
Muhammad Asad Ullah
Keyword(s):  
Exact Solutions ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Maxwell Fluid ◽  
Heat Transfer Analysis ◽  
Flow Parameters ◽  
Fluid Parameter ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Temperature And Velocity Fields

A comparative analysis is carried out to study the unsteady flow of a Maxwell fluid in the presence of Newtonian heating near a vertical flat plate. The fractional derivatives presented by Caputo and Caputo–Fabrizio are applied to make a physical model for a Maxwell fluid. Exact solutions of the non-dimensional temperature and velocity fields for Caputo and Caputo–Fabrizio time-fractional derivatives are determined via the Laplace transform technique. Numerical solutions of partial differential equations are obtained by employing Tzou’s and Stehfest’s algorithms to compare the results of both models. Exact solutions with integer-order derivative (fractional parameter α = 1) are also obtained for both temperature and velocity distributions as a special case. A graphical illustration is made to discuss the effect of Prandtl number Pr and time t on the temperature field. Similarly, the effects of Maxwell fluid parameter λ and other flow parameters on the velocity field are presented graphically, as well as in tabular form.

CFD Investigation of Al2O3 Nanoparticles Effect on Heat Transfer Enhancement of Newtonian and Non-Newtonian Fluids in a Helical Coil

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Javad Aminian Dehkordi ◽  
Arezou Jafari
Keyword(s):  
Heat Transfer ◽  
Aqueous Solution ◽  
Nusselt Number ◽  
Base Fluid ◽  
Volume Fraction ◽  
Reynolds Numbers ◽  
Helical Coil ◽  
Al2o3 Nanoparticles ◽  
Nanoparticles Volume Fraction ◽  
Computational Fluid Dynamics Cfd

Abstract The present study applied computational fluid dynamics (CFD) to investigate the heat transfer of Newtonian (water) and non-Newtonian (0.3 %wt. aqueous solution of carboxymethylcellulose (CMC)) fluids in the presence of Al2O3 nanoparticles. To analyze the heat transfer rate, investigations were performed in a vertical helical coil as essential heat transfer equipment, at different inlet Reynolds numbers. To verify the accuracy of the simulation model, experimental data reported in the literature were employed. Comparisons showed the validity of simulation results. From the results, compared to the aqueous solution of CMC, water had a higher Nusselt number. In addition, it was observed that adding nanoparticles to a base fluid presented different results in which water/Al2O3 nanofluid with nanoparticles’ volume fraction of 5 % was more effective than the same base fluid with a volume fraction of 10 %. In lower ranges of Reynolds number, adding nanoparticles was more effective. For CMC solution (10 %), increasing concentration of nanoparticles caused an increase in the apparent viscosity. Consequently, the Nusselt number was reduced. The findings reveal the important role of fluid type and nanoparticle concentration in the design and development of heat transfer equipment.

scholarly journals New exact and numerical solutions for the effect of suction or injection on flow of nanofluids past a stretching sheet

2019 ◽  
Vol 8 (1) ◽  
pp. 172-178
Author(s):  
Nader Y. Abd Elazem
Keyword(s):  
Nusselt Number ◽  
Exact Solutions ◽  
Sherwood Number ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Lewis Number ◽  
Suction Or Injection ◽  
Wall Mass ◽  
Good Agreement

Abstract The flow of nanofluids past a stretching sheet has attracted much attention due to its wide applications in industry and engineering. Theoretical and numerical solutions have been discussed in this paper for studying the effect of suction or injection on flow of nanofluids past a stretching sheet. In the absence of thermophoresis the analytical exact solution of the stream function was obtained in terms of exponential function, while the exact solutions for temperature and nanoparticle volume fraction were obtained in terms of the generalized incomplete gamma function. In addition, in the presence of thermophoresis, the exact solutions are not available. Therefore, the numerical results, carried out by using Chebyshev collocation method (ChCM). It is found that a good agreement exists between the present results and with those published works. Useful results for temperature profile, concentration profile, reduced Nusselt number and reduced Sherwood number are discussed in details graphically. It was also demonstrated that both temperature and concentration profiles decrease by an increase from injection to suction. Finally, the present results showed that increase of the wall mass transfer from injection to suction decreased both reduced Nusselt number and the reduced Sherwood number when Brownian motion parameter and Lewis number increased.

scholarly journals MHD Free Convective Heat Transfer in a Triangular Enclosure Filled with Copper-Water Nanofluid

2020 ◽  
pp. 29-38 ◽  
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Free Convective Flow ◽  
Nanoparticles Volume Fraction ◽  
Triangular Enclosure ◽  
Element Technique ◽  
Horizontal Side

Two-dimensional time-independent free convective flow and temperature flow into a right-angled triangle shape cavity charged by Cu-H2O nanofluid has been performed. The horizontal side of the enclosure is warmed uniformly T=Th whilst the standing wall is cooled at low-temperature T=Tc and hypotenuse of the triangular is insulated. The dimensionless non-linear governing PDEs have been solved numerically employing the robust PDE solver the Galerkin weighted residual finite element technique. An excellent agreement is founded between the previous, and present studies. The outcomes are displayed through streamline contours, isotherm contours, and local and average Nusselt number for buoyancy-driven parameter Rayleigh number, Hartmann number, and nanoparticles volume fraction. The outcomes show that the temperature flow value significantly changes for the increases of Rayleigh number, Hartmann number, and nanoparticles volume fraction. Average Nusselt number is increased for the composition of nanoparticles whereas diminishes with the increase of Hartmann number.

scholarly journals Numerical study of heat transfer enhancement in the entrance region for low-pressure gaseous laminar pipe flows using Al2O3–air nanofluid

2018 ◽  
Vol 10 (7) ◽  
pp. 168781401878441 ◽  
Author(s):  
Wael Al-Kouz ◽  
Rafat Al-Waked ◽  
Ma’en Sari ◽  
Wahib Owhaib ◽  
Anas Atieh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Knudsen Number ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Low Pressure ◽  
Entrance Region ◽  
Physical Parameters ◽  
Nanoparticles Volume Fraction

The gaseous low-pressure nanofluid flow of a steady-state two-dimensional laminar forced convection heat transfer in the entrance region of pipes is numerically investigated. Such flows are of interest for many engineering applications like the nuclear reactor and electronic equipment cooling, heat exchangers, and many others. Physical parameters considered in this study are Reynolds number ( Re), Prandtl number ( Pr), nanosolid particles volume fraction [Formula: see text], Knudsen number ( Kn), and the aspect ratio ( AR). These parameters ranges are as follows: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. The outcome of this study shows that by increasing Kn, velocity slip and temperature jump at the solid boundaries increase. In addition, heat transfer is enhanced by dispersing Al2O3 nanoparticles in the base low-pressure gaseous flow. Results show that there is no effect of the nanoparticles volume fraction with values below 0.03 on the average Nusselt number. The average Nusselt number increases [Formula: see text] as the value of the nanoparticles volume fraction exceeds 0.03. For instance, at Re = 1000, results show that when dispersing Al2O3 nanosolid particles with volume fractions of 0.3 and 0.5; there is an enhancement in the average Nusselt number of 30.35% and 136.74%, respectively, when compared to the case of dispersing Al2O3 nanosolid particles of 0.03 volume fraction.. Moreover, it is concluded that the average Nusselt number [Formula: see text] depends directly on Reynolds ( Re), Prandtl ( Pr) numbers, and the nanoparticles volume fraction [Formula: see text] and inversely on Knudsen number ( Kn) and the aspect ratio ( AR) for the investigated range of parameters considered in this study. Finally, a correlation of Nusselt number among all the investigated parameters in this study is proposed as [Formula: see text].

scholarly journals Control of the free convective heat transfer using a U-shaped obstacle in an Al2O3-water nanofluid filled cubic cavity

2021 ◽  
Vol 8 (7) ◽  
pp. 23-30
Author(s):  
Rajab Al-Sayagh ◽  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Free Convection ◽  
Convective Heat Transfer ◽  
Volume Fraction ◽  
Temperature Fields ◽  
Flow Structures ◽  
Nanoparticles Volume Fraction ◽  
Al2o3 Nanofluid

This paper deals with the study of free convection in a 3D enclosure filled with Al2O3-nanofluid and equipped with a U-shaped obstacle. The used U-shaped obstacle is considered perfectly conductive. The effect of the dimension and the orientation of the obstacle is investigated. In addition, the parameters governing the problem are varied as Rayleigh number (103 to 106), and nanoparticles volume fraction (0 to 7.5%). Results are depicted in terms of flow structures, temperature fields, and Nusselt number. Results show that the obstacle dimension and orientation can control the flow and optimize the heat transfer and the addition of nanoparticles enhances significantly Nusselt number.

Three-Dimensional Numerical Simulation of Mixed Convective Heat Transfer in a Horizontal Rectangular Duct Utilizing Nanofluids

2014 ◽  
Vol 1016 ◽  
pp. 738-742
Author(s):  
Nur Irmawati Om ◽  
H.A. Mohammed
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Rectangular Duct ◽  
Thermal Fields ◽  
Nanoparticles Volume Fraction

Predictions are reported for three-dimensional laminar mixed convective heat transfer using nanofluids in a horizontal rectangular duct. Five different types of nanoparticle, Ag, Al2O3, Au, Cu and SiO2 with nanoparticles volume fractions range of 2% to 10% are investigated. In this study, the effects of nanofluids type, nanoparticles volume fraction of nanofluids and the effect of aspect ratio on the thermal fields were examined. Results reveal that the addition of nanoparticles to the base fluid and their volume fraction tend to increase the Nusselt number along the horizontal rectangular duct (i.e., increases the rate of heat transfer). It was also found that the Nusselt number increases as the aspect ratio decreases.

Slip Effects on the Peristaltic Motion of Nanofluid in a Channel With Wall Properties

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
M. Mustafa ◽  
S. Hina ◽  
T. Hayat ◽  
A. Alsaedi
Keyword(s):  
Brownian Motion ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Slip Effects ◽  
Homotopy Analysis ◽  
Analytic Expressions ◽  
Nanoparticles Concentration ◽  
Compliant Walls ◽  
Nanoparticles Volume Fraction ◽  
Brownian Motion And Thermophoresis

This article looks at the peristaltic flow of nanofluid in a channel with compliant walls. Brownian motion and thermophoresis effects are taken into consideration. Mathematical model is formulated by using long wavelength and low Reynolds number assumptions. The analytic expressions of temperature and nanoparticles concentration are developed by homotopy analysis method (HAM). The solutions are validated through the numerical solutions obtained by employing the built in routine for solving nonlinear boundary value problem via shooting method through software mathematica. Special emphasis is given to the role of key parameters including the Brownian motion parameter (Nb), thermophoresis parameter (Nt), Prandtl number (Pr), Eckert number (Ec) on temperature, and nanoparticles concentration. It is observed that both temperature and nanoparticles volume fraction increase when the Brownian motion and thermophoresis effects intensify. Moreover, the heat transfer coefficient is increasing function of Nb and Nt.

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