Thermal Analysis of 3D Electromagnetic Radiative Nanofluid Flow with Suction/Blowing: Darcy–Forchheimer Scheme

This paper discusses the Darcy–Forchheimer three dimensional (3D) flow of a permeable nanofluid through a convectively heated porous extending surface under the influences of the magnetic field and nonlinear radiation. The higher-order chemical reactions with activation energy and heat source (sink) impacts are considered. We integrate the nanofluid model by using Brownian diffusion and thermophoresis. To convert PDEs (partial differential equations) into non-linear ODEs (ordinary differential equations), an effective, self-similar transformation is used. With the fourth–fifth order Runge–Kutta–Fehlberg (RKF45) approach using the shooting technique, the consequent differential system set is numerically solved. The influence of dimensionless parameters on velocity, temperature, and nanoparticle volume fraction profiles is revealed via graphs. Results of nanofluid flow and heat as well as the convective heat transport coefficient, drag force coefficient, and Nusselt and Sherwood numbers under the impact of the studied parameters are discussed and presented through graphs and tables. Numerical simulations show that the increment in activation energy and the order of the chemical reaction boosts the concentration, and the reverse happens with thermal radiation. Applications of such attractive nanofluids include plastic and rubber sheet production, oil production, metalworking processes such as hot rolling, water in reservoirs, melt spinning as a metal forming technique, elastic polymer substances, heat exchangers, emollient production, paints, catalytic reactors, and glass fiber production.

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Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

International Journal of Numerical Methods for Heat &amp Fluid Flow ◽

10.1108/hff-03-2020-0135 ◽

2020 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Soraya Torkaman ◽

Ghasem Barid Loghmani ◽

Mohammad Heydari ◽

Abdul-Majid Wazwaz

Keyword(s):

Mass Transfer ◽

Differential Equations ◽

Heat And Mass Transfer ◽

Stretching Sheet ◽

Volume Fraction ◽

Three Dimensional ◽

Operational Matrices ◽

Nanofluid Flow ◽

Content Type ◽

Nonlinearly Stretching Sheet

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

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Significance of Thermal Slip and Convective Boundary Conditions in Three Dimensional Rotating Darcy-Forchheimer Nanofluid Flow

Symmetry ◽

10.3390/sym12050741 ◽

2020 ◽

Vol 12 (5) ◽

pp. 741 ◽

Cited By ~ 10

Author(s):

Anum Shafiq ◽

Ghulam Rasool ◽

Chaudry Masood Khalique

Keyword(s):

Activation Energy ◽

Boundary Conditions ◽

Skin Friction ◽

Three Dimensional ◽

Brownian Diffusion ◽

Thermal Slip ◽

Convective Boundary Conditions ◽

Nanofluid Flow ◽

Convective Boundary ◽

Forchheimer Number

This article is concerned with the nanofluid flow in a rotating frame under the simultaneous effects of thermal slip and convective boundary conditions. Arrhenius activation energy is another important aspect of the present study. Flow phenomena solely rely on the Darcy–Forchheimer-type porous medium in three-dimensional space to tackle the symmetric behavior of viscous terms. The stretching sheet is assumed to drive the fluid. Buongiorno’s model is adopted to see the features of Brownian diffusion and thermophoresis on the basis of symmetry fundamentals. Governing equations are modeled and transformed into ordinary differential equations by suitable transformations. Solutions are obtained through the numerical RK45-scheme, reporting the important findings graphically. The outputs indicate that larger values of stretching reduce the fluid velocity. Both the axial and transverse velocity fields undergo much decline due to strong retardation produced by the Forchheimer number. The thermal radiation parameter greatly raises the thermal state of the field. The temperature field rises for a stronger reaction within the fluid flow, however reducing for an intensive quantity of activation energy. A declination in the concentration profile is noticed for stronger thermophoresis. The Forchheimer number and porosity factors result in the enhancement of the skin friction, while both slip parameters result in a decline of skin friction. The thermal slip factor results in decreasing both the heat and mass flux rates. The study is important in various industrial applications of nanofluids including the electro-chemical industry, the polymer industry, geophysical setups, geothermal setups, catalytic reactors, and many others.

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Soret–Dufour impact on a three-dimensional Casson nanofluid flow with dust particles and variable characteristics in a permeable media

Scientific Reports ◽

10.1038/s41598-021-93797-2 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Naila Shaheen ◽

Muhammad Ramzan ◽

Ahmed Alshehri ◽

Zahir Shah ◽

Poom Kumam

Keyword(s):

Activation Energy ◽

Particle Interaction ◽

Three Dimensional ◽

Concentration Field ◽

Fluid Particle ◽

Dust Particles ◽

Force Coefficient ◽

Nanofluid Flow ◽

Heat Condition ◽

Casson Nanofluid

AbstractIn this study, the effects of variable characteristics are analyzed on a three-dimensional (3D) dusty Casson nanofluid flow past a deformable bidirectional surface amalgamated with chemical reaction and Arrhenius activation energy. The surface is deformable in the direction of the x-axis and y-axis. The motion of the flow is induced due to the deformation of the surface. The impression of Soret and Dufour's effects boost the transmission of heat and mass. The flow is analyzed numerically with the combined impacts of thermal radiation, momentum slip, and convective heat condition. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The dimensionless parameters are graphically illustrated and discussed for the involved profiles. It is perceived that on escalating the Casson fluid and porosity parameters, the velocity field declines for fluid-particle suspension. Also, for augmented activation energy and Soret number, the concentration field enhances. An opposite behavior is noticed in the thermal field for fluctuation in fluid-particle interaction parameters for fluid and dust phase. Drag force coefficient increases on escalating porosity parameter and Hartmann number. On amplifying the radiation parameter heat and mass flux augments. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem.

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Three-Dimensional Water-Based Magneto-Hydrodynamic Rotating Nanofluid Flow over a Linear Extending Sheet and Heat Transport Analysis: A Numerical Approach

Energies ◽

10.3390/en14165133 ◽

2021 ◽

Vol 14 (16) ◽

pp. 5133

Author(s):

Azad Hussain ◽

Mubashar Arshad ◽

Aysha Rehman ◽

Ali Hassan ◽

S. K. Elagan ◽

...

Keyword(s):

Differential Equations ◽

Comparative Study ◽

Skin Friction ◽

Three Dimensional ◽

Numerical Approach ◽

Nanofluid Flow ◽

Two Phase ◽

Transport Analysis ◽

The Impact ◽

Phase Fluid

This comparative study inspects the heat transfer characteristics of magnetohydrodynamic (MHD) nanofluid flow. The model employed is a two-phase fluid flow model. Water is utilized as the base fluid, and zinc and titanium oxide (Zn and TiO2) are used as two different types of nanoparticles. The rotation of nanofluid is considered along the z-axis, with velocity ω*. A similarity transformation is used to transform the leading structure of partial differential equations to ordinary differential equations. By using a powerful mathematical BVP-4C technique, numerical results are obtained. This study aims to describe the possessions of different constraints on temperature and velocity for rotating nanofluid with a magnetic effect. The outcomes for the rotating nanofluid flow and heat transference properties for both types of nanoparticles are highlighted with the help of graphs and tables. The impact of physical concentrations such as heat transference rates and coefficients of skin friction are examined. It is noted that rotation increases the heat flux and decreases skin friction. In this comparative study, Zn-water nanofluid was demonstrated to be a worthy heat transporter as compared to TiO2-water nanofluid.

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Computational Investigation of the Combined Impact of Nonlinear Radiation and Magnetic Field on Three-Dimensional Rotational Nanofluid Flow across a Stretchy Surface

Processes ◽

10.3390/pr9081453 ◽

2021 ◽

Vol 9 (8) ◽

pp. 1453

Author(s):

Azad Hussain ◽

Mohamed Abdelghany Elkotb ◽

Mubashar Arshad ◽

Aysha Rehman ◽

Kottakkaran Sooppy Nisar ◽

...

Keyword(s):

Volume Fraction ◽

Three Dimensional ◽

Transfer Constant ◽

Nanofluid Flow ◽

Flow And Heat Transfer ◽

Distribution Shape ◽

Significant Temperature ◽

The Difference ◽

Combined Impact ◽

The Impact

This comparative study inspects the MHD three-dimensional revolving flow and temperature transmission of a radiative stretching surface. The flow of nanofluid is modeled using the Tiwari and Das model. Water is the base fluid, and the nanoparticles are composed of two different types of nanoparticle, i.e., gold and silver (Au and Ag). The non-radiative heat flow notion is examined in a temperature field that results in a nonlinear energy equation. Conformist transformations are used to generate a self-similar arrangement of the leading differential system. The resulting system has an intriguing temperature ratio constraint, which shows whether the flow has a little or significant temperature differential. By using a powerful mathematical technique, numerical results are obtained. The solutions are influenced by both stretching and rotation. The difference in velocity constituents with the elements’ volume fraction is non-monotonic. Results for the rotating nanofluid flow and heat transfer properties for both types of nanoparticles are highlighted with graphs. The impact of physical concentrations, such as heat flux rates and skin friction constants, are examined at the linear extending surface and clarified graphically. Ag-water nanofluid has a high-temperature transfer constant compared to Au-water nanofluid. The velocity profile was also discovered to have a parabolic distribution shape.

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Computational Study on Three-Dimensional Convective Casson Nanofluid Flow past a Stretching Sheet with Arrhenius Activation Energy and Exponential Heat Source Effects

Complexity ◽

10.1155/2021/5058751 ◽

2021 ◽

Vol 2021 ◽

pp. 1-16

Author(s):

P. Ragupathi ◽

S. Saranya ◽

H.V.R. Mittal ◽

Qasem M. Al-Mdallal

Keyword(s):

Activation Energy ◽

Differential Equations ◽

Heat Source ◽

Stretching Sheet ◽

Three Dimensional ◽

Arrhenius Activation Energy ◽

Nanofluid Flow ◽

Casson Nanofluid ◽

Source Effects ◽

Bio Engineering

The effective applications of Casson fluid in drilling processes, biological treatments, food processing, and bio-engineering activities have caught the interest of a wide range of researchers. The suitable knowledge of heat transfer via non-Newtonian fluid is essential for the achievement of best quality products in industry. Thus, the three-dimensional Casson nanofluid flow over a stretching sheet with Arrhenius activation energy and exponential heat source effects is investigated in this paper using a computational process based on iterative power series (IPS) method. To provide useful insights into the physical and dynamic examinations of this topic, convective heat and convective mass boundary conditions are used. The developed model of nonlinear partial differential equations (PDEs) has been transformed into ordinary differential equations (ODEs) using similarity transformations. The numerical solution of the transformed ODEs is obtained by employing the IPS technique combined with shooting iteration approach. The results of this study are validated with the previous studies, and excellent agreements have been obtained. The behavior of various capable physical parameters is analyzed. It is observed that the thermal and concentration fields show an enhancement with respect to the exponential heat source parameter and thermal and concentration Biot numbers. Further, the Arrhenius activation energy parameter has shown a significant effect on the concentration field.

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Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

Scientific Reports ◽

10.1038/s41598-020-74855-7 ◽

2020 ◽

Vol 10 (1) ◽

Cited By ~ 1

Author(s):

Muhammad Ramzan ◽

Jae Dong Chung ◽

Seifedine Kadry ◽

Yu-Ming Chu ◽

Muhammad Akhtar

Keyword(s):

Mathematical Model ◽

Carbon Nanotubes ◽

Drag Force ◽

Chemical Reaction ◽

Slip Velocity ◽

Volume Fraction ◽

Surface Drag ◽

Nanofluid Flow ◽

Velocity Parameter ◽

The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

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Mathematical analysis of bio-convective micropolar nanofluid

Journal of Computational Design and Engineering ◽

10.1016/j.jcde.2019.04.001 ◽

2019 ◽

Vol 6 (3) ◽

pp. 233-242 ◽

Cited By ~ 10

Author(s):

Sohail Nadeem ◽

Muhammad Naveed Khan ◽

Noor Muhammad ◽

Shafiq Ahmad

Keyword(s):

Differential Equations ◽

Microbial Fuel Cells ◽

Shooting Method ◽

Stretching Sheet ◽

Volume Fraction ◽

Three Dimensional ◽

Convection Flow ◽

Micropolar Nanofluid ◽

Exponentially Stretching ◽

Micro Organisms

Abstract The present investigation concentrates on three dimensional unsteady forced bio-convection flow of a viscous fluid. An incompressible flow of a micropolar nanofluid encloses micro-organisms past an exponentially stretching sheet with magnetic field is analyzed. By employing convenient transformation the partial differential equations are converted into the ordinary differential equations which are non-linear. By using shooting method to solved these equations numerically. The influence of the determining parameters on the velocity, temperature, micro-rotation, nanoparticle volume fraction, microorganism are incorporated. The skin friction, heat transfer rate, and the microorganism rate are analyzed. The results depicts that the value of the wall shear stress and Nusselt number are declined while an enhancement take place in the microorganism number. The slip parameters increases the velocity, thermal energy, and microorganism number consequentially. The present investigation are important in improving achievement of microbial fuel cells.

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Numerical Simulation of Heat Mass Transfer Effects on MHD Flow of Williamson Nanofluid by a Stretching Surface with Thermal Conductivity and Variable Thickness

Coatings ◽

10.3390/coatings11060684 ◽

2021 ◽

Vol 11 (6) ◽

pp. 684

Author(s):

Saeed Islam ◽

Haroon Ur Rasheed ◽

Kottakkaran Sooppy Nisar ◽

Nawal A. Alshehri ◽

Mohammed Zakarya

Keyword(s):

Thermal Conductivity ◽

Boundary Layer ◽

Mass Transfer ◽

Differential Equations ◽

Variable Thickness ◽

Heat Mass Transfer ◽

Mathematical Formulation ◽

Stretching Surface ◽

Nanofluid Flow ◽

The Impact

The current analysis deals with radiative aspects of magnetohydrodynamic boundary layer flow with heat mass transfer features on electrically conductive Williamson nanofluid by a stretching surface. The impact of variable thickness and thermal conductivity characteristics in view of melting heat flow are examined. The mathematical formulation of Williamson nanofluid flow is based on boundary layer theory pioneered by Prandtl. The boundary layer nanofluid flow idea yields a constitutive flow laws of partial differential equations (PDEs) are made dimensionless and then reduce to ordinary nonlinear differential equations (ODEs) versus transformation technique. A built-in numerical algorithm bvp4c in Mathematica software is employed for nonlinear systems computation. Considerable features of dimensionless parameters are reviewed via graphical description. A comparison with another homotopic approach (HAM) as a limiting case and an excellent agreement perceived.

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Computational Modeling of Hybrid Sisko Nanofluid Flow over a Porous Radially Heated Shrinking/Stretching Disc

Coatings ◽

10.3390/coatings11101242 ◽

2021 ◽

Vol 11 (10) ◽

pp. 1242

Author(s):

Umair Khan ◽

Aurang Zaib ◽

Anuar Ishak ◽

Fahad S. Al-Mubaddel ◽

Sakhinah Abu Bakar ◽

...

Keyword(s):

Differential Equations ◽

Flow Problem ◽

Shear Thickening ◽

Hybrid Nanofluid ◽

Nanofluid Flow ◽

Shear Thinning Fluids ◽

Water Based ◽

New Type ◽

The Impact ◽

The Magnetic Field

The present study reveals the behavior of shear-thickening and shear-thinning fluids in magnetohydrodynamic flow comprising the significant impact of a hybrid nanofluid over a porous radially shrinking/stretching disc. The features of physical properties of water-based Ag/TiO2 hybrid nanofluid are examined. The leading flow problem is formulated initially in the requisite form of PDEs (partial differential equations) and then altered into a system of dimensionless ODEs (ordinary differential equations) by employing suitable variables. The renovated dimensionless ODEs are numerically resolved using the package of boundary value problem of fourth-order (bvp4c) available in the MATLAB software. The non-uniqueness of the results for the various pertaining parameters is discussed. There is a significant enhancement in the rate of heat transfer, approximately 13.2%, when the impact of suction governs about 10% in the boundary layer. Therefore, the heat transport rate and the thermal conductivity are greater for the new type of hybrid nanofluid compared with ordinary fluid. The bifurcation of the solutions takes place in the problem only for the shrinking case. Moreover, the sketches show that the nanoparticle volume fractions and the magnetic field delay the separation of the boundarylayer.

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