Forced convection in 3D Maxwell nanofluid flow via Cattaneo–Christov theory with Joule heating

2021 ◽  
pp. 095440892199963
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Mahnoor Sarfraz ◽  
Jawad Ahmed ◽  
Zahoor Iqbal
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Joule Heating ◽  
Energy Transport ◽  
Fluid Motion ◽  
Analytical Technique ◽  
Maxwell Nanofluid ◽  
Homotopy Analysis ◽  
Non Linear System ◽  
The Impact

In this article, an investigation of the thermal and solutal energy transport in the 3 D flow of Maxwell nanofluid through a porous medium under the influence of the magnetic field is performed. The heat generation source and chemical reaction are also taken in account as a controlling agent for the heat and mass transport in the Maxwell liquid. A novel idea of Cattaneo-Christov theory and Buongiorno model for nanofluid is employed under the impact of Joule heating for the present analysis. The governing partial differential equations (PDEs) are transformed into a non-linear system of ordinary differential equations (ODEs) by using flow similarities. The solution of similar ODEs is constructed through a well known semi-analytical technique which is the homotopy analysis method. The results of the investigation are explored in the form of graphs. It is observed that higher values of magnetic field decline the flow field. The temperature and concentration distributions decrease with the higher magnitude of thermal and solutal relaxation time phenomena, respectively. Moreover, the temperature field enhances when the Brownian motion of nanoparticles increases in flow while the concentration profile decreases. Also, it is found that the increase in resistive heating boosts up the thermal energy transport in the fluid motion.

Influence of rotating magnetic field on Maxwell saturated ferrofluid flow over a heated stretching sheet with heat generation/absorption

2019 ◽  
Vol 20 (5) ◽  
pp. 502 ◽  
Author(s):  
Aaqib Majeed ◽  
Ahmed Zeeshan ◽  
Farzan Majeed Noori ◽  
Usman Masud
Keyword(s):  
Magnetic Field ◽  
Temperature Field ◽  
Velocity Field ◽  
Differential Equations ◽  
Heat Transport ◽  
Viscous Dissipation ◽  
Heat Generation ◽  
Fluid Motion ◽  
Numerical Procedure ◽  
The Impact

This article is focused on Maxwell ferromagnetic fluid and heat transport characteristics under the impact of magnetic field generated due to dipole field. The viscous dissipation and heat generation/absorption are also taken into account. Flow here is instigated by linearly stretchable surface, which is assumed to be permeable. Also description of magneto-thermo-mechanical (ferrohydrodynamic) interaction elaborates the fluid motion as compared to hydrodynamic case. Problem is modeled using continuity, momentum and heat transport equation. To implement the numerical procedure, firstly we transform the partial differential equations (PDEs) into ordinary differential equations (ODEs) by applying similarity approach, secondly resulting boundary value problem (BVP) is transformed into an initial value problem (IVP). Then resulting set of non-linear differentials equations is solved computationally with the aid of Runge–Kutta scheme with shooting algorithm using MATLAB. The flow situation is carried out by considering the influence of pertinent parameters namely ferro-hydrodynamic interaction parameter, Maxwell parameter, suction/injection and viscous dissipation on flow velocity field, temperature field, friction factor and heat transfer rate are deliberated via graphs. The present numerical values are associated with those available previously in the open literature for Newtonian fluid case (γ 1 = 0) to check the validity of the solution. It is inferred that interaction of magneto-thermo-mechanical is to slow down the fluid motion. We also witnessed that by considering the Maxwell and ferrohydrodynamic parameter there is decrement in velocity field whereas opposite behavior is noted for temperature field.

Thermally and chemically reacted MHD Maxwell nanofluid flow past an inclined permeable stretching surface

2021 ◽  
pp. 095440892110507
Author(s):  
Amar B. Patil ◽  
Vishwambhar S. Patil ◽  
Pooja P. Humane ◽  
Nalini S. Patil ◽  
Govind R. Rajput
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Surface ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Similarity Transformations ◽  
Flow Past ◽  
Chemically Reacting ◽  
The Impact

The present work deals with chemically reacting unsteady magnetohydrodynamic Maxwell nanofluid flow past an inclined permeable stretching surface embedded in a porous medium with thermal radiation. The formulated governing partial differential equations conveying the flow model of Maxwell with Buongiorno modeled nanofluid is transformed into the system of highly non-linear ordinary differential equations via suitable similarity transformations; those equations are transmuted into an initial value problem and then solved numerically by a shooting approach with Runge–-Kutta fourth-order schema. To obtain the physical insight of the flow situation, the influence of associated parameters on the velocity, temperature, and concentration profiles is sketched graphically with the aid of MATLAB software. Furthermore, engineering quantities of interest are interpreted graphically. The computed numerical results are compared to estimate the validity of the achieved results; it has been found out that the computed results are highly accurate. The impact of the Maxwell parameter and inclination angle of the sheet on the velocity field is observed in decaying. Both thermal and solutal energy transport are progressive in nature as the Maxwell parameter and thermophoresis parameter grows, and a reverse trend is observed for Prandtl number.

Fluid relaxation and retardation time properties in the flow of Burgers fluid subject to modified heat and mass flux theory

2021 ◽  
pp. 095440892110670
Author(s):  
Zahoor Iqbal ◽  
Awais Ahmed ◽  
Amina Anwar ◽  
Sivanandam Sivasankaran ◽  
Ali Saleh Alshomrani ◽  
...  
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Flow Problem ◽  
Fluid Motion ◽  
Retardation Time ◽  
Linear Ordinary Differential Equations ◽  
Fluid Parameter ◽  
Burgers Fluid ◽  
Time Parameters ◽  
The Impact

In this study, the heat transport is scrutinized in the flow of magnetized Burgers fluid accelerated by stretching cylinder. Rather than, classical Fourier's and Fick's laws, the Cattaneo-Christov theory featuring the improved heat and mass conduction is utilized to investigate the energy transport. Further, the transport of thermal and solutal energy is controlled by the significant influence of heat generation/absorption and chemical reaction. The physical flow problem is modelled in the form of partial differential equations (PDEs) which are then transformed into the non-linear ordinary differential equations (ODEs) by invoking appropriate similarity variables. The numerical simulation to the system of ODE's is tackled by employing BVP-Midrich scheme in Maple. The numerical results for flow field, thermal and concentration distributions are exhibited graphically. The impact of fluid relaxation and retardation time parameters on the velocity field are observed in growing and decaying way, respectively. Both the thermal and solutal energy transport decline with higher values of retardation time parameter. The rise in Burgers fluid parameter enhances the transport of energy during the fluid motion. The effect of thermal and solutal relaxation time parameters on heat and mass transport in the fluid are noticed in the declining manner.

scholarly journals Three-Dimensional Casson Nanofluid Thin Film Flow over an Inclined Rotating Disk with the Impact of Heat Generation/Consumption and Thermal Radiation

Coatings ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 248 ◽  
Author(s):  
Anwar Saeed ◽  
Zahir Shah ◽  
Saeed Islam ◽  
Muhammad Jawad ◽  
Asad Ullah ◽  
...  
Keyword(s):  
Thin Film ◽  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Boundary Layer ◽  
Energy Transport ◽  
Film Flow ◽  
Three Dimensional ◽  
Concentration Profiles ◽  
Thin Film Flow ◽  
The Impact

In this research, the three-dimensional nanofluid thin-film flow of Casson fluid over an inclined steady rotating plane is examined. A thermal radiated nanofluid thin film flow is considered with suction/injection effects. With the help of similarity variables, the partial differential equations (PDEs) are converted into a system of ordinary differential equations (ODEs). The obtained ODEs are solved by the homotopy analysis method (HAM) with the association of MATHEMATICA software. The boundary-layer over an inclined steady rotating plane is plotted and explored in detail for the velocity, temperature, and concentration profiles. Also, the surface rate of heat transfer and shear stress are described in detail. The impact of numerous embedded parameters, such as the Schmidt number, Brownian motion parameter, thermophoretic parameter, and Casson parameter (Sc, Nb, Nt, γ), etc., were examined on the velocity, temperature, and concentration profiles, respectively. The essential terms of the Nusselt number and Sherwood number were also examined numerically and physically for the temperature and concentration profiles. It was observed that the radiation source improves the energy transport to enhance the flow motion. The smaller values of the Prandtl number, Pr, augmented the thermal boundary-layer and decreased the flow field. The increasing values of the rotation parameter decreased the thermal boundary layer thickness. These outputs are examined physically and numerically and are also discussed.

scholarly journals Nonlinear translational symmetric equilibria relevant to the L–H transition

2012 ◽  
Vol 79 (3) ◽  
pp. 257-265 ◽  
Author(s):  
Ap. KUIROUKIDIS ◽  
G. N. THROUMOULOPOULOS
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Plasma Flow ◽  
Sufficient Condition ◽  
Sheared Flow ◽  
Equilibrium Configurations ◽  
Shafranov Equation ◽  
The Impact ◽  
The Magnetic Field

AbstractNonlinear z-independent solutions to a generalized Grad–Shafranov equation (GSE) with up to quartic flux terms in the free functions and incompressible plasma flow non-parallel to the magnetic field are constructed quasi-analytically. Through an ansatz, the GSE is transformed to a set of three ordinary differential equations and a constraint for three functions of the coordinate x, in Cartesian coordinates (x,y), which then are solved numerically. Equilibrium configurations for certain values of the integration constants are displayed. Examination of their characteristics in connection with the impact of nonlinearity and sheared flow indicates that these equilibria are consistent with the L–H transition phenomenology. For flows parallel to the magnetic field, one equilibrium corresponding to the H state is potentially stable in the sense that a sufficient condition for linear stability is satisfied in an appreciable part of the plasma while another solution corresponding to the L state does not satisfy the condition. The results indicate that the sheared flow in conjunction with the equilibrium nonlinearity plays a stabilizing role.

Mixed convective 3D flow of Maxwell nanofluid induced by stretching sheet: Application of Cattaneo-Christov theory

2020 ◽  
pp. 095440622097324
Author(s):  
Awais Ahmed ◽  
Masood Khan ◽  
Jawad Ahmed ◽  
Asia Anjum ◽  
Sohail Nadeem
Keyword(s):  
Differential Equations ◽  
Energy Transport ◽  
Stretching Sheet ◽  
Thermal Relaxation ◽  
Maxwell Fluid ◽  
Brownian Diffusion ◽  
Flow Mechanism ◽  
Linear Ordinary Differential Equations ◽  
Maxwell Nanofluid ◽  
Text Component

The present study invokes the application of Cattaneo-Christov theory for the thermal analysis in the buoyancy driven three dimensional flow of Maxwell nanofluid. The flow is induced above the vertical bidirectional stretching sheet. The phenomena of thermophoresis and Brownian diffusion of nanoparticles in the flow Maxwell liquid are deliberated with the help of Buongiorno model for nanofluid. The physical problem is formulated in the form of boundary layer partial differential equations (PDEs). Moreover, suitable ansatz for flow mechanism are employed to reduce the governing PDEs into the non-linear ordinary differential equations (ODEs). The flow mechanism of Maxwell fluid along with energy transport is analyzed in the form of homotopic solutions of the governing ODEs. The outcomes are presented graphically and discussed with physical explanation. The analysis revealed that both buoyancy and mixed convection parameters enhanced the [Formula: see text]-component of velocity field but declined the [Formula: see text]-component. Moreover, in assisting mode these two parameters also increased the thermal and solutal energy transport in nanofluid. It is noted that the thermophorectic force boosts up the thermal energy transport in the flow in the presence of thermal relaxation phenomenon. The validation of the present results are confirmed through tabular data with some previous studies.

scholarly journals The Consequences of Thermal Radiation and Chemical Reactions on Magneto-hydrodynamics in Two Dimensions Over a Stretching Sheet with Jeffrey Fluid.

2021 ◽  
Author(s):  
Vijay Patel ◽  
Jigisha Pandya
Keyword(s):  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Homotopy Analysis Method ◽  
Stretching Sheet ◽  
Fluid Velocity ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact

In this research paper, the Homotopy Analysis Method is used to investigate the twodimensional electrical conduction of a magneto-hydrodynamic (MHD) Jeffrey Fluid across a stretching sheet under various conditions, such as when electrical current and temperature are both present, and when heat is added in the presence of a chemical reaction or thermal radiation. Applying similarity transformation, the governing partial differential equation is transformed into terms of nonlinear coupled ordinary differential equations. The Homotopy Analysis Method is used to solve a system of ordinary differential equations. The impact of different numerical values on velocity, concentration, and temperature is examined and presented in tables and graphs. The fluid velocity reduces as the retardation time parameter(2) grows, while the fluid velocity inside the boundary layer increases as the Deborah number () increases. The velocity profiles decrease when the magnetic parameter M is increased. The results of this study are entirely compatible with those of a viscous fluid. The Homotopy Analysis Method calculations have been carried out on the PARAM Shavak high-performance computing (HPC) machine using the BVPh2.0 Mathematica tool.

Nonhomogeneous model for conjugate mixed convection of nanofluid and entropy generation in an enclosure in presence of inclined magnetic field with Joule heating

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Subhasree Dutta ◽  
Somnath Bhattacharyya ◽  
Ioan Pop
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Joule Heating ◽  
Conjugate Heat Transfer ◽  
Inclined Magnetic Field ◽  
Content Type ◽  
The Impact ◽  
The Magnetic Field

Purpose This study aims to numerically analyse the impact of an inclined magnetic field and Joule heating on the conjugate heat transfer because of the mixed convection of an Al2O3–water nanofluid in a thick wall enclosure. Design/methodology/approach A horizontal temperature gradient together with the shear-driven Flow creates the mixed convection inside the enclosure. The nonhomogeneous model, in which the nanoparticles have a slip velocity because of thermophoresis and Brownian diffusion, is adopted in the present study. The thermal performance is evaluated by determining the entropy generation, which includes the contribution because of magnetic field. A control volume method over a staggered grid arrangement is adopted to compute the governing equations. Findings The Lorentz force created by the applied magnetic field has an adverse effect on the flow and thermal field, and consequently, the heat transfer and entropy generation attenuate because of the presence of magnetic force. The Joule heating enhances the fluid temperature but attenuates the heat transfer. The impact of the magnetic field diminishes as the angle of inclination of the magnetic field is increased, and it manifests as the volume fraction of nanoparticles is increased. Addition of nanoparticles enhances both the heat transfer and entropy generation compared to the clear fluid with enhancement in entropy generation higher than the rate by which the heat transfer augments. The average Bejan number and mixing-cup temperature are evaluated to analyse the thermodynamic characteristics of the nanofluid. Originality/value This literature survey suggests that the impact of an inclined magnetic field and Joule heating on conjugate heat transfer based on a two-phase model has not been addressed before. The impact of the relative slip velocity of nanoparticles diminishes as the magnetic field becomes stronger.

Analytical simulation of nanoparticle-embedded blood flow control with magnetic field influence through spectra homotopy analysis method

2021 ◽  
pp. 2150226
Author(s):  
Ebenezer Olubunmi Ige ◽  
Funmilayo Helen Oyelami ◽  
Emmanuel Segun Adedipe ◽  
Iskander Tlili ◽  
M. Ijaz Khan ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Stagnation Point ◽  
Homotopy Analysis Method ◽  
Mathematical Problem ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
The Impact ◽  
Field Influence

Nanoparticles-based infusion strategies are presently being employed for a range of clinical interventions either for in vivo or in vitro applications while imposition of magnetic field is also identified as an important technique for fluid manipulation during nanoparticles-based propulsion. The impact of magnetic field to control of the transport of nanoparticles-based blood flow is demonstrated numerically over an elaborate variant of transport mechanisms. Mathematical formulations were undertaken and stability analysis of the mathematical problem was a scrutinized by generation of eigen values using the Lyapunov scheme. The numerical solution based on Chebysehev pseudo-spectra and spectra homotopy analysis method (SHAM) was implemented to handle the combination on nonlinear ordinary differential equations derived from the transport models. We observed that far-field of the stagnation point, nanoparticles specie dispersion increased with higher thermal diffusivity, while the decrease in concentration profile around the vicinity of stagnation point depicts clustering of nanoparticles-embedded blood flow. The observations revealed that higher magnitude of thermophoretic parameters constitute significantly to increase in momentum as well as energy fields during transport of nanoparticles-containing blood flow under magnetic field influence. These findings showed the potentials of magnetic-field for control of suspended particles in transport medium which could be harnessed to manipulate transport of nanoparticles-containing fluids in microfluidic platforms with intricate configurations.

Impact of Joule heating and multiple slips on a Maxwell nanofluid flow past a slendering surface

2021 ◽  
Author(s):  
Shafiq Ahmad ◽  
Muhammmad Naveed Khan ◽  
Sohail Nadeem ◽  
Aysha Rehman ◽  
Hijaz Ahmad ◽  
...  
Keyword(s):  
Joule Heating ◽  
Concentration Distribution ◽  
Three Dimensional ◽  
Fluid Temperature ◽  
Slip Boundary Conditions ◽  
Nanofluid Flow ◽  
Slip Boundary ◽  
Maxwell Nanofluid ◽  
The Impact ◽  
Multiple Slips

Abstract This manuscript presents a study of three-dimensional MHD Maxwell nanofluid flow across a slendering stretched surface with Joule heating. The impact of binary chemical reactions, heat generation, thermal radiation, and thermophoretic effect is also taken into consideration. The multiple slip boundary conditions are utilized at the boundary of the surface. The appropriate similarity variable is used to transfer the flow modeled equations into ODEs, which are numerically solved by the utilization of the MATLAB bvp4c algorithm. The involved parameter's impact on the concentration, velocity, and temperature distribution are scrutinized with graphs. The transport rates (mass, heat) are also investigated using the same variables, with the results reported in tabulated form. It is seen that the fluid relaxation, magnetic, and wall thickness characteristics diminish the velocities of fluid. Further, the velocity, concentration, and temperature slip parameters reduce the velocities of fluid, temperature, and concentration distribution. The results are compared to existing studies and showed to be in dependable agreement.

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