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Significance of nanoparticle radius and inter-particle spacing toward the radiative water-based alumina nanofluid flow over a rotating disk

  • Muhammad Ramzan , Showkat Ahmad Lone , Abdullah Dawar , Anwar Saeed , Wiyada Kumam EMAIL logo and Poom Kumam EMAIL logo
Published/Copyright: January 30, 2023
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 12 Issue 1

Abstract

The study of nanofluid flow over a rotating disk has significant importance because of its enormous range of implementations, including cancer treatments, chemotherapy, nanomedicines, fermentation sciences, selective drug delivery, food sciences, biosensors, biomedicines, and electronics. Due to these applications of nanofluid, the present problem investigates the magnetohydrodynamic flow of nanofluid with nonlinear thermal radiation and viscous dissipation. In this analysis, the aluminum oxide nanoparticles are mixed with water. Furthermore, the mechanism for inter-particle spacing and radius of aluminum oxide nanoparticles on the dynamics of the two-dimensional flow of nanofluid are investigated. The present problem is modeled in the form of partial differential equations (PDEs), and these PDEs are converted into ordinary differential equations with the help of suitable similarity transformations. The analytical solution to the current modeled problem has been obtained by using the homotopy analysis technique. The main purpose of the present research work is to analyze the behavior of the velocity and temperature of the nanofluid for small and large radius of the aluminum oxide nanoparticles and inter-particle spacing. Also, the role of heat transport is computed for linear and nonlinear thermal radiation cases. The major findings and principal results of this investigation are concluded that the primary velocity of nanoliquid is augmented due to the intensification in suction parameter for both the small and larger radius of aluminum oxide nanoparticles. Furthermore, it is perceived that the heat rate transfer is larger when the Eckert number and nanoparticle volume fraction are higher for both nonlinear and linear thermal radiation cases.

Keywords: aluminum oxide nanoparticles; inter-particle spacing; nonlinear thermal radiation; radius of nanoparticles; rotating disk; homotopy analysis method

1 Introduction

The mixture of nano-sized particles (nanoparticles) suspended in a base liquid is known as nanofluid. Nanofluid is used for the improvement of the rate of heat transmission, and its thermal conductivity is higher compared to the base liquid. Nanofluids are used in several manufacturing and engineering fields. So, the applications of nanofluids are vehicle thermal management, fuel cells, hybrid-powered engines, refrigerators, microelectronics, heat transfer, engine cooling, pharmaceutical processes, heat exchangers, etc. Due to these applications, many investigators used the phenomena of nanofluid in their field of study. Shamshuddin and Eid [1] examined the mixed convection flow of water-based silver ( Ag ), copper ( Cu ), and gold ( Au ) nanoparticles with the Joule heating effect under the stretched surface. They found that the Nusselt number is higher for Cu and Au nanoparticles. Tayyab et al. [2] deliberated the upshot of the magnetic field over the rotating flow of nanoliquid and analyzed that the increment in the Brownian motion parameter increased the concentration profile of the nanofluid. Ramzan et al. [3] addressed the bioconvective flow of Williamson ferro-nanofluid containing the copper oxide ( CuO ) and iron oxide ( Fe 3 O 4 ) nanoparticles toward the stretched surface. In this assessment, the increasing performance of the nanofluid concentration is determined due to the activation energy. Ahmed et al. [4] have determined the role of Maxwell nanoliquid flow above an exponentially stretched surface. In this investigation, it was found that the liquid velocity graph diminished against higher estimates of Deborah’s number. Abd-Alla et al. [5] have studied the effect of the viscous dissipation and heat transport on the magnetohydrodynamic (MHD) peristaltic radiating fourth-grade nanofluid flow, and they obtained the solution of their model numerically through the implementation of the fourth-order Runge–Kutta scheme. Dawar et al. [6] have scrutinized the MHD flow of Cu / CuO nanoparticles with Brownian and thermophoresis diffusivity between the two parallel plates. In this inquiry, they obtained that the Cu / CuO nanoliquid flow speed is decreased when the nanoparticle volume fraction is enlarged. Hafeez et al. [7] have discussed the prevalence of the Joule heating effect on the Oldroyd-B nanofluid flow across the rotational disk. Nabwey et al. [8] addressed the simulation of the Carreau nanoliquid flow with the magnetic flux, motile microorganisms, and chemical reaction effects under the inclined stretching cylinder and obtained that the magnitude of the drag force is increased for the power law factor. Shafiq et al. [9] used a moving thin needle to study the flow of nanofluid with Soret and Dufour numbers by using the convective heat conditions and obtained that the temperature of the nanofluid is enhanced for increasing values of the Brownian motion parameter. Colak et al. [10] have inspected experimentally the flow of Powell–Eyring nanofluid along the application of Darcy–Forchheimer and motile microorganisms toward the stretched surface. They have obtained that the drag force coefficient is rising due to the increase in the Darcy–Forchheimer parameter. Shafiq et al. [11] presented the simulation of the Newtonian heating conditions on the flow of Walter-B nanofluid under the Riga surface. Bhatti et al. [12] have simulated some physical characteristics of cobalt oxide ( Co 3 O 4 ) and graphene ( GO ) nanoparticles in the numerical study of the hybrid nanofluid toward the elastic circular surface. Rashidi et al. [13] have demonstrated the applications of the nanofluid in different arenas of the industrial and engineering level. They also discussed the significance of entropy generation and heat transport. More studies related to nanofluid flow problems are discussed [14,15,16,17].

In the last few decades, for the enhancement of the thermophysical properties of fluids, scientists and researchers have developed different techniques. In heat transport, the addition of the nanoparticles enhances the thermal conductivity and the thermophysical properties of fluids. Khan et al. [18] described the simulation of the mixed convection hybrid nanofluid flow comprising the Cu and aluminum oxide ( Al 2 O 3 ) nanoparticles with a heat source/sink. Numerical simulation of their model is obtained with the implementation of the bvp4c technique. Acharya et al. [19] demonstrated the mixing of graphene oxide nanoparticles in a water-based liquid for the study of a two-dimensional nanofluid model. In this work, they also discussed the liquid–solid interfacial layer and nanoparticle diameter for the evaluation of the thermal integrity of the flow. Cao et al. [20] described the comparative study of carbon nanotubes, Al 2 O 3 , and graphene oxide nanoparticles on the ternary hybrid nanofluid flow with partial slip conditions, and they used water as a base fluid. Gangadhar et al. [21] carried out the study of 3D blood-based micropolar hybrid nanofluid flow. In this investigation, they used Au and magnesium oxide ( MgO ) as nanoparticles. Akram et al. [22] reported the MHD flow of peristaltic nanofluid by using the boron nitride nanotube nanoparticles in an ethylene glycol base fluid. Fares et al. [23] used the Ag nanoparticles in water base liquid for the study of magnetized Darcy–Forchheimer flow and irreversibility reaction in a square enclosure. In this simulation, they initiated that a higher nanoparticle volume fraction increased the nanoliquid Nusselt number. Ramzan et al. [24] discussed the influence of the MHD flow of nanofluid by using the bidirectional stretched surface with Hall current. Furthermore, they mix up the Fe 3 O 4 nanoparticles in a Vacuum pump oil base fluid for the formation of the nanofluid. Waini et al. [25] discussed the comparative mixtures of Al 2 O 3 and Cu nanoparticles on the radiative micropolar nanofluid flow through the existence of the magnetic and viscous effects. In this scrutiny, water is taken as a base liquid. Gumber et al. [26] have determined the physical features of the CuO and Ag on the flow of micropolar hybrid nanofluid with heat transport toward the vertical plate. They observed that the rate of heat transport is enhanced due to the addition of nanoparticles in water base fluid. Acharya [27] presented the numerical study of ferro-nanofluid with a mixture of CoFe 2 O 4 nanoparticles in base fluid water under the rotating disk. In this observation, an increment in fluid temperature is noted for higher nanoparticle diameter. Acharya [28] examined the role of solid–liquid interfacial layers and nanoparticles in the flow of ferro-nanofluid with the magnetic field past a spinning disk. Acharya [29] discussed the effect of the Al 2 O 3 nanoparticles on the flow of radiative nanofluid above the inclined spinning disk. With the aid of the spectral quasi-linearization method, a simulation of the problem is performed. Asogwa et al. [30] carried out a comparative analysis on water-based Al 2 O 3 nanofluid flow and water-based CuO nanofluid flow due to the stretching Riga plate. Bhati et al. [31] presented the applications of solar energy on the magnetized flow of water-based nanofluid containing MgO and nickel ( Ni ) nanoparticles. Solid nanoparticles in different flow problems under various geometries are studied by different researchers [32,33,34].

In recent years, MHD flow problems have piqued the interest of researchers and scientists due to their vast range of applications in discrete arenas of industries and manufacturing. The MHD effect was first investigated by Alfvén [35]. In 1970, he received the Nobel prize in physics. In industries and engineering, MHD flow problems have a number of fascinating usages such as MHD generators, nuclear reactor designs, pumps, flow meters, liquid metal cooling systems, blood flow measures, MHD-based biomedical sensors, actuators, and solar winds. On the basis of the above-mentioned applications, different scientific researchers and scholars have conducted their research on the MHD flow problems. Eswaramoorthi et al. [36] presented the upshot of MHD water-based nanofluid flow containing the Cu and Ag nanoparticles toward the heated plate. From this evaluation, it is attained that the radiation parameter augments the nanoliquid entropy. Bhatti et al. [37] analyzed the MHD Williamson nanoliquid flow toward the rotating plates along with motile gyrotactic microorganisms surrounded through the porous media and found the increment behavior in mass contour. Khan et al. [38] illustrated the heat source effects in an MHD nanofluid flow with slip conditions. In this examination, they used Cu nanoparticles. Swain et al. [39] offered the importance of the MHD flow nanoliquid through the shrinking sheet. In this inspection, it has been exposed that the nanofluid streaming is boost when the suction/injection constraint is enlarged. Nandi et al. [40] have determined the role of the activation energy and partial slip conditions in the MHD flow of Fe 3 O 4 / Cu / Ag − CH 3 OH by using the heated stretchy surface. Waini et al. [25] have established the micropolar flow model by suspending the Al 2 O 3 and Cu nanoparticles in water, and water is used as a base liquid. Furthermore, in this investigation, behavior of magnetic field and viscosity is discussed. Ramzan et al. [41] deliberated the thermal and velocity slip conditions on the mixed convection hybrid nanoliquid flow with a magnetic field toward the stretching surface. In this study, they mix up the Ag and MgO for the formation of the hybrid nanofluid. Ramzan et al. [42] investigated the prevalence of the chemical reaction and magnetic field on the flow of Casson liquid under the inclined flat plate. Joshi et al. [43] analyzed the effect of the viscous dissipation on the MHD flow of Darcy–Forchheimer hybrid nanofluid containing Cu and Ag nanoparticles via stretched surface. Hayat et al. [44] examined the flow of third-grade fluid with the effect of the magnetic field by using the stretching cylinder, and their concluding remarks explained that the higher values of the magnetic field declined the fluid particles’ speed. Hayat et al. [45] have considered the flow of third-grade fluid along with the combined effects of thermal radiation and magnetic field phenomenon toward the permeable stretched surface. In this discussion, they have analyzed that the increment in the Eckert number increases the thermal boundary layer thickness. Sharma and Shaw [46] examined the role of nonlinear thermal radiation in the flow of fluid past an extending surface with magnetic and viscous dissipation effects. Further works on the MHD flow problems are discussed in refs [38,47,48].

Nowadays, flow behavior of the fluids under the rotating disk in fluid mechanics is interesting to investigate. The applications of the flow problems through the rotating disk in industries and engineering areas are rotor–stator system, electrochemical system, manufacturing processes of glass fiber innovation, deposition of the coating on a surface, geophysics, solutal and thermal transport, and different mechanical fields. Therefore, different scientists and researchers show their keen attention in studying the flow problems related to the rotating disks. Nuwairan et al. [49] have determined the radiative Maxwell nanoliquid flow toward the rotating disk with heat generation. They found that the augmentation in heat generation factor led to improve the nanoliquid energy. Alzahrani and Khan [50] used the double rotating disks for the study of Darcy–Forchheimer on the Ree–Eyring nanofluid flow with artificial neural network and entropic behavior. Ayub et al. [51] discussed the effect of Lorentz forces and mass transportation on the 3D radiative cross-nanoliquid flow with the magnetic flux and autocatalysis chemical reaction by using the two rotating disks. In this work, it is predicted that the fluid particle speed is reduced due to the production of the Lorentz forces. Waini et al. [52] analyzed the stability analysis by using a rotating disk on the unsteady flow of hybrid nanofluid and found multiple solutions to their problem. In this examination, it is obtained that the Nusselt number for all solutions is greater when the suction is applied on the surface of the disk. Kumar et al. [53] explained the heat source/sink analysis in a dusty flow of nanofluid toward the revolving disk through the porous medium. In this analysis, they used water as the base liquid and multi-walled carbon nanotubes and single-walled carbon nanotubes (SWCNT) are the nanoparticles. Sun et al. [54] have considered the nonlinear thermal radiation impact over the thin-film Maxwell nanofluid flow with Brownian and thermal diffusivity under the rotating disk. In this inquiry, it is attained that the rotation constraint augmented the nanoliquid Sherwood number. Ramzan et al. [55] analyzed the impacts of mixed convection nanofluid flow toward the revolving disk. In this study, they used Au , silicon dioxide ( SiO 2 ), and Ag as the nanoparticles, and the base liquid is water. Usman et al. [56] studied the Cu and SWCNT nanoparticles on the power-law nanoliquid flow between the two-rotational disks with heat transport phenomena. In this scrutiny, blood is used as a base liquid. Simulation of their problem is obtained by using the shooting method.

In this work, the flow of two-dimensional electrically conducting nanofluid with the effect of a magnetic field toward the spinning disk has been investigated. Nanofluid is created by mixing Al 2 O 3 nanoparticles in water. The heat transport mechanism is simulated by using the role of viscous dissipation and nonlinear thermal radiation. Furthermore, the effects of the radius of Al 2 O 3 nanoparticles and inter-particle spacing on the electrically conducting nanofluid flow are elaborated. Because the Al 2 O 3 nanoparticles have a lot of real-world applications such as transparent ceramics, cosmetic fillers, high-pressure sodium lamps, integrated circuit baseboards, packaging materials, plastic wear-resistant reinforcement, aerospace aircraft wing leading edges, and fluorescent materials. The following questions are to be addressed at the end of this research work:

  • What is the behavior of velocity profiles and skin friction coefficients of the nanofluid for small and large inter-particle spacing?

  • How do the nanofluid skin friction coefficients and velocity profiles behave for a small and large radius of Al 2 O 3 nanoparticles?

  • What is the effect of the Lorentz force on the nanofluid velocity with the applications of the magnetic field?

  • How do the linear and nonlinear thermal radiation phenomena affect the nanofluid temperature profiles and heat transfer rate?

2 Problem formulation

Let us assume the two-dimensional electrically conducting water-based nanofluid containing the Al 2 O 3 nanoparticles over a rotating disk. Normal to the plane of the disk, the strength of magnetic field B 0 is employed. The disk rotates with an angular velocity Ω along z -axis. The rotating disk is placed at z = 0 . For the calculation of heat transmission, the viscous dissipation and nonlinear thermal radiation are deliberated. Furthermore, the effect of suction is discussed. Inside the boundary layer, by using the similarity transformations, the pressure remains constant ∂ p ∂ r = 0 [57] and the free-stream pressure is p ∞ . Along the directions of r , φ , and z -axes, the velocity components are symbolized by u , v , and w . The surface temperature is T w , and the ambient temperature of the nanofluid is T ∞ . Figure 1 demonstrates the geometrical representation of the flow problem.

Figure 1 Geometry of the flow problem.
Figure 1

Geometry of the flow problem.

The leading equations for the present model on the base of the above-mentioned flow assumptions are as follows [58–61]:

(1) ∂ u ∂ r + u r + ∂ w ∂ z = 0 ,

(2) u ∂ u ∂ r + w ∂ u ∂ z − v 2 r + ∂ p ∂ r = ν nf ∂ 2 u ∂ r 2 − u r 2 + ∂ 2 u ∂ z 2 + 1 r ∂ u ∂ r − σ nf ρ nf B 0 2 u ,

(3) u ∂ v ∂ r + w ∂ v ∂ z + u v r + ∂ p ∂ r = ν nf ∂ 2 v ∂ r 2 − v r 2 + ∂ 2 v ∂ z 2 + 1 r ∂ v ∂ r − σ nf ρ nf B 0 2 v ,

(4) u ∂ w ∂ r + w ∂ w ∂ z + ∂ p ∂ r = ν nf ∂ 2 w ∂ r 2 + ∂ 2 w ∂ z 2 + 1 r ∂ w ∂ r ,

(5) u ∂ T ∂ r + w ∂ T ∂ z = k nf ( ρ C p ) nf ∂ 2 T ∂ r 2 + ∂ 2 T ∂ z 2 + 1 r ∂ T ∂ r + 1 ( ρ C p ) nf ∂ ∂ z 16 σ ⁎ T 3 3 k ⁎ ∂ T ∂ z + μ nf ( ρ C p ) nf ∂ u ∂ z 2 + ∂ v ∂ z 2 .

The boundary conditions are as follows:

(6) u = 0 , v = r Ω , w = w 0 , T = T w when z = 0 , u → 0 , v → 0 , T → T ∞ , as z → ∞ , ,

where ν nf is the nanoliquid kinematics viscosity, p is the pressure, ρ nf is the nanoliquid density, the electrical conductivity of the nanoliquid is designated by σ nf , μ nf is the dynamic viscosity of the nanoliquid, B 0 is the magnetic field strength, k nf is the thermal conductivity of the nanoliquid, specific heat of the nanoliquid is denoted by ( C p ) nf , T is the temperature, w 0 is the suction/injection, Stefan–Boltzmann constant is denoted by σ ⁎ , and k ⁎ represents the absorption coefficient.

2.1 Suggested thermophysical properties of nanofluid

According to the study of Graham [62] and Gosukonda et al. [63], the viscosity model is deliberated as:

(7) μ nf μ f = 1 + 2.5 Δ + 4.5 1 h R p 2 + h R p 1 + h R p 2 ,

where h represents the inter-particle spacing, R p indicates the radius of nanoparticle, and Δ represents the solid volume fraction. Furthermore, thermophysical properties of the Al 2 O 3 nanofluid are discussed as:

(8) ρ nf = ( 1 − Δ ) ρ f + Δ ρ Al 2 O 3 .

In 1998, first, the density was discussed by Pak and Cho [64]. After this, a lot of research and scientists [65–67] have discussed the behavior of the density in different flow problems.

The heat capacitance was first offered by Pak and Cho [64] and deliberated as:

(9) ( ρ C p ) nf = ( 1 − Δ ) ( ρ C p ) f + Δ ( ρ C p ) Al 2 O 3 ,

where ( C p ) f is the specific heat of water.

In 1962, Hamilton and Crosser [68] initially discussed the thermal conductivity of the nanofluid and discussed as:

(10) k nf k f = k Al 2 O 3 + 2 k f − 2 Δ ( k f − k Al 2 O 3 ) k Al 2 O 3 + 2 k f + Δ ( k f − k Al 2 O 3 ) ,

where k f is the thermal conductivity of water.

The electrical conductivity was initially presented by Cruz et al. [69] and is defined as:

(11) σ nf σ f = σ Al 2 O 3 + 2 σ f − 2 Δ ( σ f − σ Al 2 O 3 ) σ Al 2 O 3 + 2 σ f + Δ ( σ f − σ Al 2 O 3 ) ,

where σ f is the electrical conductivity of water.

The physical characteristics of nanoparticles and base fluid are depicted in Table 1.

Table 1

Thermophysical characteristics of the base liquid and nanoparticles

Property Water Al 2 O 3
C p ( J/kg K ) 4,179 880
ρ ( kg/m 3 ) 997.1 3,890
k ( W/m K ) 0.613 35
σ ( S/m ) 5.5 × 10−6 3.5 × 107

In the present analysis, the similarity transformations are discussed [58–61]:

(12) u = r Ω f ′ ( ξ ) , v = r Ω g ( ξ ) , w = − 2 Ω ν f f ( ξ ) , p = p ∞ + 2 Ω μ f P ( ξ ) , θ ( ξ ) = T − T ∞ T w − T ∞ , ξ = 2 Ω ν f 1 2 z .

By applying the above similarity transformations in equation (12), equations (2)–(5) are converted into following form:

(13) 2 μ nf μ f ρ f ρ nf f ‴ + 2 f f ″ − f ′ 2 + g 2 − σ nf σ f ρ f ρ nf M f ′ = 0 ,

(14) 2 μ nf μ f ρ f ρ nf g ″ + 2 f g ′ − 2 f ′ g − σ nf σ f ρ f ρ nf M g = 0 ,

(15) ( ρ C p ) f ( ρ C p ) nf k nf k f + Rd ( 1 + ( θ w − 1 ) θ ) 3 θ ″ + Pr f θ ′ + ( ρ C p ) f ( ρ C p ) nf μ nf μ f Ec ( f ″ 2 + g ′ 2 ) = 0 ,

and transformed boundary conditions:

(16) f ( ξ ) = − f w , f ′ ( ξ ) = 0 , g ( ξ ) = 1 , θ ( ξ ) = 1 when → ξ = 0 , f ′ ( ξ ) → 0 , g ( ξ ) → 0 , θ ( ξ ) → 0 when → ζ = ∞ .

The leading dimensionless parameters from the present investigation are discussed here. The similarity variable is ξ , the magnetic field parameter is represented by M = B 0 2 σ f ρ f Ω , the radiation parameter is represented by Rd = 16 σ ⁎ T ∞ 3 3 k f k ⁎ , the Prandtl number is Pr = ( μ C p ) f k f , the Eckert number is signified by Ec = r 2 Ω 2 ( C p ) f ( T w − T ∞ ) , f w = w 0 2 Ω ν f is the section/injection parameter in which f w < 0 signifies the injection, while f w > 0 signifies the suction, and temperature ratio parameter is θ w = T w T ∞ .

Some physical quantities are described as:

(17) C f = 2 μ nf ρ f 1 ( r Ω ) 2 ∂ u ∂ z z = 0 , C g = 2 μ nf ρ f 1 ( r Ω ) 2 ∂ v ∂ z z = 0 , Nu = r k f ( T w − T ∞ ) q r − k nf ∂ T ∂ z z = 0 .

Now, the dimensionless forms of C fr , C gr , and Nu r are as follows:

(18) C fr = ( Re z ) 1 2 C f = 1 + 2.5 Δ + 4.5 1 h R p 2 + h R p 1 + h R p 2 f ″ ( 0 ) , C gr = ( Re z ) 1 2 C g = 1 + 2.5 Δ + 4.5 1 h R p 2 + h R p 1 + h R p 2 g ′ ( 0 ) , Nu r = Nu ( Re z ) 1 2 = − k nf k f + Rd ( 1 + ( θ w − 1 ) θ ) 3 θ ′ ( 0 ) ,

where Re z = Ω r 2 ν f is the Reynolds number.

3 Homotopy analysis method solution

The initial guesses and linear operator for the present case are as follows:

(19) f 0 ( ξ ) = − f w e − ξ , g 0 ( ξ ) = e − ξ , θ 0 ( ξ ) = e − ξ .

(20) L f = f ‴ − f ′ , L g = g ″ − g , L θ = θ ″ − θ .

As such,

(21) L f [ Ψ 1 + Ψ 2 e ξ ( ξ ) + Ψ 3 e − ξ ] = 0 , L g [ Ψ 4 e ξ + Ψ 5 e − ξ ] = 0 , L θ [ Ψ 6 e ξ + Ψ 7 e − ξ ] = 0 ,

and Ψ i ( i = 1 , 2 , 3 , … , 7 ) are the arbitrary constants.

3.1 Zeroth-order deformation problems

The zero-order deformation problems are discussed as:

(22) ( 1 − ℓ ) L f [ f ( ξ ; ℓ ) − f 0 ( ξ ) ] = q h f N f [ f ( ξ ; ℓ ) , g ( ξ ; ℓ ) ] ,

(23) ( 1 − ℓ ) L g [ g ( ξ ; ℓ ) − g 0 ( ξ ) ] = q h g N g [ f ( ξ ; ℓ ) , g ( ξ ; ℓ ) ] ,

(24) ( 1 − ℓ ) L θ [ θ ( ξ ; ℓ ) − θ 0 ( ξ ) ] = q h θ N θ [ f ( ξ ; ℓ ) , g ( ξ ; ℓ ) , θ ( ξ ; ℓ ) ] .

Here, the embedding parameter is ℓ , and the nonzero auxiliary parameters are h f , h g , and h θ . N f , N g , and N θ are the nonlinear operators that are discussed as:

(25) N f [ f ( ξ ; ℓ ) , g ( ξ ; ℓ ) ] = 2 μ nf μ f ρ f ρ nf ∂ 3 f ( ξ ; ℓ ) ∂ ξ 3 + 2 f ( ξ ; ℓ ) ∂ 2 f ( ξ ; ℓ ) ∂ ξ 2 − ∂ f ( ξ ; ℓ ) ∂ ξ 2 + g ( ξ ; ℓ ) 2 − σ nf σ f ρ f ρ nf M ∂ f ( ξ ; ℓ ) ∂ ξ ,

(26) N g [ f ( ξ ; ℓ ) , g ( ξ ; ℓ ) ] = 2 μ nf μ f ρ f ρ nf ∂ 2 g ( ξ ; ℓ ) ∂ ξ 2 + 2 f ( ξ ; ℓ ) ∂ g ( ξ ; ℓ ) ∂ ξ − 2 g ( ξ ; ℓ ) ∂ f ( ξ ; ℓ ) ∂ ξ − σ nf σ f ρ f ρ nf M g ( ξ ; ℓ ) ,

(27) N θ [ f ( ξ ; ℓ ) , g ( ξ ; ℓ ) , θ ( ξ ; ℓ ) ] = ( ρ C p ) f ( ρ C p ) nf k nf k f + Rd ( 1 + ( θ w − 1 ) θ ( ξ ; ℓ ) ) 3 ∂ 2 θ ( ξ ; ℓ ) ∂ ξ 2 + Pr f ( ξ ; ℓ ) ∂ θ ( ξ ; ℓ ) ∂ ξ − ( ρ C p ) f ( ρ C p ) nf μ nf μ f Ec ∂ 2 f ( ξ ; ℓ ) ∂ ξ 2 2 + ∂ g ( ξ ; ℓ ) ∂ ξ 2 ,

(28) f ( 0 ; ℓ ) = − f w , f ′ ( 0 ; ℓ ) = 0 , and f ′ ( ∞ ; ℓ ) = 0 ,

(29) g ( 0 ; ℓ ) = 1 , and g ( ∞ ; ℓ ) = 0 ,

(30) θ ( 0 ; ℓ ) = 1 , and θ ( ∞ ; ℓ ) = 0 .

For ℓ = 0 and ℓ = 1 , then equations (22)–(24) become as:

(31) ℓ = 0 ⇒ f ( ξ ; 0 ) = f 0 ( ξ ) and ℓ = 1 ⇒ f ( ξ ; 1 ) = f ( ξ ) ,

(32) ℓ = 0 ⇒ g ( ξ ; 0 ) = g 0 ( ξ ) and ℓ = 1 ⇒ g ( ξ ; 1 ) = g ( ξ ) ,

(33) ℓ = 0 ⇒ θ ( ξ ; 0 ) = θ 0 ( ξ ) and ℓ = 1 ⇒ θ ( ξ ; 1 ) = θ ( ξ ) .

According to Taylor’s series expansion, we have

(34) f ( ξ ; ℓ ) = f 0 ( ξ ) + ∑ m = 1 ∞ f m ( ξ ) ℓ m , f m ( ξ ) = 1 m ! ∂ m f ( ξ ; ℓ ) ∂ ξ m | ℓ = 0 ,

(35) g ( ξ ; ℓ ) = g 0 ( ξ ) + ∑ m = 1 ∞ g m ( ξ ) ℓ m , g m ( ξ ) = 1 m ! ∂ m g ( ξ ; ℓ ) ∂ ξ m ℓ = 0 ,

(36) θ ( ξ ; ℓ ) = θ 0 ( ξ ) + ∑ m = 1 ∞ θ m ( ξ ) ℓ m , θ m ( ξ ) = 1 m ! ∂ m θ ( ξ ; ℓ ) ∂ ξ m ℓ = 0 .

By putting ℓ = 1 in equations (34)–(36), the convergence of the series is accomplished as:

(37) f ( ξ ) = f 0 ( ξ ) + ∑ m = 1 ∞ f m ( ξ ) ,

(38) g ( ξ ) = g 0 ( ξ ) + ∑ m = 1 ∞ g m ( ξ ) ,

(39) θ ( ξ ) = θ 0 ( ξ ) + ∑ m = 1 ∞ θ m ( ξ ) .

3.2 mth-order deformation problems

The mth-order form of the problem is

(40) L f [ f m ( ξ ) − η m f m − 1 ( ξ ) ] = h f R m f m ( ξ ) ,

(41) L g [ g m ( ξ ) − η m g m − 1 ( ξ ) ] = h g R m g m ( ξ ) ,

(42) L θ [ θ m ( ξ ) − η m θ m − 1 ( ξ ) ] = h θ R m θ ( ξ ) ,

(43) f m ( 0 ) = 0 , f m ( 0 ) = 0 , f m ( ∞ ) = 0 ,

(44) g m ( 0 ) = 0 , g m ( ∞ ) = 0 ,

(45) θ m ( 0 ) = 0 , θ m ( ∞ ) = 0 .

R m f m ( ξ ) , R m g m ( ξ ) , and R m θ m ( ξ ) are defined as:

(46) R m f ( ξ ) = 2 μ nf μ f ρ f ρ nf f m − 1 ′ ′ ′ + 2 ∑ k = 0 m − 1 f m − 1 − k f k ′ ′ − ∑ k = 0 m − 1 f m − 1 − k ′ f k ′ + ∑ k = 0 m − 1 g m − 1 − k g k − σ n f σ f ρ f ρ n f M f m − 1 ′ ,

(47) R m g ( ξ ) = 2 μ n f μ f ρ f ρ n f g m − 1 ′ ′ + 2 ∑ k = 0 m − 1 f m − 1 − k g k ″ − ∑ k = 0 m − 1 f m − 1 − k ′ g k − σ n f σ f ρ f ρ n f M g m − 1 ,

(48) R m θ ( ξ ) = ( ρ C p ) f ( ρ C p ) nf k nf k f + Rd ( 1 + ( θ w − 1 ) θ m − 1 ) 3 θ m − 1 ′ ′ + Pr ∑ 1 = 0 k f m − 1 − k θ ′ k − 1 − ( ρ C p ) f ( ρ C p ) nf μ nf μ f Ec × ∑ 1 = 0 k f ′ m − 1 − k f ″ k − 1 f ″ 2 + ∑ 1 = 0 k g m − 1 − k ′ g ′ k − 1 = 0 ,

(49) η m = 0 , m ≤ 1 1 , m > 1 .

With the assistance of particular solution, the general solution of the present enquiry is achieved:

(50) f m ( ξ ) = f m ⁎ ( ξ ) + Ψ 1 + Ψ 2 exp ( ξ ) + Ψ 3 exp ( − ξ ) ,

(51) g m ( ξ ) = g m ⁎ ( ξ ) + Ψ 3 exp ( ξ ) + Ψ 4 exp ( − ξ ) ,

(52) θ m ( ξ ) = θ m ⁎ ( ξ ) + Ψ 6 exp ( ξ ) + Ψ 7 exp ( − ξ ) .

4 Results and discussion

This segment explains that the physical significance of the MHD flow of water-based nanofluid containing Al 2 O 3 nanoparticles over a rotating disk has been deliberated. The effect of inter-particle spacing and radius of nanoparticle on the flow behavior are analyzed. The proposed nanofluid model has been solved by using the homotopy analysis technique. The velocities and temperature profiles versus discrete flow parameters are computed for large and small inter-particle spacing (say h = 1/2 and h = 10) and for small and large (say R p = 3/2 and R p = 5/2) radius of Al 2 O 3 nanoparticles. Skin friction and Nusselt number versus discrete flow parameters are also calculated and are shown with the help of tables. For inter-particle spacing and radius of Al 2 O 3 nanoparticles, the results of Δ and M on the skin friction coefficient Re z C fr are demonstrated in Table 2. It is obtained that, for h = 1/2 and h = 10, Re z C fr of the nanofluid is enhanced due to the increasing M . Moreover, Re z C fr of the nanofluid is higher for small and large radius of Al 2 O 3 nanoparticles with the increase in M . Moreover, with the intensification of the magnetic field, the Lorentz force enhances, which opposes the motion of the fluid flow. That is why Re z C fr is an upsurge. Furthermore, it is noticed that the increment in Δ increases Re z C fr of the nanofluid for small and larger inter-particle spacing and radius of Al 2 O 3 nanoparticles. Table 3 represents the variation of the skin friction coefficient Re z C gr of the nanofluid for small and large inter-particle spacing and radius of Al 2 O 3 nanoparticles against M and Δ . Table 3 explains that, for small and large inter-particle spacing and for small and large radius of Al 2 O 3 nanoparticles, Re z C gr of the nanofluid is amplified versus increasing values of M . Moreover, it is noticed that Re z C gr of the nanoliquid is declined due to augmenting estimates of Δ for small and large inter-particle spacing and radius of Al 2 O 3 nanoparticles. The effect of Rd , Ec , and Δ on the nanofluid Nusselt number Nu r Re z for the case of θ w = 3/2 and θ w = 1 is shown in Table 4. Table 4 explores that Nu r Re z of the nanofluid for the case of θ w = 3/2 and θ w = 1 increases when Rd , Ec , and Δ are enhanced. Kumar et al. [70] obtained that the thermal boundary layer thickness enhances when the temperature ratio parameter ( θ w ) increases, which consequently enhances the nanofluid temperature and heat rate transfer. Here, in the present analysis, two different linear ( θ w = 1 ) and nonlinear thermal radiation ( θ w > 1 ) cases are discussed.

Table 2

Effects of M and Δ on Re z C fr for h = 1/2, h = 10, R p = 3/2, and R p = 5/2

M Δ Re z C fr
h = 1 / 2 h = 10 R p = 3/2 R p = 5/2
0.1 0.273832 0.273829 0.024810 0.034812
0.2 0.273833 0.273831 0.024811 0.034816
0.3 0.272834 0.273834 0.024812 0.034818
0.4 0.273836 0.273836 0.024813 0.034819
0.01 0.253831 0.263532 0.283833 0.293832
0.02 0.252962 0.264668 0.282969 0.292968
0.03 0.252393 0.265793 0.282394 0.292393
0.04 0.252095 0.266794 0.282096 0.292096
Table 3

Effects of M and Δ on Re z C gr for h = 1/2, h = 10, R p = 3/2, and R p = 5/2

M Δ Re z C gr
h = 1 / 2 h = 10 R p = 3/2 R p = 5/2
0.1 2.891303 0.762811 0.819206 0.919206
0.2 2.900508 0.772016 0.824415 0.920415
0.3 2.919713 0.781221 0.835362 0.922624
0.4 2.938918 0.690426 0.840834 0.923834
0.01 3.110370 0.981878 1.226369 1.718265
0.02 3.100556 0.978780 1.222499 1.712844
0.03 3.094028 0.976719 1.219925 1.709237
0.04 3.090648 0.975652 1.218593 1.707370
Table 4

Effects of Rd , Ec , and Δ on Nu r Re z for θ w = 3/2 and θ w = 1

Rd Ec Δ Nu r Re z Nu r Re z
θ w = 3/2 θ w = 1
0.1 1.583450 1.509312
0.2 2.155726 2.983882
0.3 3.716828 3.423517
0.4 4.266756 4.828410
0.1 2.624424 3.218437
0.2 3.716828 3.423517
0.3 4.809231 3.628597
0.4 4.901634 3.833677
0.01 1.703150 1.069990
0.02 1.819742 1.247410
0.03 1.951036 1.447200
0.04 1.998451 1.671524

From this examination, it is perceived that the heat rate transfer increases more for the case of nonlinear thermal radiation by increasing the temperature ratio parameter ( θ w > 1 ) as compared to the case of linear thermal radiation. The flow chart of the present work is discussed in Figure 2. Figures 3–7 determine the fluctuation of f ′ ( ξ ) against different flow constraints such as suction f w , magnetic parameter M , and radius of nanoparticles R p for both small and large inter-particle spacing h and nanoparticle radius R p cases. Figure 3 explains the behavior of suction parameter f w on f ′ ( ξ ) of the nanofluid for both h = 1/2 and h = 10. In this figure, it is shown that f ′ ( ξ ) amplifies for larger values of the suction parameter f w for both h = 1/2 and h = 10. The effect of f w on f ′ ( ξ ) of the nanofluid for small radius of Al 2 O 3 nanoparticles is demonstrated in Figure 4. For both small and large radius of Al 2 O 3 nanoparticles, f ′ ( ξ ) of the nanofluid is enhanced due to the increase in suction parameter f w . Figure 5 determines the fluctuation in f ′ ( ξ ) of the nanofluid for both h = 1/2 and h = 10 against growing values of M . From this scrutiny, it can be determined that the larger values of M diminish f ′ ( ξ ) for both h = 1/2 and h = 10. Figure 6 displays the effect of M on f ′ ( ξ ) of the nanofluid for small and large radius of Al 2 O 3 nanoparticles. This figure explains that f ′ ( ξ ) of the nanofluid for small radius of Al 2 O 3 nanoparticles decreases when M rises. In this examination, it is inspected that by rising the magnetic field parameter M , the frictional forces between the fluid particles are produced. Also, the rate of heat transport increases due to the increase in magnetic field parameter. Lorentz force effect is produced due to higher magnetic field. The boundary layer thickness for momentum reduces with the increase in Lorentz force, and thus, the velocity of the fluid decreases. The variation in f ′ ( ξ ) of the nanofluid versus higher values of the nanoparticles radius R p for both h = 1/2 and h = 10 is discussed in Figure 7. For both h = 1/2 and h = 10, f ′ ( ξ ) increases due to the increase in nanoparticle radius R p . The effects of the various flow parameters such as f w , M , and R p on g ( ξ ) of the nanoliquid for both inter-particle spacing h and nanoparticle radius R p cases are analyzed in Figures 8–12. The impact of suction parameter f w on g ( ξ ) of the nanofluid for both h = 1/2 and h = 10 is scrutinized in Figure 8. This figure displays that g ( ξ ) is higher for both h = 1/2 and h = 10 due to enhancing suction parameter f w . Figure 9 describes the effect of f w on g ( ξ ) of the nanofluid for both small and large radius of Al 2 O 3 nanoparticles. In this graph, it is detected that as the values of the suction parameter f w rise, then g ( ξ ) increases for both small and large radius of Al 2 O 3 nanoparticles. For h = 1/2 and h = 10, variation in g ( ξ ) of the nanoliquid due to the higher values of M is deliberated in Figure 10. From this graph, the decreasing behavior in g ( ξ ) of the nanofluid is observed for h = 1/2 and h = 10 against the expanding values of M . Figure 11 explores the effect of M on g ( ξ ) of the nanofluid for both small and large radius of aluminum oxide Al 2 O 3 nanoparticles. Increment in M declines g ( ξ ) for both small and large radius of Al 2 O 3 nanoparticles. In this examination, it is perceived that by expanding the magnetic field parameter M , the frictional forces between the fluid particles are produced. Also, the heat rate transmission increases due to the increase in magnetic field parameter. The Lorentz force effect is produced due to higher magnetic field. The boundary layer thickness for momentum reduces with the increase in Lorentz force, and thus, the velocity of the fluid decreases. The effect of nanoparticle radius R p on g ( ξ ) of the nanofluid for both h = 1/2 and h = 10 is analyzed in Figure 12. g ( ξ ) is greater due to greater values of nanoparticle radius R p for both h = 1/2 and h = 10. Figures 13–15 are drawn to determine the effects of distinct flow parameters on the temperature profile θ ( ξ ) of the nanofluid for both θ w = 3/2 and θ w = 1 cases. The impact of the Eckert number on θ ( ξ ) of the nanofluid for both θ w = 3/2 and θ w = 1 is described in Figure 13. The increase in performance in θ ( ξ ) is observed against larger values of the Eckert number Ec for both θ w = 3/2 and θ w = 1. The reason behind this analysis is that by increasing the Eckert number, the electrical energy and mechanical energy are converted into the heat due to the friction and resistance of the fluid. Therefore, the thermal boundary layer thickness and nanofluid temperature increase with the increasing Eckert number. It is perceived that the surface heat of the nanofluid enhances with the increase in the Eckert number. That is why the nanofluid temperature increases. The fluctuation in θ ( ξ ) for both θ w = 3/2 and θ w = 1 due to the growing values of Rd is represented in Figure 14. In this observation, it is noticed that the intensifying values of Rd increase θ ( ξ ) for both θ w = 3/2 and θ w = 1. The radiation parameter is deliberated as the relative consequence of the conduction heat transport to the radiation transport. It is noticed that the boundary layer thickness enhances due to the increase in the radiation parameter. Thus, the molecular movement or energy level between the particles of the fluid is higher. Therefore, temperature profile of the fluid is amplifying due to the increase in radiation parameter. The effect of nanoparticle radius R p on θ ( ξ ) for both θ w = 3/2 and θ w = 1 is investigated in Figure 15. This figure explores that θ ( ξ ) is greater when the nanoparticle radius R p is higher for both θ w = 3/2 and θ w = 1.

Figure 2 Flow chart.
Figure 2

Flow chart.

Figure 3 Effect of f w {f}_{\text{w}} on f ′ ( ξ ) f^{\prime} (\xi ) when h h = 10 and h h = 1/2.
Figure 3

Effect of f w on f ′ ( ξ ) when h = 10 and h = 1/2.

Figure 4 Effect of f w {f}_{\text{w}} on f ′ ( ξ ) f^{\prime} (\xi ) when R p {R}_{\text{p}} = 5/2 and R p {R}_{\text{p}} = 3/2.
Figure 4

Effect of f w on f ′ ( ξ ) when R p = 5/2 and R p = 3/2.

Figure 5 Effect of M M on f ′ ( ξ ) f^{\prime} (\xi ) when h h = 10 and h h = 1/2.
Figure 5

Effect of M on f ′ ( ξ ) when h = 10 and h = 1/2.

Figure 6 Effect of M M on f ′ ( ξ ) f^{\prime} (\xi ) when R p {R}_{\text{p}} = 5/2 and R p {R}_{\text{p}} = 3/2.
Figure 6

Effect of M on f ′ ( ξ ) when R p = 5/2 and R p = 3/2.

Figure 7 Effect of R p {R}_{\text{p}} on f ′ ( ξ ) f^{\prime} (\xi ) when h h = 10 and h h = 1/2.
Figure 7

Effect of R p on f ′ ( ξ ) when h = 10 and h = 1/2.

Figure 8 Effect of f w {f}_{\text{w}} on g ( ξ ) g(\xi ) when h h = 10 and h h = 1/2.
Figure 8

Effect of f w on g ( ξ ) when h = 10 and h = 1/2.

Figure 9 Effect of f w {f}_{\text{w}} on g ( ξ ) g(\xi ) when R p {R}_{\text{p}} = 5/2 and R p {R}_{\text{p}} = 3/2.
Figure 9

Effect of f w on g ( ξ ) when R p = 5/2 and R p = 3/2.

Figure 10 Effect of M M on g ( ξ ) g(\xi ) when h h = 10 and h h = 1/2.
Figure 10

Effect of M on g ( ξ ) when h = 10 and h = 1/2.

Figure 11 Effect of M M on g ( ξ ) g(\xi ) when R p {R}_{\text{p}} = 5/2 and R p {R}_{\text{p}} = 3/2.
Figure 11

Effect of M on g ( ξ ) when R p = 5/2 and R p = 3/2.

Figure 12 Effect of R p {R}_{\text{p}} on g ( ξ ) g(\xi ) when h h = 10 and h h = 1/2.
Figure 12

Effect of R p on g ( ξ ) when h = 10 and h = 1/2.

Figure 13 Effect of Ec \text{Ec} on θ ( ξ ) \theta (\xi ) when θ w {\theta }_{\text{w}} = 1 and θ w {\theta }_{\text{w}} = 3/2.
Figure 13

Effect of Ec on θ ( ξ ) when θ w = 1 and θ w = 3/2.

Figure 14 Effect of Rd \text{Rd} on θ ( ξ ) \theta (\xi ) when θ w {\theta }_{\text{w}} = 1 and θ w {\theta }_{\text{w}} = 3/2.
Figure 14

Effect of Rd on θ ( ξ ) when θ w = 1 and θ w = 3/2.

Figure 15 Effect of R p {R}_{\text{p}} on θ ( ξ ) \theta (\xi ) when θ w {\theta }_{\text{w}} = 1 and θ w {\theta }_{\text{w}} = 3/2.
Figure 15

Effect of R p on θ ( ξ ) when θ w = 1 and θ w = 3/2.

5 Conclusion

In this work, an MHD flow of nanofluid containing Al 2 O 3 nanoparticles has been considered over a rotating disk. The flow behavior is affected by the radius of nanoparticle and inter-particle spacing. For the investigation of heat transport, the role of viscous dissipation and nonlinear thermal radiation is incorporated. Suction effect is also deliberated in the present analysis. The major results of the present work are pointed as:

  1. The enhancement in Re z C fr is noted with the increase in magnetic field parameter due to lower or higher inter-particle spacing.

  2. For the case of lower or higher radius of Al 2 O 3 nanoparticles, Re z C fr enhances due to the augmentation of nanoparticle volume fraction. Also, for lower inter-particle spacing, Re z C fr reduces but for higher inter-particle spacing, Re z C fr increases due to higher nanoparticle volume fraction.

  3. When the radius of Al 2 O 3 nanoparticles is small or larger, Re z C gr of the nanoliquid is augmented due to higher magnetic parameter. Furthermore, it is determined that Re z C gr is larger for the case of small or larger inter-particle spacing against the greater magnetic parameter.

  4. It is witnessed that Nu r Re z enhances due to the higher radiation parameter, Eckert number, and nanoparticle volume fraction for both linear and nonlinear thermal radiation cases.

  5. In case of lower or higher inter-particle spacing, f ′ ( ξ ) is increased for suction parameter, whereas f ′ ( ξ ) is decreased for magnetic field parameter. Furthermore, it is examined that f ′ ( ξ ) is higher for suction parameter, whereas f ′ ( ξ ) is lower against magnetic field parameter for the case of small or larger radius of nanoparticles.

  6. For the case of small or larger inter-particle spacing, increment in suction parameter led to enhance g ( ξ ) while diminishes against magnetic field parameter. Furthermore, for both small and larger radius of nanoparticles case, g ( ξ ) is augmented due to the increase in suction parameter, while opposite trend is observed against magnetic field parameter.

  7. f ′ ( ξ ) and g ( ξ ) are augmented due to the higher nanoparticle’s radius for the case of lower or higher inter-particle spacing.

  8. θ ( ξ ) shows increasing behavior versus Eckert number, radiation parameter, and nanoparticle radius for both linear and nonlinear thermal radiation.

  1. Funding information: This research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2023 under project number FRB660073/0164. The first author appreciates the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship (Grant No. 14/2562 and Grant No. 25/2563).

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

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Received: 2022-08-06
Revised: 2022-11-14
Accepted: 2022-11-28
Published Online: 2023-01-30

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/ntrev-2022-0501
Keywords for this article
aluminum oxide nanoparticles; inter-particle spacing; nonlinear thermal radiation; radius of nanoparticles; rotating disk; homotopy analysis method
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Preparation of CdS–Ag2S nanocomposites by ultrasound-assisted UV photolysis treatment and its visible light photocatalysis activity
  3. Significance of nanoparticle radius and inter-particle spacing toward the radiative water-based alumina nanofluid flow over a rotating disk
  4. Aptamer-based detection of serotonin based on the rapid in situ synthesis of colorimetric gold nanoparticles
  5. Investigation of the nucleation and growth behavior of Ti2AlC and Ti3AlC nano-precipitates in TiAl alloys
  6. Dynamic recrystallization behavior and nucleation mechanism of dual-scale SiCp/A356 composites processed by P/M method
  7. High mechanical performance of 3-aminopropyl triethoxy silane/epoxy cured in a sandwich construction of 3D carbon felts foam and woven basalt fibers
  8. Applying solution of spray polyurea elastomer in asphalt binder: Feasibility analysis and DSR study based on the MSCR and LAS tests
  9. Study on the chronic toxicity and carcinogenicity of iron-based bioabsorbable stents
  10. Influence of microalloying with B on the microstructure and properties of brazed joints with Ag–Cu–Zn–Sn filler metal
  11. Thermohydraulic performance of thermal system integrated with twisted turbulator inserts using ternary hybrid nanofluids
  12. Study of mechanical properties of epoxy/graphene and epoxy/halloysite nanocomposites
  13. Effects of CaO addition on the CuW composite containing micro- and nano-sized tungsten particles synthesized via aluminothermic coupling with silicothermic reduction
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  15. Design of functional vancomycin-embedded bio-derived extracellular matrix hydrogels for repairing infectious bone defects
  16. Study on nanocrystalline coating prepared by electro-spraying 316L metal wire and its corrosion performance
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  18. Tungsten trioxide nanocomposite for conventional soliton and noise-like pulse generation in anomalous dispersion laser cavity
  19. Microstructure and electrical contact behavior of the nano-yttria-modified Cu-Al2O3/30Mo/3SiC composite
  20. Melting rheology in thermally stratified graphene-mineral oil reservoir (third-grade nanofluid) with slip condition
  21. Re-examination of nonlinear vibration and nonlinear bending of porous sandwich cylindrical panels reinforced by graphene platelets
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  23. Chitosan-capped silver nanoparticles with potent and selective intrinsic activity against the breast cancer cells
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  31. Brownian and thermal diffusivity impact due to the Maxwell nanofluid (graphene/engine oil) flow with motile microorganisms and Joule heating
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  45. Performance of polycarboxylate superplasticisers in seawater-blended cement: Effect from chemical structure and nano modification
  46. Entropy minimization of GO–Ag/KO cross-hybrid nanofluid over a convectively heated surface
  47. Oxygen plasma assisted room temperature bonding for manufacturing SU-8 polymer micro/nanoscale nozzle
  48. Performance and mechanism of CO2 reduction by DBD-coupled mesoporous SiO2
  49. Polyarylene ether nitrile dielectric films modified by HNTs@PDA hybrids for high-temperature resistant organic electronics field
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  51. Hygrothermal bending analysis of sandwich nanoplates with FG porous core and piezomagnetic faces via nonlocal strain gradient theory
  52. Design and optimization of a TiO2/RGO-supported epoxy multilayer microwave absorber by the modified local best particle swarm optimization algorithm
  53. Mechanical properties and frost resistance of recycled brick aggregate concrete modified by nano-SiO2
  54. Self-template synthesis of hollow flower-like NiCo2O4 nanoparticles as an efficient bifunctional catalyst for oxygen reduction and oxygen evolution in alkaline media
  55. High-performance wearable flexible strain sensors based on an AgNWs/rGO/TPU electrospun nanofiber film for monitoring human activities
  56. High-performance lithium–selenium batteries enabled by nitrogen-doped porous carbon from peanut meal
  57. Investigating effects of Lorentz forces and convective heating on ternary hybrid nanofluid flow over a curved surface using homotopy analysis method
  58. Exploring the potential of biogenic magnesium oxide nanoparticles for cytotoxicity: In vitro and in silico studies on HCT116 and HT29 cells and DPPH radical scavenging
  59. Enhanced visible-light-driven photocatalytic degradation of azo dyes by heteroatom-doped nickel tungstate nanoparticles
  60. A facile method to synthesize nZVI-doped polypyrrole-based carbon nanotube for Ag(i) removal
  61. Improved osseointegration of dental titanium implants by TiO2 nanotube arrays with self-assembled recombinant IGF-1 in type 2 diabetes mellitus rat model
  62. Functionalized SWCNTs@Ag–TiO2 nanocomposites induce ROS-mediated apoptosis and autophagy in liver cancer cells
  63. Triboelectric nanogenerator based on a water droplet spring with a concave spherical surface for harvesting wave energy and detecting pressure
  64. A mathematical approach for modeling the blood flow containing nanoparticles by employing the Buongiorno’s model
  65. Molecular dynamics study on dynamic interlayer friction of graphene and its strain effect
  66. Induction of apoptosis and autophagy via regulation of AKT and JNK mitogen-activated protein kinase pathways in breast cancer cell lines exposed to gold nanoparticles loaded with TNF-α and combined with doxorubicin
  67. Effect of PVA fibers on durability of nano-SiO2-reinforced cement-based composites subjected to wet-thermal and chloride salt-coupled environment
  68. Effect of polyvinyl alcohol fibers on mechanical properties of nano-SiO2-reinforced geopolymer composites under a complex environment
  69. In vitro studies of titanium dioxide nanoparticles modified with glutathione as a potential drug delivery system
  70. Comparative investigations of Ag/H2O nanofluid and Ag-CuO/H2O hybrid nanofluid with Darcy-Forchheimer flow over a curved surface
  71. Study on deformation characteristics of multi-pass continuous drawing of micro copper wire based on crystal plasticity finite element method
  72. Properties of ultra-high-performance self-compacting fiber-reinforced concrete modified with nanomaterials
  73. Prediction of lap shear strength of GNP and TiO2/epoxy nanocomposite adhesives
  74. A novel exploration of how localized magnetic field affects vortex generation of trihybrid nanofluids
  75. Fabrication and physicochemical characterization of copper oxide–pyrrhotite nanocomposites for the cytotoxic effects on HepG2 cells and the mechanism
  76. Thermal radiative flow of cross nanofluid due to a stretched cylinder containing microorganisms
  77. In vitro study of the biphasic calcium phosphate/chitosan hybrid biomaterial scaffold fabricated via solvent casting and evaporation technique for bone regeneration
  78. Insights into the thermal characteristics and dynamics of stagnant blood conveying titanium oxide, alumina, and silver nanoparticles subject to Lorentz force and internal heating over a curved surface
  79. Effects of nano-SiO2 additives on carbon fiber-reinforced fly ash–slag geopolymer composites performance: Workability, mechanical properties, and microstructure
  80. Energy bandgap and thermal characteristics of non-Darcian MHD rotating hybridity nanofluid thin film flow: Nanotechnology application
  81. Green synthesis and characterization of ginger-extract-based oxali-palladium nanoparticles for colorectal cancer: Downregulation of REG4 and apoptosis induction
  82. Abnormal evolution of resistivity and microstructure of annealed Ag nanoparticles/Ag–Mo films
  83. Preparation of water-based dextran-coated Fe3O4 magnetic fluid for magnetic hyperthermia
  84. Statistical investigations and morphological aspects of cross-rheological material suspended in transportation of alumina, silica, titanium, and ethylene glycol via the Galerkin algorithm
  85. Effect of CNT film interleaves on the flexural properties and strength after impact of CFRP composites
  86. Self-assembled nanoscale entities: Preparative process optimization, payload release, and enhanced bioavailability of thymoquinone natural product
  87. Structure–mechanical property relationships of 3D-printed porous polydimethylsiloxane films
  88. Nonlinear thermal radiation and the slip effect on a 3D bioconvection flow of the Casson nanofluid in a rotating frame via a homotopy analysis mechanism
  89. Residual mechanical properties of concrete incorporated with nano supplementary cementitious materials exposed to elevated temperature
  90. Time-independent three-dimensional flow of a water-based hybrid nanofluid past a Riga plate with slips and convective conditions: A homotopic solution
  91. Lightweight and high-strength polyarylene ether nitrile-based composites for efficient electromagnetic interference shielding
  92. Review Articles
  93. Recycling waste sources into nanocomposites of graphene materials: Overview from an energy-focused perspective
  94. Hybrid nanofiller reinforcement in thermoset and biothermoset applications: A review
  95. Current state-of-the-art review of nanotechnology-based therapeutics for viral pandemics: Special attention to COVID-19
  96. Solid lipid nanoparticles for targeted natural and synthetic drugs delivery in high-incidence cancers, and other diseases: Roles of preparation methods, lipid composition, transitional stability, and release profiles in nanocarriers’ development
  97. Critical review on experimental and theoretical studies of elastic properties of wurtzite-structured ZnO nanowires
  98. Polyurea micro-/nano-capsule applications in construction industry: A review
  99. A comprehensive review and clinical guide to molecular and serological diagnostic tests and future development: In vitro diagnostic testing for COVID-19
  100. Recent advances in electrocatalytic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid: Mechanism, catalyst, coupling system
  101. Research progress and prospect of silica-based polymer nanofluids in enhanced oil recovery
  102. Review of the pharmacokinetics of nanodrugs
  103. Engineered nanoflowers, nanotrees, nanostars, nanodendrites, and nanoleaves for biomedical applications
  104. Research progress of biopolymers combined with stem cells in the repair of intrauterine adhesions
  105. Progress in FEM modeling on mechanical and electromechanical properties of carbon nanotube cement-based composites
  106. Antifouling induced by surface wettability of poly(dimethyl siloxane) and its nanocomposites
  107. TiO2 aerogel composite high-efficiency photocatalysts for environmental treatment and hydrogen energy production
  108. Structural properties of alumina surfaces and their roles in the synthesis of environmentally persistent free radicals (EPFRs)
  109. Nanoparticles for the potential treatment of Alzheimer’s disease: A physiopathological approach
  110. Current status of synthesis and consolidation strategies for thermo-resistant nanoalloys and their general applications
  111. Recent research progress on the stimuli-responsive smart membrane: A review
  112. Dispersion of carbon nanotubes in aqueous cementitious materials: A review
  113. Applications of DNA tetrahedron nanostructure in cancer diagnosis and anticancer drugs delivery
  114. Magnetic nanoparticles in 3D-printed scaffolds for biomedical applications
  115. An overview of the synthesis of silicon carbide–boron carbide composite powders
  116. Organolead halide perovskites: Synthetic routes, structural features, and their potential in the development of photovoltaic
  117. Recent advancements in nanotechnology application on wood and bamboo materials: A review
  118. Application of aptamer-functionalized nanomaterials in molecular imaging of tumors
  119. Recent progress on corrosion mechanisms of graphene-reinforced metal matrix composites
  120. Research progress on preparation, modification, and application of phenolic aerogel
  121. Application of nanomaterials in early diagnosis of cancer
  122. Plant mediated-green synthesis of zinc oxide nanoparticles: An insight into biomedical applications
  123. Recent developments in terahertz quantum cascade lasers for practical applications
  124. Recent progress in dielectric/metal/dielectric electrodes for foldable light-emitting devices
  125. Nanocoatings for ballistic applications: A review
  126. A mini-review on MoS2 membrane for water desalination: Recent development and challenges
  127. Recent updates in nanotechnological advances for wound healing: A narrative review
  128. Recent advances in DNA nanomaterials for cancer diagnosis and treatment
  129. Electrochemical micro- and nanobiosensors for in vivo reactive oxygen/nitrogen species measurement in the brain
  130. Advances in organic–inorganic nanocomposites for cancer imaging and therapy
  131. Advancements in aluminum matrix composites reinforced with carbides and graphene: A comprehensive review
  132. Modification effects of nanosilica on asphalt binders: A review
  133. Decellularized extracellular matrix as a promising biomaterial for musculoskeletal tissue regeneration
  134. Review of the sol–gel method in preparing nano TiO2 for advanced oxidation process
  135. Micro/nano manufacturing aircraft surface with anti-icing and deicing performances: An overview
  136. Cell type-targeting nanoparticles in treating central nervous system diseases: Challenges and hopes
  137. An overview of hydrogen production from Al-based materials
  138. A review of application, modification, and prospect of melamine foam
  139. A review of the performance of fibre-reinforced composite laminates with carbon nanotubes
  140. Research on AFM tip-related nanofabrication of two-dimensional materials
  141. Advances in phase change building materials: An overview
  142. Development of graphene and graphene quantum dots toward biomedical engineering applications: A review
  143. Nanoremediation approaches for the mitigation of heavy metal contamination in vegetables: An overview
  144. Photodynamic therapy empowered by nanotechnology for oral and dental science: Progress and perspectives
  145. Biosynthesis of metal nanoparticles: Bioreduction and biomineralization
  146. Current diagnostic and therapeutic approaches for severe acute respiratory syndrome coronavirus-2 (SARS-COV-2) and the role of nanomaterial-based theragnosis in combating the pandemic
  147. Application of two-dimensional black phosphorus material in wound healing
  148. Special Issue on Advanced Nanomaterials and Composites for Energy Conversion and Storage - Part I
  149. Helical fluorinated carbon nanotubes/iron(iii) fluoride hybrid with multilevel transportation channels and rich active sites for lithium/fluorinated carbon primary battery
  150. The progress of cathode materials in aqueous zinc-ion batteries
  151. Special Issue on Advanced Nanomaterials for Carbon Capture, Environment and Utilization for Energy Sustainability - Part I
  152. Effect of polypropylene fiber and nano-silica on the compressive strength and frost resistance of recycled brick aggregate concrete
  153. Mechanochemical design of nanomaterials for catalytic applications with a benign-by-design focus
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