Computer Modeling in Engineering & Sciences |

DOI: 10.32604/cmes.2022.017539

ARTICLE

Flow and Melting Thermal Transfer Enhancement Analysis of Alumina, Titanium Oxide-Based Maxwell Nanofluid Flow Inside Double Rotating Disks with Finite-Element Simulation

1Chongqing Water Resources and Electric Engineering Collage, Chongqing, 402160, China

2Department of Mathematics, Government College Women University, Faisalabad, 38000, Pakistan

3Department of Mathematics, Government College University Faisalabad, Layyah Campus, Layyah, 31200, Pakistan

4Department of Mathematics, College of Sciences, King Khalid University, Abha, 61413, Saudi Arabia

5Department of Mathematics, Government College University, Faisalabad, 38000, Pakistan

*Corresponding Authors: Madeeha Tahir. Email: dr.madeeha.2017@gmail.com; Muhammad Imran Email: drmimranranchaudhry@gmail.com

Received: 19 May 2021; Accepted: 17 September 2021

Abstract: The energy produced by the melting stretching disks surface has a wide range of commercial applications, including semi-conductor material preparation, magma solidification, permafrost melting, and frozen land refreezing, among others. In view of this, in the current communication we analyzed magnetohydrodynamic flow of Maxwell nanofluid between two parallel rotating disks. Nanofluids are important due to their astonishing properties in heat conduction flows and in the enhancement of electronic and manufacturing devices. Furthermore, the distinct tiny-sized particles

Keywords: Maxwell nanofluid; melting phenomenon; thermal radiation; revolving stretching disks; finite element method (FEM)

Nomenclature | |

Magnetic field strength | |

Nusselt number | |

Pressure | |

Dimensionless temperature | |

Stretching parameter at upper disk | |

Prandtl number | |

Ambient temperature attained | |

Radiative heat flux | |

Fluid temperature | |

Radiation parameter | |

Skin friction coefficient | |

Reynolds number | |

Base fluid density | |

Nanoparticle mass density | |

dimensionless stream function | |

Nanofluid heat capacitance | |

Gravitational acceleration | |

Nanofluid density | |

Viscosity of fluid | |

Stream function | |

Coefficient of mean absorption | |

Constant | |

Electric conductivity | |

Stephan-Boltzmann constant | |

Thermal conductivity of nanoparticles | |

Pressure parameter | |

Magnetic parameter | |

Shear stress | |

Thermal diffusivity of base fluid | |

Maxwell parameter | |

Similarity variable | |

Angular velocities | |

Nanofluid thermal conductivity | |

Different stretching rates |

Advanced technologies realize the critical value of a unique type of energy transport fluids known as nanoliquid, because of the growing requirements of heat. The most significant aspect of the heat transfer system is the heat efficiency of the base fluid. Since non-metallic materials have poorer thermal efficiency than metallic substances. High thermal efficiency nanoparticles dispersed in regular fluids, which are typically made up of metals and oxides, greatly improve the heat proficiency of the host liquid. Therefore, metals are more useful to improving the thermal transfer rate. Choi and Eastman in (1995) coined the term “nanofluid” to describe the regular fluid that contained very tiny (1–100 nm) nanomaterials. Hayat et al. [1] reviewed the analysis of activation in Ree-Eyring nanofluid flow inside double disks. Qayyum et al. [2] scrutinized the entropy production inspirations on Williamson nanoliquid flow insides double rotating disks. Muhammad et al. [3] observed the slip impacts with activation energy across a three-dimensional sheet. Rafiq et al. [4] examined the numerical computations effects of nanofluid containing six different particles namely

The development of hybrid nanofluids, which are essentially an aqueous mixture of two or more forms of nanostructures in mixture or composite shape, is the next advancement in nanofluids technology. Hybrid nanofluids are being developed to solve the drawbacks of single suspension and to take benefit of nanoparticle synergy. Hybrid nanomaterials demonstrated that nanofluids have enhanced energy transfer and thermal conductivity, resulting in cost savings in commercial applications. There is little experimental, theoretical, and computational research on hybrid nanofluids. Li et al. [12] simulated the fractional study of hybrid nanoliquid flow across a spinning disk. Gul et al. [13] highlights the conical gap between cone and disk under hybrid nanofluid flow by adopting Homotopy analysis method. Waqas et al. [14] introduced the hybrid nanofluid flow over radiative disk. Shafee et al. [15] introduced the Entropy generation effects along NEPCM charging mechanics utilizing hybrid nanomaterials. Armaghani et al. [16] discussed the role of magnetized hybrid nanofluid flow through L-shape cavity. Shoaib et al. [17] explored the joule heating effects on magneto hybrid nanofluid over radiative rotating disk. The significance of magnetic dipole in hybrid nanofluid across stretchable surface is illustrated by Gul et al. [18]. Several evaluations have been discussed and presented in the literature, see for illustration [19,20].

Magnetohydrodynamics (MHD) is a class of physics that describes the magnetic properties of electrically interacting liquids. It usually influences thermal transport and manifests itself as Joule heating and Lorentz strength. MHD includes things like refrigerator cooling, saltwater, plasma, tumor therapy,

The concept of porous media is used in various fields of technology and applied science, including mechanics, filtration, petroleum engineering, construction engineering, hydrogeology, and biophysics. MHD

The thermal radiation behavior in thermal transfer has applications in a variety of thermal engineering fields, including hybrid power solar systems, rocket propulsion, nuclear reactors, rockets, aircraft, and communication technology. It is worth noting that linear radiation is adequate to produce thermal equipment and is widely used in several technological processes. Hayat et al. [27] analyzed the impacts of thermal radiation on

Melting heat has piqued the interest of scientists and researchers owing to its various uses in novel industrial processes. In recent times, scientists have concentrated their efforts on creating more long-term, reliable, and affordable energy storing technologies. Unintended thermal efficiency, solar energy and power are all examples of such technologies. Roberts [31] the first to depict the nature of melting thermal transfer in a hot air stream of ice surface. The behavior of melting impact with bioconvection in generalized second grade nanofluid configured by stretching surface is illustrated by Waqas et al. [32]. Hayat et al. [33] introduced the melting thermal transport in stagnation point flow of nanofluid with zero mass flux condition across a stretching surface. Ullah et al. [34] discussed the numerical solution of

As reviewed above, the non-Newtonian nature of nanofluid has vital applications. The key determination of this article is to scrutinize the MHD flow and melting heat transfer for a nanofluid model through a two parallel rotating disks. Novelty of the communication is firstly to scrutinize the axisymmetric flow of Maxwell-water based nanofluid with thermal radiation. Secondly the numerical solution of current problem is solved numerically by applied Finite element method. The numerical solutions are obtained and the role of physical factors on the subjective dimensionless profiles is scrutinized and reflected by graphs.

2.1 Mathematical and Physical Flow Description

Considerable the effect of steady incompressible, axisymmetric electromagnetic flow with heat transformation by using different particles based on Maxwell nanofluid between both revolving stretching disks at the distance h from upper to lower disks. The upper and lower disks have the distinct angular velocities denoted by

2.2 Dimensional Governing Boundary Flow Expressions

The governing flow equations are given bellow [36,37]:

With,

The melting condition is addressed as

Here the electrical conductivity represented by

where

Now by employing the Rosseland evaluation of radiative heat flux

Here consider that the heat transfers in the flow field are such that the expression

In above Eq. (8) eliminate the terms of multi order and outer the first degree in

Now putting Eq. (9) into Eq. (7) then we have,

2.3 Similarity Transformations

The stream function

The transformations are as follows:

After applying the similarity variables, we obtain the non-dimensional expressions are as follows:

With

2.5 Non-Dimensional Parameters

The dimension-less sundry parameters are given bellow:

Here the Eq. (13) differentiated w.r.t. to

Through Eqs. (13) and (17) the parameter

The above Eq. (15) integrated with respect to

The Physical industrial inters in which the coefficients of skin frictions

Here we take stress

The skin frictions coefficients in non-dimensional forms are

And the coefficients of Nusselt numbers in non-dimensional forms are

Here the total shear stress

3 Numerical Process: Finite Element Method (FEM)

Here, the nonlinear dimensionless ODE's (14)–(16) and (19) with specific boundary conditions (17) are tackled by utilizing the finite element method (FEM) or finite element analysis (FEA). These ODEs are highly nonlinear, so analytical techniques are not useful to solve these expressions. Therefore, the (FEM) is used to compute the solution of highly nonlinear system. The FEM is more effective than other technique.

3.1 Finite Element Technique (FET)

We get the exact solution through the finite element analysis the coupled nonlinearly ODE's structure (14)–(16) and (19) with specified boundary conditions (17) firstly we let

With

The variational method associated with the expressions (28)–(32) by typical linear component

Here

3.3 Finite-Element Description

Substitute finite element estimation of the form declared below; the finite element method may be attained from the abovementioned expressions:

By

For typical components

The structure of finite-element method for nonlinear governing equations is mentioned as:

Here

We used finite element method for tackling the nonlinear set of ODEs. Because fewer nodes are required in finite element, less memory is required to perform the full program, resulting in improved accuracy and, as a result, a shorter calculation time than FEM. Physical features like density, heat capacity, thermal conductivity and electrical conductivity of some particles and base liquid are given in Table 1. Characteristics for some physical properties of nanofluids are given in Table 2. For validation of code we compare current outcomes with the numerical outcomes found by Lance et al. [40], Turkyilmazoglu [41] and Kumar et al. [42] for the rotation parameter

Fig. 2 indicates the radial velocity profile

The effect of thermal radiation parameter

The current study novelty is recent progress in melting heat transfer transportation of Maxwell

• An increase in radial velocity of single Maxwell water-based nanofluid is analyzed vs. an improvement in nanoparticles volume friction.

• Tlhe radial velocity of nanofluid is reducing function of larger magnitudes of the melting parameter.

• The fluid flow declines with fluid parameter.

• The significant value of the tangential velocity is noticed via stretching parameter for upper disk.

• Temperature distribution raises for thermal radiation parameter.

• The thermal field of the fluid reduces as Prandtl number [44] increases.

• Larger solid volume friction decreases the temperature distribution.

Acknowledgement: This work was sponsored in part by National Natural Science Foundation of China (No. 51869031); and Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJQN201903801) and Huzhou Key Laboratory of Green Building Technology.

Funding Statement: This work is financially supported by the Government College University, Faisalabad and Higher Education Commission, Pakistan.

Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the current analysis.

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We have

Putting all required values in Eq. (A1) we, have

Hence equation of continuity trivially satisfied.

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