scholarly journals Caputo Time Fractional Model Based on Generalized Fourier’s and Fick’s Laws for Jeffrey Nanofluid: Applications in Automobiles

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Jawad Ahmad ◽  
Farhad Ali ◽  
Saqib Murtaza ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Transfer Rate ◽  
Energy Equation ◽  
Special Function ◽  
Volume Fraction ◽  
Classical Model ◽  
Fractional Model ◽  
Jeffrey Nanofluid ◽  
Mass And Heat Transfer ◽  
Jeffery Nanofluid

This article aims to examine Jeffery nanofluid with joint effects of mass and heat transfer in a horizontal channel. The classical model is transferred to the Caputo fractional model by using the generalized Fourier’s and Fick’s laws. The nanofluids are formed by dispersing two different nanoparticles, silver and copper, into a based fluid. A novel transformation has been applied to the mass and energy equation and then solved by using the sine Fourier and the Laplace transformation jointly. The exact solution is given in terms of a special function, that is, the Mittag-Leffler function. The Sherwood number and Nusselt number are calculated and displayed in the tabular form. The effect of embedded parameters on the velocity, concentration, and temperature profile is discussed graphically. It is noted that the heat transfer rate of EO is improved by 28.24% when the volume fraction of Ag nanoparticles is raised from 0.00 to 0.04.

scholarly journals Fractional model for MHD flow of Casson fluid with cadmium telluride nanoparticles using the generalized Fourier’s law

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nadeem Ahmad Sheikh ◽  
Dennis Ling Chuan Ching ◽  
Ilyas Khan ◽  
Hamzah Bin Sakidin ◽  
Muhammad Jamil ◽  
...  
Keyword(s):  
Energy Equation ◽  
Volume Fraction ◽  
Mhd Flow ◽  
Integral Transforms ◽  
Casson Fluid ◽  
Physical Parameters ◽  
Fourier’S Law ◽  
Fractional Model ◽  
Laplace Transformations ◽  
Fourier's Law

AbstractThe present work used fractional model of Casson fluid by utilizing a generalized Fourier’s Law to construct Caputo Fractional model. A porous medium containing nanofluid flowing in a channel is considered with free convection and electrical conduction. A novel transformation is applied for energy equation and then solved by using integral transforms, combinedly, the Fourier and Laplace transformations. The results are shown in form of Mittag-Leffler function. The influence of physical parameters have been presented in graphs and values in tables are discussed in this work. The results reveal that heat transfer increases with increasing values of the volume fraction of nanoparticles, while the velocity of the nanofluid decreases with the increasing values of volume fraction of these particles.

Effects of uniform or non-uniform heating at bottom wall on MHD mixed convection in a porous cavity saturated by nanofluid

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Subramanian Muthukumar ◽  
Selvaraj Sureshkumar ◽  
Arthanari Malleswaran ◽  
Murugan Muthtamilselvan ◽  
Eswari Prem
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Transfer Rate ◽  
Hartmann Number ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Darcy Number ◽  
Bottom Wall ◽  
Uniform Heating ◽  
The Magnetic Field

Abstract A numerical investigation on the effects of uniform and non-uniform heating of bottom wall on mixed convective heat transfer in a square porous chamber filled with nanofluid in the appearance of magnetic field is carried out. Uniform or sinusoidal heat source is fixed at the bottom wall. The top wall moves in either positive or negative direction with a constant cold temperature. The vertical sidewalls are thermally insulated. The finite volume approach based on SIMPLE algorithm is followed for solving the governing equations. The different parameters connected with this study are Richardson number (0.01 ≤ Ri ≤ 100), Darcy number (10−4 ≤ Da ≤ 10−1), Hartmann number (0 ≤ Ha ≤ 70), and the solid volume fraction (0.00 ≤ χ ≤ 0.06). The results are presented graphically in the form of isotherms, streamlines, mid-plane velocities, and Nusselt numbers for the various combinations of the considered parameters. It is observed that the overall heat transfer rate is low at Ri = 100 in the positive direction of lid movement, whereas it is low at Ri = 1 in the negative direction. The average Nusselt number is lowered on growing Hartmann number for all considered moving directions of top wall with non-uniform heating. The low permeability, Da = 10−4 keeps the flow pattern same dominating the magnetic field, whereas magnetic field strongly affects the flow pattern dominating the high Darcy number Da = 10−1. The heat transfer rate increases on enhancing the solid volume fraction regardless of the magnetic field.

scholarly journals Heat Transmission Reinforcers Induced by MHD Hybrid Nanoparticles for Water/Water-EG Flowing over a Cylinder

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 623
Author(s):  
Firas A. Alwawi ◽  
Mohammed Z. Swalmeh ◽  
Amjad S. Qazaq ◽  
Ruwaidiah Idris
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Liquid Velocity ◽  
Flow Characteristics ◽  
Hybrid Nanoparticles ◽  
Critical Parameters ◽  
Heat Transmission ◽  
Constant Wall Temperature

The assumptions that form our focus in this study are water or water-ethylene glycol flowing around a horizontal cylinder, containing hybrid nanoparticles, affected by a magnetic force, and under a constant wall temperature, in addition to considering free convection. The Tiwari–Das model is employed to highlight the influence of the nanoparticles volume fraction on the flow characteristics. A numerical approximate technique called the Keller box method is implemented to obtain a solution to the physical model. The effects of some critical parameters related to heat transmission are also graphically examined and analyzed. The increase in the nanoparticle volume fraction increases the heat transfer rate and liquid velocity; the strength of the magnetic field has an adverse effect on liquid velocity, heat transfer, and skin friction. We find that cobalt nanoparticles provide more efficient support for the heat transfer rate of aluminum oxide than aluminum nanoparticles.

scholarly journals Parametric analysis of the heat transfer behavior of the nano-particle ionic-liquid flow between concentric cylinders

2021 ◽  
Vol 13 (6) ◽  
pp. 168781402110240
Author(s):  
Rehan Ali Shah ◽  
Hidayat Ullah ◽  
Muhammad Sohail Khan ◽  
Aamir Khan
Keyword(s):  
Heat Transfer ◽  
Ionic Liquid ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Heat Source ◽  
Ordinary Differential Equations ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Concentric Cylinders

This paper investigates the enhanced viscous behavior and heat transfer phenomenon of an unsteady two di-mensional, incompressible ionic-nano-liquid squeezing flow between two infinite parallel concentric cylinders. To analyze heat transfer ability, three different type nanoparticles such as Copper, Aluminum [Formula: see text], and Titanium oxide [Formula: see text] of volume fraction ranging from 0.1 to 0.7 nm, are added to the ionic liquid in turns. The Brinkman model of viscosity and Maxwell-Garnets model of thermal conductivity for nano particles are adopted. Further, Heat source [Formula: see text], is applied between the concentric cylinders. The physical phenomenon is transformed into a system of partial differential equations by modified Navier-Stokes equation, Poisson equation, Nernst-Plank equation, and energy equation. The system of nonlinear partial differential equations, is converted to a system of coupled ordinary differential equations by opting suitable transformations. Solution of the system of coupled ordinary differential equations is carried out by parametric continuation (PC) and BVP4c matlab based numerical methods. Effects of squeeze number ( S), volume fraction [Formula: see text], Prandtle number (Pr), Schmidt number [Formula: see text], and heat source [Formula: see text] on nano-ionicliquid flow, ions concentration distribution, heat transfer rate and other physical quantities of interest are tabulated, graphed, and discussed. It is found that [Formula: see text] and Cu as nanosolid, show almost the same enhancement in heat transfer rate for Pr = 0.2, 0.4, 0.6.

scholarly journals Numerical Analysis of Nanofluids in Differentially Heated Enclosure Undergoing Orthogonal Rotation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
H. Saleh ◽  
I. Hashim
Keyword(s):  
Heat Transfer ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Convection Heat Transfer ◽  
Staggered Grid ◽  
Governing Equations ◽  
Nanoparticles Concentration ◽  
Quantity Of Heat ◽  
Velocity Pressure

Natural convection heat transfer in a rotating, differentially heated enclosure is studied numerically in this paper. The rotating enclosure is filled with water-Ag, water-Cu, water-Al2O3, or water-TiO2nanofluids. The governing equations are in velocity, pressure, and temperature formulation and solved using the staggered grid arrangement together with MAC method. The governing parameters considered are the solid volume fraction,0.0 ≤ ϕ ≤ 0.05, and the rotational speeds,3.5≤ Ω ≤ 17.5 rpm, and the centrifugal force is smaller than the Coriolis force and both forces were kept below the buoyancy force. It is found that the angular locations of the local maximums heat transfer were sensitive to rotational speeds and nanoparticles concentration. The global quantity of heat transfer rate increases about 1.5%, 1.1%, 0.8%, and 0.6% by increasing 1%ϕof the nanoparticles Ag, Cu, Al2O3, and TiO2, respectively, for the considered rotational speeds.

scholarly journals 3D Magneto-Buoyancy-Thermocapillary Convection of CNT-Water Nanofluid in the Presence of a Magnetic Field

Processes ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 258 ◽  
Author(s):  
Lioua Kolsi ◽  
Salem Algarni ◽  
Hussein A. Mohammed ◽  
Walid Hassen ◽  
Emtinene Lajnef ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Flow Structure ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Numerical Study ◽  
Flow Stabilization ◽  
Magnetic Field Magnitude ◽  
The Magnetic Field

A numerical study is performed to investigate the effects of adding Carbon Nano Tube (CNT) and applying a magnetic field in two directions (vertical and horizontal) on the 3D-thermo-capillary natural convection. The cavity is differentially heated with a free upper surface. Governing equations are solved using the finite volume method. Results are presented in term of flow structure, temperature field and rate of heat transfer. In fact, results revealed that the flow structure and heat transfer rate are considerably affected by the magnitude and the direction of the magnetic field, the presence of thermocapillary forces and by increasing nanoparticles volume fraction. In opposition, the increase of the magnetic field magnitude leads to the control the flow causing flow stabilization by merging vortexes and reducing heat transfer rate.

scholarly journals Role of Rotating Cylinder toward Mixed Convection inside a Wavy Heated Cavity via Two-Phase Nanofluid Concept

Nanomaterials ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 1138 ◽  
Author(s):  
Ammar I. Alsabery ◽  
Mohammad Ghalambaz ◽  
Taher Armaghani ◽  
Ali Chamkha ◽  
Ishak Hashim ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Rotating Cylinder ◽  
Alumina Nanoparticles ◽  
Optimum Number ◽  
Two Phase ◽  
Rotation Direction

The mixed convection two-phase flow and heat transfer of nanofluids were addressed within a wavy wall enclosure containing a solid rotating cylinder. The annulus area between the cylinder and the enclosure was filled with water-alumina nanofluid. Buongiorno’s model was applied to assess the local distribution of nanoparticles in the host fluid. The governing equations for the mass conservation of nanofluid, nanoparticles, and energy conservation in the nanofluid and the rotating cylinder were carried out and converted to a non-dimensional pattern. The finite element technique was utilized for solving the equations numerically. The influence of the undulations, Richardson number, the volume fraction of nanoparticles, rotation direction, and the size of the rotating cylinder were examined on the streamlines, heat transfer rate, and the distribution of nanoparticles. The Brownian motion and thermophoresis forces induced a notable distribution of nanoparticles in the enclosure. The best heat transfer rate was observed for 3% volume fraction of alumina nanoparticles. The optimum number of undulations for the best heat transfer rate depends on the rotation direction of the cylinder. In the case of counterclockwise rotation of the cylinder, a single undulation leads to the best heat transfer rate for nanoparticles volume fraction about 3%. The increase of undulations number traps more nanoparticles near the wavy surface.

3D optimization of baffle arrangement in a multi-phase nanofluid natural convection based on numerical simulation

2019 ◽  
Vol 30 (5) ◽  
pp. 2583-2605 ◽  
Author(s):  
Mohammad Mohsen Peiravi ◽  
Javad Alinejad ◽  
D.D. Ganji ◽  
Soroush Maddah
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Target Function ◽  
Optimal Arrangement ◽  
Content Type ◽  
Multi Phase

Purpose The purpose of this study is investigating the effect of using multi-phase nanofluids, Rayleigh number and baffle arrangement simultaneously on the heat transfer rate and Predict the optimal arrangement type of baffles in the differentiation of Rayleigh number in a 3D enclosure. Design/methodology/approach Simulations were performed on the base of the L25 Taguchi orthogonal array, and each test was conducted under different height and baffle arrangement. The multi-phase thermal lattice Boltzmann based on the D3Q19 method was used for modeling fluid flow and temperature fields. Findings Streamlines, isotherms, nanofluid volume fraction distribution and Nusselt number along the wall surface for 104 < Ra < 108 have been demonstrated. Signal-to-noise ratios have been analyzed to predict optimal conditions of maximize and minimize the heat transfer rate. The results show that by choosing the appropriate height and arrangement of the baffles, the average Nusselt number can be changed by more than 57 per cent. Originality/value The value of this paper is surveying three-dimensional and two-phase simulation for nanofluid. Also using the Taguchi method for Predicting the optimal arrangement type of baffles in a multi-part enclosure. Finally statistical analysis of the results by using of two maximum and minimum target Function heat transfer rates.

The impacts of non-uniform magnetic field on free convection heat transfer of a magnetizable micropolar nanofluid

2019 ◽  
Vol 29 (10) ◽  
pp. 3685-3706
Author(s):  
Zafar Namazian ◽  
S.A.M. Mehryan
Keyword(s):  
Heat Transfer ◽  
Free Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Convection Heat Transfer ◽  
Content Type ◽  
Viscosity Parameter ◽  
Micropolar Nanofluid ◽  
Free Convection Heat

Purpose The purpose of this study is to numerically study the heat transfer of free convection of a magnetizable micropolar nanofluid inside a semicircular enclosure. Design/methodology/approach The flow domain is under simultaneous influences of two non-uniform magnetic fields generated by current carrying wires. The directions of the currents are the same. Although the geometry is symmetric, it is physically asymmetric. The impacts of key parameters, including Rayleigh number Ra = 103-106, Hartman number Ha = 0-50, vortex viscosity parameter Δ = 0-4, nanoparticles volume fraction φ = 0-0.04 and magnetic number Mnf = 0-1000, on the macro- and micro-scales flows, temperature and heat transfer rate are studied. Finding The outcomes show that dispersing of the nanoparticles in the host fluid increases the strength of macro- and micro-scale flows. When Mnf = 0, the increment of the vortex viscosity parameter increases the strength of the particles micro-rotations, while this characteristic is decreased by growing Δ for Mnf ≠ 0. The increment of Δ and Ha decreases the rate of heat transfer. The increment of Ha decreases the enhancement percentage of heat transfer rate because of dispersing nanoparticles, known as En parameter. In addition, the value of Δ has no effect on En. Moreover, the average Nusselt number Nuavg and En remain constant by increasing the magnetic number Mnf for different volume fraction values. Originality/value The authors believe that all of the results, both numerical and asymptotic, are original and have not been published elsewhere yet.

scholarly journals Mixed convective hybrid nanofluid flow in lid-driven undulated cavity: effect of MHD and Joule heating

2019 ◽  
Vol 16 (2) ◽  
pp. 109-126 ◽  
Author(s):  
Ishrat Zahan ◽  
R Nasrin ◽  
M A Alim
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Rate ◽  
Joule Heating ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Hybrid Nanoparticles ◽  
Wave Number ◽  
Hybrid Nanofluid

A numerical analysis has been conducted to show the effects of magnetohydrodynamic (MHD) and Joule heating on heat transfer phenomenon in a lid driven triangular cavity. The heat transfer fluid (HTF) has been considered as water based hybrid nanofluid composed of equal quantities of Cu and TiO2 nanoparticles. The bottom wall of the cavity is undulated in sinusoidal pattern and cooled isothermally. The left vertical wall of the cavity is heated while the inclined side is insulated. The two dimensional governing partial differential equations of heat transfer and fluid flow with appropriate boundary conditions have been solved by using Galerkin's finite element method built in COMSOL Multyphysics. The effects of Hartmann number, Joule heating, number of undulation and Richardson number on the flow structure and heat transfer characteristics have been studied in details. The values of Prandtl number and solid volume fraction of hybrid nanoparticles have been considered as fixed. Also, the code validation has been shown. The numerical results have been presented in terms of streamlines, isotherms and average Nusselt number of the hybrid nanofluid for different values of governing parameters. The comparison of heat transfer rate by using hybrid nanofluid, Cu-water nanofluid,  TiO2 -water nanofluid and clear water has been also shown. Increasing wave number from 0 to 3 enhances the heat transfer rate by 16.89%. The enhanced rate of mean Nusselt number for hybrid nanofluid is found as 4.11% compared to base fluid.

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