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The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis

  • Humaira Yasmin EMAIL logo , Showkat Ahmad Lone , Ali M. Mahnashi , Waleed Hamali , Zehba Raizah and Anwar Saeed EMAIL logo
Published/Copyright: February 6, 2024
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Open Physics
From the journal Open Physics Volume 22 Issue 1

Abstract

A metallic alloy is a combination of two or more elements, often called a compound or a solution. Steel is largely composed of carbon, a nonmetal, but alloys are often made up of metals. In this article, the authors have explored the electrically conducting water-based viscous nanofluids flow past a rotating disk surface. The nanofluids flow is composed of titanium and aluminum alloys where water is used as a base fluid. Two important cases, namely the stretching case and the shrinking case, were investigated to analyze the flow behaviors due to the different embedding factors. The impacts of viscous Joule heating, thermophoresis, Brownian motion, activation energy, nonlinear thermal radiation, and chemical reaction are investigated here. By employing an appropriate set of variables for shifting the leading equations to dimension-free form. The mathematical model is solved numerically by incorporating the bvp4c MATLAB scheme. Current work is validated with previous studies. The outcomes showed that the radial velocity increases when the disk surface stretches and reduces when the disk surface shrinks. On the other hand, the Azimuthal velocity increases when the disk surface shrinks and reduces when disk surface stretches. Both the radial and Azimuthal velocities are the diminishing functions of the magnetic factor, whereas temperature is the growing function of magnetic factor. In addition, the temperature is more influenced by the magnetic factor in the case of nonlinear radiation. The higher magnetic factor increases skin friction. In addition, the stretching case experiences more surface drag than the shrinking case. It is found that nanofluid flow containing titanium alloy has perceived the greater impacts of the embedded factors compared to the nanofluid flow containing aluminum alloy.

Keywords: nanofluids; water; titanium and aluminum alloys; Joule heating; viscous dissipation; rotating disk; stretching/shrinking cases

Nomenclature

u , v , w

components of flow

r , φ , z

coordinates

B 0

strength of the magnetic field

Ω

angular velocity

u w = ar

stretching velocity

S

stretching/shrinking factor

v w = r Ω

rotational velocity

T

temperature

T f

reference temperature

C

concentration

C f

reference concentration

a

constant

ρ

density

μ

viscosity

σ , k

electrical and thermal conductivities

p

pressure

C p

specific heat

D B

Brownian diffusivity coefficient

D T

thermophoretic coefficient

k r

reaction coefficient

E a

coefficient of activation energy

n

power index

h f , h c

heat and mass transfer coefficients

ϕ

nanoparticle volume fraction

M

magnetic factor

Pr

Prandtl number

ω

temperature difference factor

Bi T , Bi C

thermal and concentration Biot numbers

K r

chemical reaction factor

Nt

thermophoretic factor

Rd

thermal radiation factor

Nb

Brownian motion factor

E

activation energy factor

Sc

Schmidt number

θ w

temperature ratio factor

1 Introduction

It is difficult to achieve high competence in thermal-mass fluidity while working with ordinary fluids that have subpar thermophysical properties. The introduction of the idea of nanofluids brought the issue to some actuality. A fluid that has been infused with quite conductive nanoparticles is known as a nanofluid. In contrast to larger particles, these nanoparticles are easily suspended in the base fluid for long enough duration. The prodigious effort of nanofluid was presented by Choi [1]. Due to the magnificent heat performances, the nanofluid is accepted as a dominant source of energy and has many applications in modern thermal technological and industrial developments. Wen and Ding [2] examined the electrostatic stability processes and the use of a high-shear mixing homogenizer to distribute titanium nanoparticles in pure water. In order to investigate the performance of nanofluids in terms of thermal transference under the conditions of natural convection, these nanofluids are discovered to be extremely stable. Lin and Ghaffari [3] explored heat transmission phenomena of power-law fluid within two extending disks separated by a fixed distance and rotate coaxially. They discovered that rotation improves the velocity components. Wang et al. [4] summarized the fundamental ideas of slip conditions including their definition and categories. An analysis was conducted by Tyler et al. [5] to determine how nanoparticles, specifically nanodiamonds, affect heat transfer in fluids and polymer solids. Techniques are discussed for dispersing nanoparticles in liquids and solids. Heat transfer properties of liquid suspensions are qualitatively compared using a custom thermal transport test setup that measures particle size distributions and fluid viscosities. Using a flash lamp technique, the thermal conductivity of polymer samples is measured to ensure nanoparticle dispersion. A hybrid nanofluid is another creation with enhanced thermal properties than traditional base fluids and nanofluids. Nanoparticles are mixed into a base fluid to form this mixture. In the composition of nanofluids or hybrid nanofluids, metal carbide, metal nitride, metals, metal oxides, and other carbon-based compounds are the most often employed nanoparticles. Sajid and Ali [6] presented an inclusive review of the hybrid nanofluids’ thermal conductivity by overviewing the theoretical and experimental studies on the hybrid nanofluids. They discussed various dynamics affecting thermal conductivity, including nanoparticle type, temperature, variability of pH, and sonication time. The hybrid nanofluid slip flow was inspected by Wahid et al. [7] over a permeable sheet that was stretching/shrinking exponentially over time. The application of alumina and copper in a hybrid system using H 2 O as base fluid is examined and proved that volume fractions on copper nanoparticles can increase both the dragging force and Nusselt number. Yasir and Khan [8] addressed the blood-based hybrid nanofluid flow containing Cu and Ag nanoparticles past a stretching surface using porous media. Their results show that the hybrid nanofluid flow has better performance in terms of heat transfer when compared to blood fluid. Babu et al. [9] investigated the slip flow of a nanofluid past a nonlinear stretching surface. They observed that the rate of heat transfer is higher on the nonlinear stretching surface when compared to linear stretching surface. Yasir et al. [10] presented the stability analysis of a hybrid nanofluid flow over a shrinking/stretching curved surface with nonlinear thermal radiation and heat source and found that the rate of heat transfer increases with the higher thermal radiation factor. Kumaraswamy Naidu et al. [11] examined the sodium alginate-based nanofluid flow containing Fe3O4 nanoparticles over a thermally convective extending surface. They found that the higher thermal Biot number heightens the rate of heat transfer. Harish Babu and Satya Narayana [12] investigated the Jeffrey nanofluid flow due to rotating stretching surface. Yasir et al. [13] addressed the heat transfer analysis of hybrid nanofluid flows over a stretching/shrinking surface. They found that the skin friction increases and velocity distribution reduces with the higher magnetic factor. Some other relevant studies can be seen in refs [14–16].

In order to illustrate the impression of Brownian motion and thermophoretic diffusion, different investigators have used the prominent Buongiorno model. Pakravan and Yaghoubi [17] considered the nanoparticle passage of a natural convective thermal transfer of nanofluids. Sheikholeslami and Ganji [18] investigated the heat transmission characteristics of a three-dimensional flow on a rotating sheet with the effects of magnetic field, thermophoresis, and Brownian motion factors. They observed that the magnetic and rotating factors have a direct relation with the skin friction. Also, the Reynolds number has a similar relation with the Nusselt number. Goudarzi et al. [19] addressed the Brownian motion of the water-based hybrid nanofluid comprising Ag and MgO nanoparticles in an enclosure. They showed that there is 11% increment in Nusselt number due to the increasing thermophoresis diffusion of both Ag and MgO nanoparticles. Abdelmalek et al. [20] discussed the bioconvection magnetohydrodynamics nanofluid flow over an extending sheet with the features of thermal absorption/generation and activation energy by considering the velocity slips and convective conditions. Abdelmalek et al. [21] analyzed the 3D flow of cross-liquid with chemical reaction. Dawar et al. [22] examined hybrid nanofluid flow on a convectively heated curved surface with variable internal heating and Brownian motion. They found that the hybrid nanofluid case experienced more effects from the embedded factor when compared to the nanofluid case.

The importance of rotating disk induced flows in a variety of real-world applications, including aerospace engineering, and food processing technologies, rotational air cleaners, centrifugal pumps, rotor-stator systems, gas turbine engineering, chemical industries, chemical engineering, and turbomachinery. A steady rotating flow of liquid close to a spinning disk was proposed by Kármán [23]. An approximate integral approach was used in the study by Kármán [23] to obtain analytical solutions. Miklavčič [24] identified a few errors in Von Kármán analysis and produced precise numerical estimates for the principal equations. Stuart [25] investigated the Von Kármán flow over a revolving disk of infinite radius with uniform suction and found that the radial component of the flow decreases with the increasing suction factor. Ackroyd [26] studied the laminar flow of fluid past a gyrating disc with suction and injection cases by using series solution with exponents as negative. This method is proven to consistently yield highly accurate solutions for all suction scenarios and for low injection values at the disk surface, demonstrating excellent precision. Shah et al. [27] examined fluid flow on a rotating disk with Hall current. Alreshidi et al. [28] deliberated on the impacts of Brownian motion and thermophoresis on magnetized nanofluid flow with Joule heating and slip conditions due to porous spinning disk. Jyothi et al. [29] considered the effect of activated energy on fluid flow over a revolving disk. Qayyum et al. [30] examined the heat transmission of a dissipative flow of fluid amid two revolving disks. Later on, numerous studies [31,32,33,34,35,36,37,38,39] have been conducted by researchers to investigate different types of flow by considering different physical conditions.

Nanometer-sized metal particles or non-metals and metalloids form the alloy. There are many different types of alloys, but the best ones are brass, steel, phosphor bronze, solder, and gold. In addition to their use in biomedicine, alloys are employed in a wide range of engineering uses like advanced powder technology, fuel cells, surgical implantation, aerospace science technology, drug delivery systems, hip joint replacement processes, nuclear reactors, and various biological treatments. For corrosion protection, nanoparticle coatings of aluminum ( AA7075 ) and titanium ( Ti 6 Al 4 V ) alloy nanoparticles are applied to chemical processing equipment, transpiration cooling, wire, fiber, and heat exchangers. Due to the high susceptibility of metallic alloy nanoparticles to magnetic fields, interactions of flows with magnetic fields can alter the physical as well as thermal features of nanofluids, thereby regulating their flow and thermal transference. Hybrid nanofluids, combining titanium alloy and aluminum alloy nanoparticles, offer intriguing possibilities, especially in applications involving rotating disk surfaces. These applications include heat transfer enhancement, tribological applications, cooling systems in electronics, energy conversion systems, material processing and manufacturing, aerospace and automotive applications, and thermal management in renewable energy systems. Being inspired by the above applications of alloys, the authors are interested in investigating the alloys of aluminum ( AA7075 ) and titanium ( Ti 6 Al 4 V ) over a rotating disk surface. To make novel this study, the following questions, which are not yet addressed, are to be addressed in the present investigation:

  • In which scenario (stretching or shrinking), do the radial and azimuthal velocities exhibit higher values?

  • In which scenario (stretching or shrinking), a magnetic field has diverse impact on the Azimuthal velocity, radial velocity, and drag force at the surface of the rotating disk?

  • In which case (i.e., linear or nonlinear), the thermal radiation has maximum impact on the temperature of the nanofluids flow?

Which water-based nanofluid flow (i.e., Ti 6 Al 4 V nanofluid or AA7075 nanofluid) is greatly influenced by the embedded factors?

Thus, to address the above research questions, the authors have taken the water-based nanofluids flow over an angularly rotating disk surface. Two types of alloys called aluminum alloy and titanium alloy are mixed with water to form the water-based nanofluids flow. Initially, a mathematical framework was proposed in the form of PDEs as presented in Section 2. The numerical solution of the mathematical design is done by using bvp4c MATLAB scheme, which is shown in Section 3. The authentication of the current flow problem and discussion of results are presented in Section 4. The final remarks are concluded in Section 5.

2 Model formulation

Consider a laminar flow of a viscous nanofluid on a rotating disk. The angular velocity of the disk surface is denoted by Ω , which rotates along z - axis. The components of velocity ( u , v , w ) are analyzed, respectively, in r - , φ - , and z - directions. The flow is influenced by the strength of the magnetic field B 0 , which is normal to the flow direction. The rotating disk stretches along a radial direction with velocity u ( r , 0 ) = Su w , where u w = ar is the stretching velocity, S > 0 denotes the stretching scenario, and S < 0 denotes the contracting scenario. In addition, the disk rotates with velocity v ( r , 0 ) = v w (in anticlockwise direction) with velocity v w = r Ω such that Ω ≥ 0 . C w , C f , and C ∞ denote the surface, fluid, and free-stream concentrations, respectively. In addition, T w , T f , and T ∞ depict the surface, fluid, and free-stream temperatures, respectively. A geometrical representation is shown in Figure 1. Moreover, the flow assumptions are as follows:

  1. Thermophoresis and Brownian motion

  2. Chemical reaction and activation energy

  3. Viscous dissipation

  4. Nonlinear thermal radiation

  5. Joule heating

  6. Convective conditions

Figure 1 Flow geometry of the problem.
Figure 1

Flow geometry of the problem.

Thus, the leading equations are defined as follows [38,40,41]:

(1) ∂ u ∂ r + u r + ∂ w ∂ z = 0 ,

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

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

(4) ρ nf w ∂ w ∂ z + u ∂ w ∂ r = − ∂ p ∂ z + μ nf ∂ 2 w ∂ r 2 + ∂ w ∂ r 1 r + ∂ 2 w ∂ z 2 ,

(5) ( ρ C p ) nf u ∂ T ∂ r + w ∂ T ∂ z = k nf ∂ 2 T ∂ r 2 + ∂ 2 T ∂ z 2 + 1 r ∂ T ∂ r + 16 σ ⁎ T ∞ 3 3 k ⁎ T ∂ 2 T ∂ z 2 + 3 ∂ T ∂ z 2 + ( ρ C p ) np D B ∂ C ∂ r ∂ T ∂ r + ∂ C ∂ z ∂ T ∂ z + D T T ∞ ∂ T ∂ z 2 + ∂ T ∂ r 2 + σ nf B 0 2 ( u 2 + v 2 ) + μ nf ∂ u ∂ z + ∂ v ∂ z ,

(6) u ∂ C ∂ r + w ∂ C ∂ z = D B 1 r ∂ C ∂ r + ∂ 2 C ∂ r 2 + ∂ 2 C ∂ z 2 + D T T ∞ ∂ T ∂ r 1 r + ∂ 2 T ∂ r 2 + ∂ 2 T ∂ z 2 − k r T T ∞ n e − E a K T ( C − C ∞ ) .

The boundary limitations are

(7) u = u w , v = v w , w = 0 , − k nf ∂ T ∂ z = h f ( T f − T ) , − D B ∂ C ∂ z = h c ( C f − C ) at z = 0 , u → 0 , T → T ∞ , v → 0 , C → C ∞ as z → ∞ .

The thermophysical features of nanofluid are characterized as follows:

(8) μ nf μ f = 1 ( 1 − ϕ ) 2.5 , ρ nf = ρ f ( 1 − ϕ ) + ϕ ρ np , ( ρ C p ) nf = ( ρ C p ) f ( 1 − ϕ ) + ϕ ( ρ C p ) np , σ nf = σ np + 2 σ f − 2 ( σ f − σ np ) ϕ σ np + 2 σ f + ( σ f − σ np ) ϕ σ f , k nf = k np + 2 k f − 2 ( k f − k np ) ϕ k np + 2 k f + ( k f − k np ) ϕ k f , .

Table 1 shows the thermophysical features of the base fluid and nanoparticles.

Table 1

Thermophysical features of the base fluid and nanoparticles [42,43]

Properties H 2 O AA7075 Ti 6 Al 4 V
σ 0.005 26.77 × 106 5.8 × 105
k 0.613 173 7.2
C p 4,179 960 0.56
ρ 997.1 2,810 4,420

The similarity variables are defined as follows [23,40,44]:

(9) u = Ω r f ( η ) , v = r Ω h ( η ) , w = Ω ν f g ( η ) , ψ ( η ) = C − C ∞ C f − C ∞ , θ ( η ) = T − T ∞ T f − T ∞ , η = Ω ν f z .

Using Eq. (9) in Eqs. (1)–(7), we have

(10) g ′ + 2 f = 0 ,

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

(12) μ nf / μ f ρ nf / ρ f h ″ − 2 f h − g h ′ − σ nf / σ f ρ nf / ρ f M h = 0 ,

(13) k nf k f + Rd ( 1 + ( θ w − 1 ) θ ) 3 θ ″ + Rd ( θ w − 1 ) ( 1 + ( θ w − 1 ) θ ) 2 θ ′ 2 + σ nf σ f M EcPr ( f 2 + h 2 ) + μ nf μ f M ( ( f ′ 2 + h ′ 2 ) ) − Pr ( ρ C p ) hnf ( ρ C p ) f g θ ′ + Pr Nt θ ′ 2 + Pr Nb θ ′ ψ ′ = 0 ,

(14) ψ ″ + Nt Nb θ ″ − Sc g ψ ′ − K r Sc ( 1 + σ θ ) e − E ( 1 + σ θ ) ψ = 0 ,

(15) f ( 0 ) = S , h ( 0 ) = 1 , g ( 0 ) = 0 , k nf k f θ ′ ( 0 ) = − Bi T ( 1 − θ ( 0 ) ) , ψ ′ ( 0 ) = − Bi C ( 1 − ψ ( 0 ) ) , f ( ∞ ) = 0 , h ( ∞ ) = 0 , θ ( ∞ ) = 0 , ψ ( ∞ ) = 0 .

The main factors are described as follows:

(16) M = σ f B 0 2 ρ f Ω , Pr = ν f ( ρ C p ) f k f , ω = T f − T ∞ T ∞ , Bi T = h f k f ν f Ω , Rd = 16 σ ⁎ T ∞ 3 3 k ⁎ k f , K r = k r Ω , Sc = ν f D B , Nt = ( ρ C p ) np D T ( T f − T ∞ ) ( ρ C p ) f T ∞ ν f , Nb = ( ρ C p ) np D B ( C w − C ∞ ) ( ρ C p ) f ν f , Bi C = h m D B ν f Ω , E = E a K T ∞ , θ w = T f T ∞ , .

Skin friction coefficient and Nusselt and Sherwood numbers are described mathematically as follows [45]:

(17) C fr = τ wr 2 + τ wz 2 ρ f ( Ω r ) 2 , Nu r = r q w k f ( T f − T ∞ ) , Sh r = r q m D B ( C f − C ∞ ) ,

where

(18) τ wr = μ nf ∂ u ∂ z + ∂ w ∂ r z = 0 , τ wz = μ nf 1 r ∂ w ∂ φ + ∂ v ∂ z z = 0 , q w = − r k f 1 + 16 σ ⁎ 3 k ⁎ k f ∂ T ∂ z z = 0 , q m = − r D B ∂ C ∂ z z = 0 .

Thus, the above equation is reduced as follows:

(19) Re r C f = μ nf μ f f ′ 2 ( 0 ) + h ′ 2 ( 0 ) , 1 Re r Nu = − k nf k f + Rd ( 1 + ( θ w − 1 ) θ ( 0 ) ) 3 θ ′ ( 0 ) , 1 Re r Sh = − ψ ′ ( 0 ) ,

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

3 Numerical solution

The shooting method is used in the current model to carry out the numerical analysis [46,47,48,49]. The bvp4c MATLAB scheme is used to investigate the first-order system of equations. This approach has the benefits of solving nonlinear system of equations with small effect, allows us to define the error tolerance on our own, can solve those systems that are challenging by using analytical methods, and provides solutions faster than other methods. To apply this technique, let us assume that

(20) g = ξ ( 1 ) , g ′ = ξ ′ ( 1 ) f = ξ ( 2 ) , f ′ = ξ ( 3 ) , f ″ = ξ ′ ( 3 ) h = ξ ( 4 ) , h ′ = ξ ( 5 ) , h ″ = ξ ′ ( 5 ) θ = ξ ( 6 ) , θ ′ = ξ ( 7 ) , θ ″ = ξ ′ ( 7 ) ψ = ξ ( 8 ) , ψ ′ = ξ ( 9 ) , ψ ″ = ξ ′ ( 9 ) .

Then, the modeled ODEs can be written as follows:

(21) ξ ′ ( 1 ) = − 2 ξ ( 2 ) ,

(22) ξ ′ ( 3 ) = − ( ξ ( 4 ) ) 2 − ( ξ ( 3 ) ) 2 − ξ ( 1 ) ξ ( 3 ) − σ nf / σ f ρ nf / ρ f M ξ ( 2 ) μ nf / μ f ρ nf / ρ f ,

(23) ξ ′ ( 5 ) = − 2 ξ ( 2 ) ξ ( 4 ) − ξ ( 1 ) ξ ( 5 ) − σ nf / σ f ρ nf / ρ f M ξ ( 4 ) μ nf / μ f ρ nf / ρ f ,

(24) ξ ′ ( 7 ) = − Rd ( θ w − 1 ) ( 1 + ( θ w − 1 ) ξ ( 6 ) ) 2 ( ξ ( 7 ) ) 2 + σ nf σ f MEcPr ( ( ξ ( 2 ) ) 2 + ( ξ ( 4 ) ) 2 ) + μ nf μ f M ( ( ( ξ ( 3 ) ) 2 + ( ξ ( 5 ) ) 2 ) ) − Pr ( ρ C p ) hnf ( ρ C p ) f ξ ( 5 ) ξ ( 7 ) + PrNt ( ξ ( 7 ) ) 2 + Pr Nb ξ ( 7 ) ξ ( 9 ) k nf k f + Rd ( 1 + ( θ w − 1 ) ξ ( 6 ) ) 3 ,

(25) ξ ′ − Nt Nb ξ ′ ( 7 ) − Sc ξ ( 4 ) ξ ( 9 ) − K r Sc ( 1 + σ ξ ( 6 ) ) e − E ( 1 + σ ξ ( 6 ) ) ξ ( 8 ) ,

(26) ξ Initial ( 2 ) = S , ξ Initial ( 4 ) = 1 , ξ Initial ( 1 ) = 0 , k nf k f ξ Initial ( 7 ) = − Bi T ( 1 − ξ Initial ( 6 ) ) , ξ Initial ( 9 ) = − Bi C ( 1 − ξ Initial ( 8 ) ) , ξ Boundary ( 2 ) = 0 , ξ Boundary ( 4 ) = 0 , ξ Boundary ( 6 ) = 0 , ξ Boundary ( 8 ) = 0 .

4 Discussion of results

In this section, we have presented the physical discussion of the flow profiles. The nanofluids flow ( Ti 6 Al 4 V – H 2 O nanofluid and AA7075 – H 2 O nanofluid) over a disk surface that rotates angularly is considered here. Two important cases, namely the stretching case and the shrinking case, were investigated to analyze the flow behaviors due to the different embedding factors. Figures 2–8 and Tables 3–5 are displayed in this regard. Figure 2(a) displays the impact of stretching/shrinking ( S ) on radial velocity profile ( f ( ζ ) ). Here, the results of S are shown for two different cases of the disk: (i) when the disk stretches ( S > 0 ) and (ii) when the disk shrinks ( S < 0 ). For S > 0 , f ( ζ ) increases, and for S < 0 , f ( ζ ) reduces. These effects are obvious due to the physical phenomena of the surface. In addition, the effect of S is greater for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 – H 2 O nanofluid for both S > 0 and S < 0 . Figure 2(b) displays the impression of stretching/shrinking ( S ) on Azimuthal velocity profile ( h ( ζ ) ). Here, the results of S are shown for two different cases of the disk: (i) when the disk stretches ( S > 0 ) and (ii) when the disk shrinks ( S < 0 ). For S < 0 , h ( ζ ) increases, and for S > 0 , h ( ζ ) reduces. In addition, it is concluded that when the disk shrinks, h ( ζ ) increases, and when the disk stretches, h ( ζ ) reduces as shown in Figure 3(a). In addition, AA7075 − H 2 O nanofluid has maximum velocity for both the shrinking and stretching disks when compared to Ti 6 Al 4 V − H 2 O nanofluid. Figures 3(b) and 4(b) show consequences of magnetic factor ( M ) on f ( ζ ) , h ( ζ ) , and temperature ( θ ( ζ ) ) panels. Both f ( ζ ) and h ( ζ ) reduce with greater M while θ ( ζ ) reduces. Physically, the greater M produces the contrasting force to the flow because of the Lorentz force. The Lorentz force is impeding force performing in contradiction of the flow particles motion. As we increase M , the greater Lorentz forces produce that declines velocity of fluid. Therefore, both f ( ζ ) and h ( ζ ) reduce with higher M . In addition, M increases when the disk stretches. Furthermore, this effect is greater for AA7075 − H 2 O nanofluid when compared to Ti 6 Al 4 V − H 2 O nanofluid. On the other hand, the greater Lorentz force produces higher thermal transference rate at the surface of disk and results in augmentation of thermal distribution. Therefore, the greater M augments θ ( ζ ) . In addition, an important phenomenon is discussed here (linear and nonlinear thermal radiation). θ w = 1 shows the linear and θ w > 1 shows the nonlinear thermal radiation. θ w is ratio of reference temperature ( T f ) to free-stream temperature ( T ∞ ). So by definition, θ w > 1 shows the more significance impact than θ w = 1 . This is only possible for reference temperature to be greater than as it is at free-stream. The higher the reference temperature, the greater the heat generated in the flow system. The more heat in the flow system definitely shows the higher temperature. This phenomenon is shown Figure 5(a). Figure 5(b) expresses the impression of thermal Biot number ( Bi T ) on θ ( ζ ) . The results show that the increasing Bi T increases θ ( ζ ) . Actually, the increasing Bi T increases the coefficient of heat transfer. The increasing coefficient of heat transfer has direct relation with Bi T . So by this fact, the increasing Bi T heightens the thermal transference rate, which consequently increases the temperature distribution. In addition, the impression of Bi T is maximum for the nonlinear thermal radiation case. Also, the higher impact of Bi T is perceived for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. Figure 6(a) shows the impact of activation energy parameter ( E ) on concentration distribution ( ψ ( ζ ) ). The higher E heightens the concentration boundary layers, which results in an augmenting impact on ψ ( ζ ) . In addition, the greater impact is found for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. Figure 6(b) expresses the result of chemical reactivity factor ( K r ) on ψ ( ζ ) . The increasing K r reduces ψ ( ζ ) . Actually, the increasing K r diminishes the molecular diffusivity of the nanofluids flow, which results in reduction in the concentration layers at boundary. Therefore, the increasing K r declines ψ ( ζ ) . In addition, the greater impact of K r is observed for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. Figure 6(a) exhibits the result of Sc on ψ ( ζ ) . The higher Sc reduces ψ ( ζ ) . This is due to the reason that the escalating Sc diminishes the molecular diffusivities of the nanofluids flow, which affects the solutal boundary layer thicknesses to decreases. The reduction in the thicknesses of the boundary layers results in a declining impact of the concentration distribution. Therefore, the higher Sc reduces ψ ( ζ ) . When compared the two different nanofluids, the maximum impact is found for Ti 6 Al 4 V − H 2 O nanofluid than AA7075 − H 2 O nanofluid. Figure 7(a) expresses the impression of concentration Biot number ( Bi C ) on ψ ( ζ ) . The results show that the increasing Bi C increases ψ ( ζ ) . The reason is that the increasing Bi C increases the coefficient of mass transfer. The increasing coefficient of mass transfer has direct relation with Bi C . So by this fact, the increasing Bi C heightens the mass transfer rate and boundary layer of the concentration profile, which consequently increases the concentration distribution. In addition, the higher impact of Bi C is perceived for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. Figures 7(b) and 8(a) show the impact of Nt on θ ( ζ ) and ψ ( ζ ) , respectively. The higher Nt augments both θ ( ζ ) and ψ ( ζ ) . Actually, the higher Nt strengthens the thermophoretic force, which forces the particles of the nanofluids to move toward the hot region from colder one. This movement of the nanofluid particles enhances the thermal boundary layer and temperature of the nanofluids. Thus, the growing Nt heightens θ ( ζ ) . In addition, the impression of Nt is maximum for the nonlinear thermal radiation case. Also, the higher impact of Nt is perceived for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. On the other hand, the concentration boundary layer thicknesses also enhance with increasing Nt , which results in an enhanced impact on the concentration distribution, as shown in Figure 8(b). In addition, the higher impact of Nt is perceived for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. Figure 8(a) and (b) shows the impact of Nb on θ ( ζ ) and ψ ( ζ ) , respectively. From these figures, we see that the increasing Nb increases θ ( ζ ) but reduces ψ ( ζ ) . The fact is that the higher Nb increases Brownian motion of the nanofluids particles, which leads to an increase in the temperature and the thermal boundary layers, resulting in augmenting behavior in θ ( ζ ) . Furthermore, the impact of Nb is maximum for the nonlinear thermal radiation case. Also, the higher impact of Nb is perceived for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. On the other hand, the increasing Nb reduces the mass transfer rate and so are the concentration boundary layers. Thus, the higher Nb reduces ψ ( ζ ) . In addition, the greater effect of Nb is perceived for Ti 6 Al 4 V − H 2 O nanofluid when compared to AA7075 − H 2 O nanofluid. Table 2 expresses the assessment of current analysis with published results of the previous studies. Here, close relations between the present and published results are found, which validate the present analysis. Table 3 displays the impressions of M and S on Re r C f . The higher magnetic factor augments Re r C f . The reason is that the higher M enhances the Lorentz force, which always opposes the motion of the fluid particles. Thus, the enhancing Lorentz force increases the drag force at the surface. Therefore, Re r C f increases with greater M . In addition, the effect of M on Re r C f is higher when S > 0 . Also, Ti 6 Al 4 V − H 2 O nanofluid has maximum surface drag than the AA7075 − H 2 O nanofluid. The impact of S on Re r C f is also shown in Table 3. This is obvious that the higher stretching rate will increase the surface drag force, but this effect is opposite for the case of shrinking sheet. Similar impacts are perceived here. In addition, Ti 6 Al 4 V − H 2 O nanofluid has maximum surface drag than the AA7075 − H 2 O nanofluid. Table 4 show the impacts of Rd , Nb , Nt , and Bi T on local Nusselt number ( 1 Re r Nu ). It is observed that 1 Re r Nu increases with higher values of Rd and Bi T and reduces with higher values of Nt and Nb . The increasing Rd means that extra heat generates in the flow system, which obviously increases 1 Re r Nu . Similarly, the increasing Bi T increases the coefficient of heat transfer, which results in an increase in the rate of heat transfer. Thus, 1 Re r Nu increases with higher Bi T . On the other hand, 1 Re r Nu reduces with higher values of Nt and Nb . This indicates that the distribution of nanoparticles in the flow regime may benefit from the Brownian motion process. Moreover, low Nt and Nb values may contribute to temper the flow regime. In addition, Ti 6 Al 4 V − H 2 O nanofluid has maximum heat transfer rate than the AA7075 − H 2 O nanofluid. Table 5 expresses the impression of Sc , Nb , Nt , and Bi C on 1 Re r Sh . It is perceived that the greater values of Sc , Nt , and Bi C heightens 1 Re r Sh , while the greater values of Nb diminishes 1 Re r Sh . In addition, Ti 6 Al 4 V − H 2 O nanofluid has maximum mass transfer rate than the AA7075 − H 2 O nanofluid.

Figure 2 (a) f ( ζ ) f(\zeta ) vs S S . (b) h ( ζ ) h(\zeta ) vs S S .
Figure 2

(a) f ( ζ ) vs S . (b) h ( ζ ) vs S .

Figure 3 (a) f ( ζ ) f(\zeta ) vs M M . (b) h ( ζ ) h(\zeta ) vs M M .
Figure 3

(a) f ( ζ ) vs M . (b) h ( ζ ) vs M .

Figure 4 (a) θ ( ζ ) \theta (\zeta ) vs M M . (b) θ ( ζ ) \theta (\zeta ) vs Bi T {\text{Bi}}_{\text{T}} .
Figure 4

(a) θ ( ζ ) vs M . (b) θ ( ζ ) vs Bi T .

Figure 5 (a) ψ ( ζ ) \psi (\zeta ) vs E E . (b) ψ ( ζ ) \psi (\zeta ) vs K r {K}_{\text{r}} .
Figure 5

(a) ψ ( ζ ) vs E . (b) ψ ( ζ ) vs K r .

Figure 6 (a) ψ ( ζ ) \psi (\zeta ) vs Sc \text{Sc} . (b) ψ ( ζ ) \psi (\zeta ) vs Bi C {\text{Bi}}_{\text{C}} .
Figure 6

(a) ψ ( ζ ) vs Sc . (b) ψ ( ζ ) vs Bi C .

Figure 7 (a) θ ( ζ ) \theta (\zeta ) vs Nt \text{Nt} . (b) ψ ( ζ ) \psi (\zeta ) vs Nt \text{Nt} .
Figure 7

(a) θ ( ζ ) vs Nt . (b) ψ ( ζ ) vs Nt .

Figure 8 (a) θ ( ζ ) \theta (\zeta ) vs Nb \text{Nb} . (b) ψ ( ζ ) \psi (\zeta ) vs Nb \text{Nb} .
Figure 8

(a) θ ( ζ ) vs Nb . (b) ψ ( ζ ) vs Nb .

Table 2

Validation of the present results with previous studies when Pr = 6.2 , S = 0.0 , and ϕ = 0.0

Outcomes f ′ ( 0 ) ‒ h ′ ( 0 ) ‒ g ( 0 ) ‒ θ ′ ( 0 )
Present 51.03537103 × 10‒2 61.58881969 × 10‒2 0.8882966310 93.38779486 × 10‒2
Kelson and Desseaux [50] 51.0233 × 10‒2 61.5922 × 10‒2 88.4474 × 10‒2 —
Bachok et al. [34] 51.02 × 10‒2 61.59 × 10‒2 — 93.37 × 10‒2
Turkyilmazoglu [51] 51.023262 × 10‒2 61.592201 × 10‒2 88.447411 × 10‒2 93.387794 × 10‒2
Abbas et al. [52] 50.9175 × 10‒2 61.5375 × 10‒2 88.2042 × 10‒2 93.1855 × 10‒2
Table 3

Impacts of M and S on Re r C f

M S AA7075 – H 2 O Ti 6 Al 4 V – H 2 O
1.50 0.1 1.749404207 1.773694765
1.75 0.1 1.863047936 1.884131577
2.00 0.1 1.971631862 1.990188495
1.50 −0.1 1.637009762 1.649974856
1.75 −0.1 1.755704601 1.765142631
2.00 −0.1 1.869070098 1.875921695
1.75 0.1 1.863047936 1.884131577
1.75 0.2 1.943502204 1.970664495
1.75 0.3 2.042922023 2.076507283
1.75 −0.1 1.755704601 1.765142630
1.75 −0.2 1.725669558 1.729275744
1.75 −0.3 1.708472324 1.706096980
Table 4

Impacts of Rd , Nb , Nt , and Bi T on 1 Re r Nu

Rd Nb Nt Bi T AA7075 – H 2 O Ti 6 Al 4 V – H 2 O
1.0 0.3 0.3 0.5 0.2939523146 0.3055227847
1.5 0.3884742454 0.4038005311
2.0 0.4793603598 0.4975608549
2.0 0.4 0.4614944500 0.4787616300
0.6 0.4257151773 0.4411786784
0.8 0.3900292450 0.4037818812
0.3 0.2 0.4609330164 0.4777864491
0.4 0.4239745672 0.4382766749
0.6 0.3870670571 0.3990251843
0.6 0.6 0.4129920515 0.4245642843
0.7 0.4334330116 0.4445941612
0.8 0.4499411309 0.4607029209
Table 5

Impacts of Sc , Nb , Nt , and Bi C on 1 Re r Sh

Sc Nb Nt Bi C AA7075 ‒ H 2 O Ti 6 Al 4 V ‒ H 2 O
1.0 0.3 0.3 0.5 0.1440435747 0.1454743799
1.5 0.1695438946 0.1716908589
2.0 0.1912788432 0.1938364811
2.0 0.4 0.1916562020 0.1943887531
0.6 0.1915873040 0.1945021543
0.8 0.1911107593 0.1941242023
0.3 0.2 0.1919489729 0.1939343527
0.4 0.1986035019 0.1996018768
0.6 0.2124578424 0.2126565364
0.6 0.6 0.2278976716 0.2283818719
0.7 0.2403584756 0.2411006010
0.8 0.2506248389 0.2515980012

5 Conclusion

The electrically conducting viscous nanofluids flow over an angularly gyrating disk is explored in this investigation. Two different types of nanoparticles, namely titanium alloys ( Ti 6 Al 4 V ) and aluminum alloys ( AA7075 ). were investigated, whereas water ( H 2 O ) is used as a base fluid. Two important cases, namely the stretching case and the shrinking case, were investigated to analyze the flow behaviors due to the different embedding factors. The impacts of viscous Joule heating, thermophoresis, nonlinear thermal radiation, Brownian motion, activation energy, and chemical reaction are investigated here. At the end of this investigation, the following key points are illustrated:

  • The radial flow increases when the surface of the disk stretches and reduces when the disk surface shrinks. On the other hand, the Azimuthal velocity increases when the disk surface shrinks and reduces when the disk surface stretches.

  • Both the radial and Azimuthal flows are the diminishing functions of the magnetic factor, whereas temperature is the escalating function of the magnetic factor. In addition, the temperature is more influenced by the magnetic factor in the case of nonlinear thermal radiation.

  • Escalation in thermal Biot number, Brownian motion, and thermophoresis factors result in a rising thermal panel. Furthermore, in a nonlinear thermal radiation scenario, the magnetic factor has a greater influence on temperature.

  • High concentration Biot number, activation energy, and thermophoresis factors heighten concentration panels, while high, Brownian motion, Schmidt number, and chemical reactivity factors reduce them.

  • Skin friction is increased by a higher magnetic factor. In addition, the higher surface drag is experienced in the elongating scenario in comparison to the contracting scenario.

  • The local Nusselt number is an escalating function of thermal radiation and thermal Biot number.

  • It is found that the nanofluid flow containing titanium alloys has perceived the greater impacts of the embedded factors when compared to the nanofluid flow containing aluminum alloys.

6 Future recommendations

The existing problem can be modified by using mass flux and zero mass flux conditions to investigate the rate of mass transfer at the surface of the rotating disk. The same model can be extended for hybrid nanofluid flow containing titanium and aluminum alloys by using different types of regular fluids.

Acknowledgments

This work was supported by the Deanship of Scientific Research, the Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia (Grant No. 5532).

  1. Funding information: This work was supported by the Deanship of Scientific Research, the Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia (Grant No. 5532).

  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.

  4. Data availability statement: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Received: 2023-10-27
Revised: 2023-12-10
Accepted: 2024-01-05
Published Online: 2024-02-06

© 2024 the author(s), published by De Gruyter

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

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  44. Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
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  73. Research on optimization of combustor liner structure based on arc-shaped slot hole
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  75. Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
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  83. Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
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  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
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  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
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  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
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  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
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  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
https://doi.org/10.1515/phys-2023-0184
Keywords for this article
nanofluids; water; titanium and aluminum alloys; Joule heating; viscous dissipation; rotating disk; stretching/shrinking cases
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BY 4.0

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  40. Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
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  42. Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
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  45. Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
  46. Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
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  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
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  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
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  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
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  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
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  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
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  114. Accumulation process in the environment for a generalized mass transport system
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  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
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  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
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  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
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