scholarly journals Magnetohydrodynamic Effects in Mixed Convection Copper-Water Nano Fluid Flow at Lower Stagnation Point on a Sliced Sphere

CFD Letters ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 21-31
Author(s):  
Basuki Widodo ◽  
Adhi Surya Nugraha ◽  
Dieky Adzkiya ◽  
Mohd Zuki Salleh
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Copper Particle ◽  
Particle Volume ◽  
Nano Fluid ◽  
Determining Factors

The study of simulation and applications of mathematics in fluid dynamics continues to grow along with the development of computer science and technology. One of them is Magnetohydrodynamics (MHD) which is closely related to its implementation in engineering and industry. And given the importance of magnetic fluid flow has attracted researchers to study and explore its benefits and uses in the industrial field, especially in convective flow and heat transfer processes. This paper therefore considers mathematical modeling on mixed convection MHD viscous fluid flow on the lower stagnation point of a magnetic sliced sphere. The study began with transforming the governing equations which are in dimensional partial differential equations to non-dimensional ordinary differential equations by using the similarity variable. The resulting similarity equations are then solved by the Keller-Box scheme. The characteristics and effects of the Prandtl number, the sliced angle, the magnetic parameter, and the mixed convection parameter are analyzed and discussed. The results depicted that the uniform magnetic field produced by Lorentz force and slicing on the sphere act as determining factors for the trend of nano fluid movement and controlling the cooling rate of the sphere surface. In addition, the viscosity depends on the copper particle volume fraction.

Mixed convection boundary layer flow from a vertical truncated cone in a nanofluid

2014 ◽  
Vol 24 (5) ◽  
pp. 1175-1190 ◽  
Author(s):  
F.O. Pătrulescu ◽  
T. Groşan ◽  
I. Pop
Keyword(s):  
Boundary Layer ◽  
Mixed Convection ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Convection Boundary Layer ◽  
Particle Volume ◽  
Content Type ◽  
Mixed Convection Parameter ◽  
Layer Flow ◽  
Convection Parameter

Purpose – The purpose of this paper is to investigate the steady mixed convection boundary layer flow from a vertical frustum of a cone in water-based nanofluids. The problem is formulated to incorporate three kinds of nanoparticles: copper, alumina and titanium oxide. The working fluid is chosen as water with the Prandtl number of 6.2. The mathematical model used for the nanofluid incorporates the particle volume fraction parameter, the effective viscosity and the effective thermal diffusivity. The entire regime of the mixed convection includes the mixed convection parameter, which is positive for the assisting flow (heated surface of the frustum cone) and negative for the opposing flow (cooled surface of the frustum cone), respectively. Design/methodology/approach – The transformed non-linear partial differential equations are solved numerically for some values of the governing parameters. The derivatives with respect to? were discretized using the first order upwind finite differences and the resulting ordinary differential equations with respect to? were solved using bvp4c routine from Matlab. The absolute error tolerance in bvp4c was 1e-9. Findings – The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. The effects of the particle volume fraction parameter \phi, the mixed convection parameter \lambda and the dimensionless coordinate? on the flow and heat transfer characteristics are determined only for the Cu nanoparticles. It is found that dual solutions exist for the case of opposing flows. The range of the mixed convection parameter for which the solution exists increases in the presence of the nanofluids. Originality/value – The paper models the mixed convection from a vertical truncated cone using the boundary layer approximation. Multiple (dual) solutions for the flow reversals are obtained and the range of existence of the solutions was found. Particular cases for ?=0 (full cone), ? >>1 and (free convection limit) \lambda>>1were studied. To the authors best knowledge this problem has not been studied before and the results are new and original.

The Investigation of Proppant Particle-Fluid Flow in the Vertical Fracture with a Contracted Aperture

SPE Journal ◽  
2021 ◽  
pp. 1-18
Author(s):  
Hai Qu ◽  
Rui Wang ◽  
Xiang Ao ◽  
Ling Xue ◽  
Zhonghua Liu ◽  
...  
Keyword(s):  
Fluid Flow ◽  
Volume Fraction ◽  
Particle Density ◽  
Particle Volume Fraction ◽  
Experimental Results ◽  
Fluid Viscosity ◽  
Flow Conditions ◽  
Particle Volume ◽  
Proppant Transport ◽  
Bed Height

Summary Proppant placement plays a crucial role in maintaining the conductivity of fractures after a hydraulic fracturing treatment. The process involves the transport of particles by fluid flow in complex fractures. Many studies have focused on proppant transport and distribution in the fracture with a constant aperture, but relatively few studies have investigated the proppant-fluid flow in a vertical fracture with a contracted aperture. In this work, we examine experimentally proppant transport in a fracture with a contracted aperture. The objective is to evaluate the distribution of particle beds in the contracted fracture at different flow conditions. In this paper, particle-fluid flow in the contracted fracture is studied experimentally by a laboratory size slot. A planar slot with a constant width is used to benchmark the experimental results, and a published correlation validates the bed equilibrium heights in the planar slot. Six types of particles are chosen to simulate the effects of particle density and size. The proppant distribution is evaluated by the bed height when the bed reaches the equilibrium states. The effects of fluid velocity, fluid viscosity, particle density, particle size, and particle volume fraction on particle distribution are investigated. The results confirm that the proppant particle-fluid flow in the contracted slot is more complicated than that in the planar slot. The phenomena of particle vortices and resuspension were observed at the contraction of the cross-section. The shape on the top of the bed is like a descending stair in which the height gradually decreases in the length direction. The bed height in the contracted slot is lower and more irregular than that in the planar slot at the same flow conditions. Smaller sands injected at a high flow rate and fluid viscosity can form a lower bed. The trend would be reversed by using denser particles and high particle volume fraction. A reliable model expressed by four dimensionless numbers is developed by the linear regression method for predicting the bed equilibrium height. The model and experimental results provide directions to quantitatively evaluate the particle transport and distribution in a fracture with a contracted aperture.

scholarly journals Mixed Convection Stagnation-Point Flow of a Nanofluid Past a Permeable Stretching/Shrinking Sheet in the Presence of Thermal Radiation and Heat Source/Sink

Energies ◽  
2019 ◽  
Vol 12 (5) ◽  
pp. 788 ◽  
Author(s):  
Anuar Jamaludin ◽  
Roslinda Nazar ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Heat Source ◽  
Mixed Convection ◽  
Thermal Radiation ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Suction Parameter ◽  
Source Sink

In this study we numerically examine the mixed convection stagnation-point flow of a nanofluid over a vertical stretching/shrinking sheet in the presence of suction, thermal radiation and a heat source/sink. Three distinct types of nanoparticles, copper (Cu), alumina (Al2O3) and titania (TiO2), were investigated with water as the base fluid. The governing partial differential equations were converted into ordinary differential equations with the aid of similarity transformations and solved numerically by utilizing the bvp4c programme in MATLAB. Dual (upper and lower branch) solutions were determined within a particular range of the mixed convection parameters in both the opposing and assisting flow regions and a stability analysis was carried out to identify which solutions were stable. Accordingly, solutions were gained for the reduced skin friction coefficients, the reduced local Nusselt number, along with the velocity and temperature profiles for several values of the parameters, which consists of the mixed convection parameter, the solid volume fraction of nanoparticles, the thermal radiation parameter, the heat source/sink parameter, the suction parameter and the stretching/shrinking parameter. Furthermore, the solutions were presented in graphs and discussed in detail.

Mixed convection stagnation point flow of a hybrid nanofluid past a vertical flat plate with a second order velocity model

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alin V. Roşca ◽  
Natalia C. Roşca ◽  
Ioan Pop
Keyword(s):  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Second Order ◽  
Hybrid Nanofluid ◽  
Content Type ◽  
Practical Applications ◽  
Hybrid Nanofluids

Purpose The purpose of this study is to describe the steady mixed convection stagnation point of a hybrid nanofluid with a second-order velocity slip. Design/methodology/approach Using appropriate similarity variables, the partial differential equations are transformed into ordinary (similar) differential equations, which are numerically solved using the bvp4c function in MATLAB. The numerical results are used to present graphical illustrations for the reduced skin friction, reduced Nusselt number, velocity and temperature profiles. Findings Dual solutions are discovered in this study. Thus, stability analysis is implemented and the first (upper branch) and second (lower branch) solutions are determined and analyzed. Research limitations/implications Hybrid nanofluids have many practical applications in the modern industry such as in micro-manufacturing, periodic heat exchanges process, nano drug delivery system and nuclear reactors. Originality/value Despite numerous studies on the mixed convection stagnation point of classical viscous fluids past a vertical plate flow, none of the researchers have focused on the effect of second-order slip velocity on hybrid nanofluids. The behavior of the flow and heat transfer has been thoroughly analyzed with the variations in governing parameters such as heat source/sink and nanoparticle volume fraction. Moreover, the use of the wall slip velocity in this hybrid nanofluid model strengthened the novelty of this study.

scholarly journals Separation time analysis of transient magnetohydrodynamic mixed convection flow of nanofluid at lower stagnation point past a sphere

2017 ◽  
Vol 13 (3) ◽  
Author(s):  
Mohamad Alif Ismail ◽  
Nurul Farahain Mohammad ◽  
Sharidan Shafie
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Stagnation Point ◽  
Magnetic Particles ◽  
Volume Fraction ◽  
Convection Flow ◽  
Mixed Convection Flow ◽  
Boundary Layer Equations ◽  
Keller Box Method

In this paper, the unsteady magnetohydrodynamics (MHD) mixed convection flow of nanofluid at lower stagnation point past a sphere is studied. Nanoparticles Cu and TiO2 with water as a base fluid are considered. The separation times of the flow as the boundary layer start to separate at the surface of the sphere are given attention. The governing boundary layer equations in the form of partial differential equations are transformed into nonlinear coupled ordinary differential equations and solved numerically using an implicit finite-difference scheme known as Keller-box method. Results of the separation times of boundary layer flow for viscous and nanofluid influenced by magnetic parameter and volume fraction are shown in tabular form and analysed. This study concluded that the separation times can be delayed by added more magnetic particles and small amount the volume fraction.

scholarly journals Mixed Convection in Lid-Driven “T” Shallow Cavity Heated From Bottom and Filled by Two Immiscible Fluids of Air and Al2O3-Water Nanofluid

2020 ◽  
Vol 330 ◽  
pp. 01008
Author(s):  
Aimad koulali ◽  
Bachir Meziani ◽  
Djamel Sadaoui ◽  
Massinissa Adnani ◽  
Adel Sahi
Keyword(s):  
Mixed Convection ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Thermal Characteristics ◽  
Immiscible Fluids ◽  
Geometrical Shape ◽  
Particle Volume ◽  
Convex Shape ◽  
Two Fluids ◽  
Shallow Cavity

This work present numerical simulation results of mixed convection in lid-driven “T” shallow cavity, filled by two immiscible fluids layers of air and Al2O3-water nanofluid. Mixed convection condition is created by the upper wall movement and temperature difference between the alveolus bottom and upper wall. Hydrodynamic and thermal characteristics of the flow have been predicted by solving the Navier- Stokes and energy equation using finite volume method. Coupling between two fluids layers are achieved using continuity of temperature and velocity at the interface air-nanofluid. Nano-particle volume fraction effect and geometrical shape of alveolus sidewalls (plane shape, concave shape and convex shape) have been chosen as discussed parameters. Analysis of obtained results shows that the heat transfer rate decreased with increasing volume fraction of solid inside the nanofluid layer. In addition, geometrical shape of alveolus sidewalls has a poor effect on flow structure and isotherms distribution in the physical domain.

scholarly journals Dusty Nanofluid Past a Centrifugally Stretching Surface

2020 ◽  
Vol 2020 ◽  
pp. 1-16 ◽  
Author(s):  
Wubshet Ibrahim ◽  
Dachasa Gamachu
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Velocity Profile ◽  
Ordinary Differential Equations ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Stretching Surface ◽  
Particle Volume ◽  
Magnetic Field Parameter ◽  
The Magnetic Field

This communication reports, the flow of Cu-water dusty nanofluid past a centrifugally stretching surface under the effect of second order slip and convective boundary conditions. The coupled nonlinear ordinary differential equations are get hold of from the partial differential equations which are derived from the conservation of momentum and energy of both nanofluid and dusty phases. Then, using apt resemblance transformation these ordinary differential equations were altered into a dimensionless form and then solved by bvp5c solver in Matlab software. The variation in velocity and temperature profiles of fluid and dusty phases for different parameters are thrash out in depth by figures and tables. The outcomes exhibit that the velocity profile of both fluid and dusty phases boot as the values of the dust particle volume fraction parameter is enlarged. Besides, the magnetic field parameter has similar effect on the velocity profile of both fluid and dusty phases. Also, the results illustrated that temperature profile of both Cu-water nanofluid and dusty particle phases are improved within an enhancement in the values of the temperature relaxation parameter, Cu-particle volume fraction, and Biot number. The results also confirm that for greater values of the magnetic field parameter the values of skin friction coefficient are enlarged for all values of the velocity ratio parameter.

The Effect of Variable Viscosities on Micropolar Flow of Two Nanofluids

2016 ◽  
Vol 71 (12) ◽  
pp. 1121-1129 ◽  
Author(s):  
S. Nadeem ◽  
Z. Ahmed ◽  
S. Saleem
Keyword(s):  
Differential Equations ◽  
Volume Fraction ◽  
Nonlinear Differential Equations ◽  
Particle Volume Fraction ◽  
Nonlinear Partial Differential Equations ◽  
Rotational Inertia ◽  
Physical Parameters ◽  
Particle Volume ◽  
Viscosity Parameter ◽  
Similarity Transformations

AbstractA study of nanofluids is carried out that reveals the effect of rotational inertia and other physical parameters on the heat transfer and fluid flow. Temperature-dependent dynamic viscosity makes the microrotation viscosity parameter and the micro inertia density variant as well. The governing nonlinear partial differential equations are converted into a set of nonlinear ordinary differential equations by introducing suitable similarity transformations. These reduced nonlinear differential equations are then solved numerically by Keller-box method. The obtained numerical and graphical result discloses many interesting behaviour of nanofluids. It is seen that the temperature gradient decreases with the increase in viscosity parameter. Also, it is observed that with the fixed values of micropolar parameter and viscosity parameter, the velocity gradient near the wall increases with increasing values of solid particle volume fraction parameter. A suitable comparison of results is also presented in this study.

Effect of Uncertainties in Physical Properties on Mixed Convection Along a Rotating Vertical Slender Cylinder With Nanofluids

2014 ◽  
Author(s):  
Puneet Rana ◽  
Lokendra Kumar
Keyword(s):  
Nusselt Number ◽  
Mixed Convection ◽  
Physical Properties ◽  
Single Phase ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Particle Volume ◽  
Linear Partial Differential Equations ◽  
Flow And Heat Transfer ◽  
Experimental Findings

The present investigation is aimed to study the effects of uncertainties in physical properties on predicting mixed convection alumina-water nanofluid flow and heat transfer characteristics along a rotating vertical slender cylinder. For this purpose, the different models for thermal conductivity and dynamic viscosity which takes into account the effects of particle size, particle volume fraction, nanolayer conductivity and temperature on the steady boundary layer are applied. The transformed set of coupled non-linear partial differential equations for the single phase nanofluid model is solved by robust Finite Element Method. The influence of various pertinent parameters on velocity profile, temperature profile and on Nusselt number are shown graphically. Excellent validation of the present numerical results has been achieved with earlier published results. It is also found that the Nusselt number increases nonlinearly with the increase of nanoparticle loading for the KKL model which correlates strongly with experimental findings.

scholarly journals Effects of magnetic field inclination and internal heat sources on nanofluid heat transfer and entropy generation in a double lid driven L-shaped cavity

2019 ◽  
pp. 325-325 ◽  
Author(s):  
Ali Chamkha ◽  
Zeinab Abdelrahman ◽  
Mohamed Mansour ◽  
Taher Armaghani ◽  
Ahmed Rashad
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Heat Source ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Internal Heat ◽  
Performance Criteria ◽  
Particle Volume

Mixed convection has been one of the most interesting subjects of study in the area of heat transfer for many years. The entropy generation due to MHD mixed convection heat transfer in L-shaped enclosure being filled with Cu-water nanofluid and having an internal heating generation is explored in this investigation by the finite volume technique. Lid-motion is presented by both right and top parts of walls to induce forced convection and the cavity is under an inclined uniform magnetic field along the positive horizontal direction. The statistics concentrated specifically on the impacts of several key parameters like as the aspect ratio of the enclosure, Hartmann number, nano-particle volume fraction, and heat source length/location on the heat transfer inside the L-shaped enclosure. Outcomes have been manifested in terms of isotherm lines, streamlines, local and average Nusselt numbers. The obtained results show that addition of nanoparticles into pure fluid leads to increase of heat transfer. The maximum value of local Nusselt pertaining to the heat source occurs when L=0.1. Impacts of heat source size and location, internal heat generation absorption, angle of magnetic field on heat transfer and entropy generation are completely analyzed and discussed. The best configuration and values of important parameters are also presented using thermal performance criteria.

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