Numerical Investigation for Radiative Transport in Magnetized Flow of Nanofluids due to Moving Surface

Waqas, Hassan; Khan, Shan Ali; Alghamdi, Metib; Muhammad, Taseer

doi:https://doi.org/10.1155/2021/1705736

Mathematical Problems in Engineering

On this page

Abstract Introduction Results and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Special Issue

Nanofluids and Entropy Analysis with Electroosmotic Phenomenon

View this Special Issue

Research Article | Open Access

Volume 2021 | Article ID 1705736 | https://doi.org/10.1155/2021/1705736

Numerical Investigation for Radiative Transport in Magnetized Flow of Nanofluids due to Moving Surface

Hassan Waqas,¹Shan Ali Khan,¹Metib Alghamdi,²and Taseer Muhammad²

Academic Editor: Ahmed Zeeshan

Received10 Aug 2021

Revised15 Sept 2021

Accepted25 Sept 2021

Published07 Oct 2021

Abstract

In this article, we examined the magnetized flow of ethylene glycol- water-based nanoliquids comprising molybdenum disulfide () across a stretching sheet. Flow properties were examined under the impacts of magnetic field and thermal radiation. The behavior of heat generation/absorption is also accounted. Similarity transformations are used on the system of PDEs to get nondimensional ODEs. The obtained nondimensional ODEs are solved with the help of the Runge–Kutta–Fehlberg method via computational software MATHEMATICA. The behavior of prominent parameters for velocity and thermal profiles is plotted graphically and discussed in detail. It is depicted that the temperature field is upgraded with increase in the heat generation/absorption parameter. Furthermore, a larger Schmidt number causes reduction in the concentration field. The current formulated model may be useful in biomedical engineering, biotechnology, nanotechnology, biosensors, crystal growth, plastic industries, and mineral and cleaning oil manufacturing.

1. Introduction

Nanofluids play an essential role in our daily life assisting innovations in industries such as HVAC, electronics, and automotive and mechanical engineering for efficient increase of heat energy of fluids and improving heat transmission in materials. Nanofluids are often characterized when nanoparticles are combined with some regular fluids. The use of a liquid with disseminated particles as a heat-transfer fluid has been around for a long time; nevertheless, owing to sedimentation of the dispersed particles, the traditional scattered fluids cannot be used. Nanofluids do not have the aforementioned drawbacks. The inclusion of nanoparticles (metals or their oxides) in very small-volume fractions significantly increases the heat proficiency of the base fluid. According to the conclusions of the first experiments on nanofluid heat capacity, nanofluids are observed to be heat-transfer fluids that are exceptionally reactive and can be utilized rather than water.

To improve the emphatically viable qualities of one another, an ideal mix of nanoparticles should be chosen. Keeping this in view, Suresh [1] first and foremost proposed the possibility of using half and half nanofluids to all the more likely improve the critical qualities of normal nanoparticles. An assortment of logical investigation distributions were obtained on the possibility of mixture nanofluids. Momin [2] provided an observational examination of convective and crossover nanoparticles for laminar streaming in tendency cylinders. Crossover nanofluids involve at least two kinds of nanoparticles having new thermophysical and compound aspects that are fit for upgrading power of thermal transportation inferable from synergic sway [3]. Tian et al. [4] discussed 2-D and 3-D executions and their impact on thermal sink viability of the MHD half-breed nanoparticle subject to slip and nonslip streams. Al-Hossainy et al. [5] reviewed the highest order rate of rotating reactants of single nanofluid and hybrid nanofluid over the stretching surface. Roy et al. [6] assessed the transport of micropolar water-based hybrid nanoliquids through a stretchable surface. Effects of porous circle with powerful properties of stage alter measure through PCM improved roundabout line all through nanofluid constrained convective in scattering working point is examined by Alizadeh et al. [7]. The outcomes of transport using water-based crossover nanoliquids with heat features were accounted by Fazeli et al. [8]. Kumar et al. [9] explored examination of thermal transport improvement observed because of the impact of significant liquid fluctuation qualities in the presence of radiation on cross-breed nanoliquids. Aziz et al. [10] discussed Powell–Eyring water-based cross-breed transport of nanoliquids with convective heat transmission under volumetric entropy improvement for the consistently flat penetrable extending sheet. Haider et al. [11] examined nanofluid transport in a Darcy–Forchheimer permeable space through a rotating plate. Few studies of hybrid nanoliquids with different geometries are provided in [12–18].

The influence of magnetic field on an electrical current-conductive liquid has an impact on boundary layer transport because of ionization. If the ionized liquid with the lower density is affected by a stronger electromagnetic field, then final conduction of the fluid decreases and, as a result, free-ion spiraling of electromagnetic field lines cause natural current in magnetic and electrical fields. This current is named as “Hall current.” The magnetic field is considered highly important in a variety of nanofluid technologies and industrial applications. Several devices, such as motors, bearings, and magnetohydrodynamic devices, geophysical configurations, and chemical processes are intensely traumatized by the effect of magnetohydrodynamics magnetostrictive physical occurrences of fluids. Magnetohydrodynamics has numerous chemical and industrial manufacturing applications in the related industrial sectors where temperature disruptions exist. Usually, variations can fall below 350 degrees centigrade. Alfven in 1942 firstly proposed the concept of magnetohydrodynamics [19]. Kholshchevnik [20] in the nineteen century employed two combined cathodes in the magnetohydrodynamic generator to observe the impact of boundary current. Zainal et al. [21] noticed magnetohydrodynamic water-based mixture (Al₂O₃/H₂O) nanoliquid transport through a permeable extended/shrinked surface with quadratic velocity. Patil et al. [22] investigated attributes of magnetohydrodynamic Prandtl nanoliquid transport through an extending surface. Elayarani et al. [23] explored the numerical framework for 2-dimensional bioconvective Carreau nanoliquid, incorporating motile microorganisms with the electromagnetic field and slip features. Sabu et al. [24] considered magnetohydrodynamic (MHD) convection ferro-nanofluids (Fe₃O₄-water) transport through a channel. Saqib et al. [25] discussed MHD transport of a ferro-nanoliquid mixture in presence of radiation. Almakki et al. [26] assessed the magnetohydrodynamic micropolar-nanoliquid transport using an extending sheet. Yasmin et al. [27] developed magnetohydrodynamic Casson nanoliquid transport using the Brinkman framework. Few studies on magnetohydrodynamics (MHD) with hybrid nanoliquids can be seen in [28–34].

Thermal radiation moves at a pace equivalent to that of lighting. Effect of thermal radiation is an important part of the research due to its realistic engineering applications such as furnace construction, glass manufacturing, gas-cooled nuclear power plant construction, polymer manufacturing, and propelled systems. Firstly, Hunt in 1978 presented the concept of generating radiation by utilizing nanoparticles [35]. Siddiqa et al. [36] assessed convection in micropolar nanoliquids in the presence of thermal radiation. Magnetohydrodynamic (MHD) transport of nanoliquids through wedges was presented by Sreedevi et al. [37]. Malek et al. [38] analyzed numerical clarification of Rosseland relation for thermal radiation in improved essential capacities. Gireesha et al. [39] assessed nanomaterials of half and half nanofluid subject to convective conditions. Zainal et al. [40] addressed thermal transport properties of water-based nanoliquids under impacts of MHD and thermal radiation through a permeable moving sheet. Hayat et al. [41] examined the features of thermal radiation on 3-D flow of nanoliquids through carbon nanotubes. Eid et al. [42] explored the gold-blood nanofluid to improve the heat-transfer rate. Rana et al. [43] investigated the thermal radiation effects on nanoliquid flow by adopting the Buongiorno model. Khan et al. [44] investigated the entropy generation aspects on the Williamson nanofluid under the effects of a chemical reaction. Gireesha et al. [39] examined the thermal radiation impacts on hybrid nanoliquids. Khan et al. [45] explored the hybrid nanoliquid with entropy of the system.

Nanoparticles have the ability to expand surface area and thermal efficiency and engage fluid particles with one another in liquids. As a result, this phenomenon is crucial in industrial operations, as well as solar sources of energy and biomedical therapies. A nanofluid has recently been found to be important in a wide range of heat transmission techniques. Generator cooling, refrigeration, and heating in structures, circuit cooling, cooling systems, the coolant in cutting, and the coolant in machining, automotive cooling, and radioactive system cooling are few applications of nanofluids. Numerous researchers were inspired to use nanofluids to solve real-world heat transfer issues as a result of these relevant implementations. Motivated from the above survey of the literature, the novelty of the current study was to obtain the numerical solution of ethylene glycol- water-based nanoliquid flow containing molybdenum disulfide () through a stretched sheet. To fulfill this gap in the current analysis, we have considered the magnetized -ethylene glycol- () water-based nanoliquid with thermal radiation and heat source/sink configured with a stretching sheet. The system of PDEs is reduced to ODEs. The numerical outcomes are found with the Runge–Kutta–Fehlberg method using software MATHEMATICA. The outcomes of velocity, temperature, and concentration according to different variations of the involved parameters are dissected graphically. The effects of nanoparticle volume fraction, thermal radiation, and heat source/sink are valuable characteristics towards the novelty of the accounted model.

2. Mathematical Formulation

Consider the two-dimensional flow of the -ethylene glycol- () water-based nanoliquid over a stretching sheet. Let us assume the Cartesian coordinate () in such a way that x-axis is along the sheet and y-axis is perpendicular to it (see Figure 1). Here, molybdenum disulfide is used as nanoparticles in ethylene glycol-water () mixture. The impacts of thermal radiation and heat generation/absorption are considered. Let and be the surface temperature and concentration, respectively. The assumptions of the current analysis are as follows [46, 47]:(i)Two-dimensional steady flow of nanofluid is developed(ii)The flow is generated through a stretching surface(iii)Heat-transfer improvement through -ethylene glycol- () water-based nanofluid is considered(iv)Heat absorption/generation and thermal radiation are present

The governing equations are [46, 48]

The boundary conditions are [46, 48]

Here, denotes the nanofluid dynamic viscosity, denotes the density of nanofluid, denotes the nanofluid specific heat, denotes the electric conductivity of nanofluid, denotes the temperature, denotes the nanofluid thermal conductivity, denotes the temperature away from the surface, and denotes the concentration away from the surface.

We considered the following similarity variables [46]:

The dimensionless system is defined by

The flow-controlling parameters and constant terms appearing in expressions (4–7) are listed as follows: magnetic parameter (); Prandtl number (); Schmidt number (); heat generation parameter (); thermal radiation parameter (). Also,

The mathematical form of Nusselt number iswhere

The dimensionless Nusselt number is addressed byin which describes the local Reynolds number.

3. Numerical Method and Validation

In this segment, governing coupled ODEs (4–6) with suitable boundary conditions (7) have been solved numerically by utilizing the Runge–Kutta–Fehlberg method with the help of computational software MATHEMATICA. In the current work, the steady 2-D ethylene glycol-water-based nanoliquid transport with magnetohydrodynamic effect is considered. The results of the current analysis are accurate and more useful in engineering problems. The following procedure is used to reduce the higher-order equations:

In Table 1, the comparative study of for different values of with already published works in a limiting situation is presented. Here, we have seen good agreement between the currents results and already published works in this limiting situation. We have set the relative tolerance to and acquired high-precision results for this scrutinization.

4. Results and Discussion

Figure 2(a) discloses the nature of the velocity field against an exponential constant for the Ag-ethylene glycol/water nanofluid. It is noted that flow is exaggerated by increasing the estimations of the exponential constant . Figure 2(b) is drawn to depict the behavior of the nanoparticle volume fraction versus the velocity profile. It is depicted that the velocity field is a decreasing function of the nanoparticle volume fraction . Figure 2(c) displays the effect of on velocity for the Ag-ethylene glycol/water nanofluid. It is analyzed that declines with larger . When the magnetic parameter rises, a significant resistance is created among the particles, causing heat to be developed in the fluid. A drag force termed “Lorentz force” was created by slapping the magnetic field. Figure 3(a) displays the estimations of the thermal field via distinguished values of the Prandtl number . It can be revealed that declines with larger . The Prandtl number has an inverse relationship with thermal diffusivity. As the Prandtl number rises, thermal diffusion weakens and the temperature distribution dissipates. The effects of nanoparticle volume fraction on the thermal field are revealed through Figure 3(b). The increment in the thermal field is observed by increasing values of the nanoparticle volume fraction . Figure 3(c) is designed to scrutinize the effect of the heat generation/absorption parameter on the thermal field . The thermal field is boosted up with a larger heat generation/absorption parameter . Figure 3(d) is drawn to examine the variations of the thermal field via the larger exponential constant . From the variations of data, we observed that the thermal field declines with greater magnitudes of exponential constant . The consequence of via the thermal field is shown in Figure 3(e). Here, is enhanced with increasing estimations of . For the higher thermal radiation parameter, the system’s interior energy source grows physically. As a result, the thermal profile rises. Figure 3(f) is depicted to visualize the impact of on the thermal field . Here, the thermal field is upgraded with an increase in magnetic parameter . Physically, the magnetic field increases the temperature, resulting in a thickening of the thermal layer. It is apparent that temperature distribution has been improved. Figure 4(a) signifies the effect of exponential constant against concentration field . It is analyzed that concentration is reduced for larger estimations of the exponential constant . Figure 4(b) is captured to observe the effect of Schmidt number against concentration distribution . It is interesting to notice that concentration is reduced via a larger Schmidt number . Tables 2 and 3 display thermophysical features of nanomaterials and base liquids.

(a)

(b)

(c)

(a)

(b)

(c)

(d)

(e)

(f)

(a)

(b)

5. Conclusions

In this work, incompressible two-dimensional ethylene glycol- () water-based nanoliquids containing molybdenum disulfide () particles over a stretching surface has been scrutinized. The analysis is executed during occurrences of thermal radiation and heat absorption/generation. Similarity transformations are used on the system of PDEs to get nondimensional ODEs. The obtained nondimensional ODEs are solved with the help of the Runge–Kutta–Fehlberg method via computational software MATHEMATICA. With increasing estimations of the exponential constant, the velocity field of the nanofluid enhances. The Prandtl number and nanoparticle volume fraction have opposite impacts on the thermal field [52–54]. The larger values of the thermal radiation parameter lead to a stronger thermal field. The concentration distribution is reduced with a higher exponential constant.

Nomenclature

:	Velocity components
:	Ambient concentration
:	Coordinates system
:	Surface temperature
:	Magnetic field strength
:	Surface concentration
:	Temperature
:	Magnetic parameter
:	Radiative heat flux
:	Thermal radiation parameter
:	Coefficient of heat generation/absorption
:	Dimensionless concentration
:	Concentration
:	Heat generation/absorption parameter
:	Ambient temperature
:	Schmidt number
:	Exponent constant
:	Prandtl number

Greek symbols and subscripts

:	Dynamic viscosity of the nanofluid
:	Wall condition
:	Electric conductivity
:	Nanofluid
:	Density of the nanofluid
:	Base fluid
:	Thermal conductivity of the nanofluid
:	Solid particle
:	Specific heat
:	Base fluid specific heat
:	Volume fraction of the nanoparticle
:	Dimensionless temperature.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

Acknowledgments

The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University, Abha, Saudi Arabia, for funding this work through the research groups program under grant number R.G.P-2/104/42.

References

S. Suresh, K. P. Venkitaraj, P. Selvakumar, and M. Chandrasekar, “Synthesis of Al2O3-Cu/water hybrid nanofluids using two step method and its thermo physical properties,” Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 388, no. 1-3, pp. 41–48, 2011.
View at: Publisher Site | Google Scholar
G. G. Momin, “Experimental investigation of mixed convection with water-Al2O3 & hybrid nanofluid in inclined tube for laminar flow,” International Journal of Environmental Science and Technology, vol. 2, no. 12, pp. 195–202, 2013.
View at: Google Scholar
J. Sarkar, P. Ghosh, and A. Adil, “A review on hybrid nanofluids: recent research, development and applications,” Renewable and Sustainable Energy Reviews, vol. 43, pp. 164–177, 2015.
View at: Publisher Site | Google Scholar
M.-W. Tian, S. Rostami, S. Aghakhani, A. S. Goldanlou, and C. Qi, “A techno-economic investigation of 2D and 3D configurations of fins and their effects on heat sink efficiency of MHD hybrid nanofluid with slip and non-slip flow,” International Journal of Mechanical Sciences, vol. 189, Article ID 105975, 2021.
View at: Publisher Site | Google Scholar
A. F. Al-Hossainy and M. R. Eid, “Combined experimental thin films, tddft-dft theoretical method, and spin effect on [PEG-H2O/ZrO2+ MgO] h hybrid nanofluid flow with higher chemical rate,” Surfaces and Interfaces, vol. 23, Article ID 100971, 2021.
View at: Publisher Site | Google Scholar
N. C. Roy, M. Hossain, and I. Pop, “Analysis of dual solutions of unsteady micropolar Hybrid nanofluid flow over a stretching/shrinking sheet,” Journal of Applied and Computational Mechanics, vol. 7, no. 1, pp. 19–33, 2021.
View at: Google Scholar
R. Alizadeh, J. M. N. Abad, A. Fattahi et al., “A machine learning approach to predicting the heat convection and thermodynamics of an external flow of hybrid nanofluid,” Journal of Energy Resources Technology, vol. 143, no. 7, 2021.
View at: Publisher Site | Google Scholar
I. Fazeli, M. R. Sarmasti Emami, and A. Rashidi, “Investigation and optimization of the behavior of heat transfer and flow of MWCNT-CuO hybrid nanofluid in a brazed plate heat exchanger using response surface methodology,” International Communications in Heat and Mass Transfer, vol. 122, Article ID 105175, 2021.
View at: Publisher Site | Google Scholar
K. G. Kumar, E. H. B. Hani, M. E. H. Assad, M. Rahimi-Gorji, and S. Nadeem, “A novel approach for investigation of heat transfer enhancement with ferromagnetic hybrid nanofluid by considering solar radiation,” Microsystem Technologies, vol. 27, no. 1, pp. 97–104, 2021.
View at: Publisher Site | Google Scholar
A. Aziz, W. Jamshed, T. Aziz, H. M. S. Bahaidarah, and K. Ur Rehman, “Entropy analysis of Powell-Eyring hybrid nanofluid including effect of linear thermal radiation and viscous dissipation,” Journal of Thermal Analysis and Calorimetry, vol. 143, no. 2, pp. 1331–1343, 2021.
View at: Publisher Site | Google Scholar
F. Haider, T. Hayat, and A. Alsaedi, “Flow of hybrid nanofluid through Darcy-Forchheimer porous space with variable characteristics,” Alexandria Engineering Journal, vol. 60, no. 3, pp. 3047–3056, 2021.
View at: Publisher Site | Google Scholar
R. J. Punith Gowda, R. Naveen Kumar, A. Aldalbahi et al., “Thermophoretic particle deposition in time-dependent flow of hybrid nanofluid over rotating and vertically upward/downward moving disk,” Surfaces and Interfaces, vol. 22, Article ID 100864, 2021.
View at: Publisher Site | Google Scholar
L. M. Jasim, H. Hamzah, C. Canpolat, and B. Sahin, “Mixed convection flow of hybrid nanofluid through a vented enclosure with an inner rotating cylinder,” International Communications in Heat and Mass Transfer, vol. 121, Article ID 105086, 2021.
View at: Publisher Site | Google Scholar
P. Tiam Kapen, C. Gervais Njingang Ketchate, D. Fokwa, and G. Tchuen, “Linear stability analysis of (Cu-Al2O3)/water hybrid nanofluid flow in porous media in presence of hydromagnetic, small suction and injection effects,” Alexandria Engineering Journal, vol. 60, no. 1, pp. 1525–1536, 2021.
View at: Publisher Site | Google Scholar
R. Ekiciler, “Effects of novel hybrid nanofluid (TiO2-Cu/EG) and geometrical parameters of triangular rib mounted in a duct on heat transfer and flow characteristics,” Journal of Thermal Analysis and Calorimetry, vol. 143, no. 2, pp. 1371–1387, 2021.
View at: Publisher Site | Google Scholar
V. Kumar, J. Sarkar, and W.-M. Yan, “Thermal-hydraulic behavior of lotus like structured rGO-ZnO composite dispersed hybrid nanofluid in mini channel heat sink,” International Journal of Thermal Sciences, vol. 164, Article ID 106886, 2021.
View at: Publisher Site | Google Scholar
S. S. M. Ajarostaghi, M. Zaboli, and M. Nourbakhsh, “Numerical evaluation of turbulence heat transfer and fluid flow of hybrid nanofluids in a pipe with innovative vortex generator,” Journal of Thermal Analysis and Calorimetry, vol. 143, no. 2, pp. 1583–1597, 2021.
View at: Publisher Site | Google Scholar
F. Abbas, H. M. Ali, M. Shaban et al., “Towards convective heat transfer optimization in aluminum tube automotive radiators: potential assessment of novel Fe2O3-TiO2/water hybrid nanofluid,” Journal of the Taiwan Institute of Chemical Engineers, 2021.
View at: Publisher Site | Google Scholar
H. Alfvén, “Existence of electromagnetic-hydrodynamic waves,” Nature, vol. 150, no. 3805, pp. 405-406, 1942.
View at: Publisher Site | Google Scholar
E. K. Kholshchevnikova, “Influence of the Hall effect on the characteristics of a MHD generator with two pairs of electrodes,” Journal of Applied Mechanics and Technical Physics, vol. 7, no. 4, pp. 48–54, 1966.
View at: Google Scholar
N. A. Zainal, R. Nazar, K. Naganthran, and I. Pop, “Stability analysis of MHD hybrid nanofluid flow over a stretching/shrinking sheet with quadratic velocity,” Alexandria Engineering Journal, vol. 60, no. 1, pp. 915–926, 2021.
View at: Publisher Site | Google Scholar
A. B. Patil, P. P. Humane, V. S. Patil, and G. R. Rajput, “MHD Prandtl Nanofluid flow due to convectively heated stretching sheet below the control of chemical reaction with thermal radiation,” International Journal of Ambient Energy, pp. 1–13, 2021.
View at: Publisher Site | Google Scholar
M. Elayarani, M. Shanmugapriya, and P. Senthil Kumar, “Intensification of heat and mass transfer process in MHD carreau nanofluid flow containing gyrotactic microorganisms,” Chemical Engineering and Processing - Process Intensification, vol. 160, Article ID 108299, 2021.
View at: Publisher Site | Google Scholar
A. S. Sabu, A. Mathew, T. S. Neethu, and K. Anil George, “Statistical analysis of MHD convective ferro-nanofluid flow through an inclined channel with hall current, heat source and soret effect,” Thermal Science and Engineering Progress, vol. 22, Article ID 100816, 2021.
View at: Publisher Site | Google Scholar
M. Saqib, I. Khan, S. Shafie, and A. Q. Mohamad, “Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating,” Scientific Reports, vol. 11, no. 1, pp. 1–22, 2021.
View at: Publisher Site | Google Scholar
M. Almakki, H. Mondal, and P. Sibanda, “Onset of unsteady MHD Micropolar nanofluid flow with entropy generation,” International Journal of Ambient Energy, pp. 1–14, 2021.
View at: Publisher Site | Google Scholar
A. Yasmin, K. Ali, and M. Ashraf, “MHD Casson nanofluid flow in a square enclosure with non-uniform heating using the Brinkman model,” The European Physical Journal Plus, vol. 136, no. 2, pp. 1–14, 2021.
View at: Publisher Site | Google Scholar
W.-F. Xia, I. L. Animasaun, A. Wakif, N. A. Shah, and S.-J. Yook, “Gear-generalized differential quadrature analysis of oscillatory convective Taylor-Couette flows of second-grade fluids subject to Lorentz and Darcy-Forchheimer quadratic drag forces,” International Communications in Heat and Mass Transfer, vol. 126, Article ID 105395, 2021.
View at: Publisher Site | Google Scholar
J. C. Umavathi and H. F. Oztop, “Investigation of MHD and applied electric field effects in a conduit cramed with nanofluids,” International Communications in Heat and Mass Transfer, vol. 121, Article ID 105097, 2021.
View at: Publisher Site | Google Scholar
A. Wakif, I. L. Animasaun, and R. Sehaqui, “A brief technical note on the onset of convection in a horizontal nanofluid layer of finite depth via wakif-galerkin weighted residuals technique (WGWRT),” in Defect and Diffusion Forum, vol. 409, pp. 90–94, Trans Tech Publications Ltd, Freienbach, Switzerland, 2021.
View at: Publisher Site | Google Scholar
B. Ali, R. A. Naqvi, A. Mariam, L. Ali, and O. M. Aldossary, “Finite element study for magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow over a faster/slower stretching wedge with activation energy,” Mathematics, vol. 9, no. 1, p. 25, 2021.
View at: Google Scholar
A. Wakif and R. Sehaqui, “Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: a proper application of the revised two‐phase nanofluid model with convective heating and through‐flow boundary conditions,” Numerical Methods for Partial Differential Equations, 2020.
View at: Google Scholar
M. Jawad, A. Saeed, and T. Gul, “Entropy generation for MHD maxwell nanofluid flow past a porous and stretching surface with dufour and soret effects,” Brazilian Journal of Physics, pp. 1–12, 2021.
View at: Publisher Site | Google Scholar
A. Kardgar, “Numerical investigation of MHD oscillating power-law non-Newtonian nanofluid flow in an enclosure,” The European Physical Journal Plus, vol. 136, no. 1, pp. 1–19, 2021.
View at: Publisher Site | Google Scholar
A. J. Hunt, Small Particle Heat Exchangers, Report LBL-78421 for the US Department of Energy, Lawrence Berkeley Laboratory, Berkeley, CA, USA, 1978.
S. Siddiqa, N. Begum, M. A. Hossain, M. N. Abrar, R. S. R. Gorla, and Q. Al-Mdallal, “Effect of thermal radiation on conjugate natural convection flow of a micropolar fluid along a vertical surface,” Computers & Mathematics with Applications, vol. 83, pp. 74–83, 2021.
View at: Publisher Site | Google Scholar
P. Sreedevi and P. Sudarsana Reddy, “Heat and mass transfer analysis of MWCNT‐kerosene nanofluid flow over a wedge with thermal radiation,” Heat Transfer, vol. 50, no. 1, pp. 10–33, 2021.
View at: Publisher Site | Google Scholar
M. Malek, N. Izem, M. S. Mohamed, M. Seaid, and M. Wakrim, “Numerical solution of Rosseland model for transient thermal radiation in non-grey optically thick media using enriched basis functions,” Mathematics and Computers in Simulation, vol. 180, pp. 258–275, 2021.
View at: Publisher Site | Google Scholar
B. J. Gireesha, G. Sowmya, M. I. Khan, and H. F. Öztop, “Flow of hybrid nanofluid across a permeable longitudinal moving fin along with thermal radiation and natural convection,” Computer Methods and Programs in Biomedicine, vol. 185, Article ID 105166, 2020.
View at: Publisher Site | Google Scholar
N. A. Zainal, R. Nazar, K. Naganthran, and I. Pop, “MHD flow and heat transfer of hybrid nanofluid over a permeable moving surface in the presence of thermal radiation,” International Journal of Numerical Methods for Heat and Fluid Flow, 2020.
View at: Publisher Site | Google Scholar
T. Hayat, F. Haider, T. Muhammad, and A. Alsaedi, “Darcy-Forchheimer three-dimensional flow of carbon nanotubes with nonlinear thermal radiation,” Journal of Thermal Analysis and Calorimetry, vol. 140, no. 6, pp. 2711–2720, 2020.
View at: Publisher Site | Google Scholar
M. R. Eid, A. Alsaedi, T. Muhammad, and T. Hayat, “Comprehensive analysis of heat transfer of gold-blood nanofluid (Sisko-model) with thermal radiation,” Results in physics, vol. 7, pp. 4388–4393, 2017.
View at: Publisher Site | Google Scholar
P. Rana, N. Srikantha, T. Muhammad, and G. Gupta, “Computational study of three-dimensional flow and heat transfer of 25 nm Cu-H2O nanoliquid with convective thermal condition and radiative heat flux using modified Buongiorno model,” Case Studies in Thermal Engineering, vol. 27, Article ID 101340, 2021.
View at: Publisher Site | Google Scholar
M. I. Khan, S. Qayyum, T. Hayat, M. I. Khan, and A. Alsaedi, “Entropy optimization in flow of Williamson nanofluid in the presence of chemical reaction and Joule heating,” International Journal of Heat and Mass Transfer, vol. 133, pp. 959–967, 2019.
View at: Publisher Site | Google Scholar
M. I. Khan, A. Alsaedi, T. Hayat, and N. B. Khan, “Modeling and computational analysis of hybrid class nanomaterials subject to entropy generation,” Computer Methods and Programs in Biomedicine, vol. 179, Article ID 104973, 2019.
View at: Publisher Site | Google Scholar
S. Qayyum, “Dynamics of Marangoni convection in hybrid nanofluid flow submerged in ethylene glycol and water base fluids,” International Communications in Heat and Mass Transfer, vol. 119, Article ID 104962, 2020.
View at: Publisher Site | Google Scholar
W. Jamshed, S. Uma Devi S, M. Goodarzi et al., “Evaluating the unsteady casson nanofluid over a stretching sheet with solar thermal radiation: an optimal case study,” Case Studies in Thermal Engineering, vol. 26, Article ID 101160, 2021.
View at: Publisher Site | Google Scholar
B. Venkateswarlu and P. V. Satya Narayana, “Cu‐Al 2 O 3/H 2 O hybrid nanofluid flow past a porous stretching sheet due to temperatue‐dependent viscosity and viscous dissipation,” Heat Transfer, vol. 50, no. 1, pp. 432–449, 2021.
View at: Publisher Site | Google Scholar
M. Ghalambaz, E. Izadpanahi, A. Noghrehabadi, and A. Chamkha, “Study of the boundary layer heat transfer of nanofluids over a stretching sheet: passive control of nanoparticles at the surface,” Canadian Journal of Physics, vol. 93, no. 7, pp. 725–733, 2015.
View at: Publisher Site | Google Scholar
W. A. Khan and I. Pop, “Boundary-layer flow of a nanofluid past a stretching sheet,” International Journal of Heat and Mass Transfer, vol. 53, no. 11-12, pp. 2477–2483, 2010.
View at: Publisher Site | Google Scholar
R. S. Reddy Gorla and I. Sidawi, “Free convection on a vertical stretching surface with suction and blowing,” Applied Scientific Research, vol. 52, no. 3, pp. 247–257, 1994.
View at: Publisher Site | Google Scholar
N. Boumaiza, M. Kezzar, M. R. Eid, and I. Tabet, “On numerical and analytical solutions for mixed convection falkner-skan flow of nanofluids with variable thermal conductivity,” Waves in Random and Complex Media, 2019.
View at: Google Scholar
R. Dadsetani, G. A. Sheikhzade, M. Goodarzi, A. Zeeshan, R. Ellahi, and M. R. Safaei, “Thermal and mechanical design of tangential hybrid microchannel and high-conductivity inserts for cooling of disk-shaped electronic components,” Journal of Thermal Analysis and Calorimetry, vol. 143, no. 3, pp. 2125–2133, 2021.
View at: Publisher Site | Google Scholar
A. Riaz, A. Zeeshan, and M. M. Bhatti, “Entropy analysis on a three-dimensional wavy flow of eyring–powell nanofluid: a comparative study,” Mathematical Problems in Engineering, 2021.
View at: Google Scholar

Copyright

Copyright © 2021 Hassan Waqas et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies