Home Thermal valuation and entropy inspection of second-grade nanoscale fluid flow over a stretching surface by applying Koo–Kleinstreuer–Li relation
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Thermal valuation and entropy inspection of second-grade nanoscale fluid flow over a stretching surface by applying Koo–Kleinstreuer–Li relation

  • Faisal Shahzad EMAIL logo , Wasim Jamshed , Rabia Safdar , Nor Ain Azeany Mohd Nasir , Mohamed R. Eid , Meznah M. Alanazi and Heba Y. Zahran
Published/Copyright: June 1, 2022
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 11 Issue 1

Abstract

There are flow research centers on magnetohydrodynamic (MHD) emission of auxiliary liquid in an extended region. The prevailing model is constrained by attractions/infusion and gooey release. The administering model is based on the Koo–Kleinstreuer–Li nanofluid model in the existence of entropy generation. Final requirements of this model are addressed by implementing the shooting strategy, which incorporates a fourth approach for the Runge–Kutta strategy. Into the bargain, the last adds (in standard ordinary differential equations (ODE) divisions) are obtained from the measurable controls partial differential equations, which were represented toward the start of the overseeing model. The varieties for all boundaries are exhibited through graphical arrangements. It is noticed that expanding the substantial volume portion diminishes speed but builds nuclear power dispersion. Likewise, the classification of mathematical qualities on divider heat move rate and skin contact is introduced. Both Reynolds and Brinkman numbers improve the entropy rate of the thermal system resulting in the growth effects of inertial forces and the surface heat dissipation, respectively.

Keywords: Koo–Kleinstreuer–Li model; second-grade nanofluid; thermal radiations; entropy generation; shooting method

1 Introduction

The limit stream is distinguished as the district of the most extensive stream field nearby, with colossal divider crashes. Since the area of interest is near the surface and it is expected to stream, the speed is roughly equivalent to the surface. We will not analyze the information related to limit layer in-stream regions impacted by the current tension angle [1]. Prandtl proposed the idea of a limit layer in 1904. This idea has considered the expectation of skin pressure, divider heat moves, and limit partition, which works with the plan of aeroplanes, ships, and different vehicles. The century of the Prandtl proposition is commended in different ways [2]. The limit layer is a layer of fluid near the limiting region where the thickness impacts are enormous. In fluid mechanics, a slender layer of streaming gas or liquid contacts an area like the wing of a plane or within a line. The fluid in the limit layer is underneath the shear strength. The speed range is across the limit layer from the top to zero, as long as the fluid contacts the surface. The limit layers are flimsy at the front edges of the aeroplane wing and thicker at the later edges [3]. The limit layer is a tiny district close to the divider, where the speed shifts from 0% to almost 100% of the all-out free-streaming velocity. This district is significant because it can influence stream conduct by influencing stream boundaries, for example, speed and strain decrease [4]. Many cross-line stream applications, particularly in the development of different materials, need to defeat the progression of liquid to work appropriately. A vehicle with an improved body works superior to a body that does not work as expected. A more coordinated body implies that the limit layer of wind current will not sever the body surface, and in this way, there will be less drag on the structure. Carriers, airfoil configuration, is fundamental for an aeroplane. Airfoils are planned by the requirement for a progression of the limit layer to be beneficial, as indicated by the need of the aircraft. What makes a difference is the approach of the airfoil. So airfoils are planned with the goal that the plane can take off and land under typical conditions. While removing the plane requirements to defeat the air opposition, so the airfoil is appropriately planned, no division of the limit layer except for a similar air obstruction is utilized to advantage when it shows up because the aeroplane needs to land. The airfoil assault point along these lines changes what breaks the limit layer, and for that reason, air drag is made, which assists with dealing back [5]. Subsequently, the idea of a limit layer recommends that the progression of Reynolds big numbers can be isolated into two significant imbalances areas. The consistency can be disregarded with the most incredible stream rate, and an inviscid limit arrangement joins the stream. The subsequent district is the littlest limit of the divider where the consistency ought to be considered [6].

Heat transfer is a warm designing discipline that includes assembling, using, changing, and trading hotness energy between versatile frameworks. Heat move is isolated into different cycles, like warm conduction, warm convection, warm radiation, and energy move through stage changes. To undertake heat move, designers likewise consider moving a broad scope of synthetic mixtures (shift in weather conditions mass exchange), either cold or blistering. Albeit these strategies have various qualities, they, as a rule, happen all the while in a similar framework. Heat trade occurs when the progression of a lot of fluid (gas or fluid) conveys its hotness in a fluid. All convective cycles also send halfway hotness to the flow [7]. Heat move is quite possibly the main modern cycle. All through the modern field, heat should be added, deducted, or eliminated from the conveyance of one cycle to another. In principle, the hotness that is disseminated by a hot fluid is never precisely equivalent to the hotness that is acquired by a chilly fluid because of the deficiency of normal hotness [8]. Application for heat move in modern creation, that is, almost 100% of creation, utilizes a particular interaction to move heat. Drying processes are altogether types of hotness move. The modern employments of hotness move liquids from straightforward, dry plans to cutting-edge measured frameworks that fill numerous roles in the creative interaction. As there are numerous varieties in the plan and use of cycles in the utilization of hotness move liquids, the number of businesses that utilized this strategy is additionally huge [9]. Scaling down gigantically affects the innovation of hotness exchangers and transforms heat exchangers into more minimized and more effective. The productivity of the hotness exchanger significantly affects the general proficiency and strength of the nuclear power framework. A miniature channel heat sink is another instrument in heat trade innovation. The benefits of an enormous hotness move region and the high cohesiveness of a little channel heat sink make it an extremely effective hotness exchanger for the utilization of electronic cooling [10].

Nanoliquids seem to be liquid–solid mixtures made up of solid particles as small as a nanometer in diameter, fibers, shafts, or chambers suspended in various basic liquids [11]. Nanoliquids also offer potential mechanical solutions for facilitating additional heat transfer due to their numerous advantages and lack of common high-temperature instabilities. Due to the size impact and Brownian progression of nanoparticles in liquids, nanofluids address further produced dependability that differs from conventional liquids enhanced with solid particles of micrometer or millimeter size. It is possible to stream nanofluid endlessly into a microchannel, and the heat transfer structure can be simplified to use nanofluids for high-efficiency heat transfer. It was a few years ago that various overview articles [12,13,14,15,16,17,18] on nanofluids that came out. This includes metals, nonmetal particles, and carbon nanotubes. All of these materials have been rigorously analyzed by a range of highly qualified experts. Nanofluid diffusion by nanodroplets has recently been described [19]. Because of their fragility, nanoemulsion liquids are well-suited for bulk delivery. However, what if the nanodroplets’ ability to deal with nanofluids’ heated conductivity could be improved? Nanoemulsion fluids must be developed for the research of heated fluids in this scenario. When it comes to warm conductivity, direct heat, consistency, and thickness, the nanofluid’s convective heat transfer coefficients are crucial in determining the fluid’s adequacy for heat transfer. Yang and Han [20] advanced a similar method based on nanoparticles and liquid metal. The importance of nanofluids should be altered in light of the advancement of nanofluid structures. At the moment, assessments of novel nanofluid structures are in the testing stage, and statements regarding the planned usage of an unprecedented nanofluid system are uncommon. The nanoparticles that are frequently employed to organize nanofluids are as follows: (i) metal particles (Cu, Al, Fe, Au, and Ag); (ii) non-metallic particles (Al2O3, CuO, Fe3O4, TiO2, and SiC); (iii) carbon and tuberculosis; and (iv) nanodroplet. Water, oil, (CH3)2CO, decene, and ethylene glycol are all examples of fundamental fluids [21]. Since the turn of the century, the speculation of as far as the feasible layer has demonstrated astounding significance and offered unimaginable power to the assessment of liquid equipment. One of the primary professions of small speculation is the evaluation of pulling bodies on the stream, for example, drawing a level plate into the zero position, this way and that, an airfoil, a plane body, or a turbine edge [22]. The current study determined where imbuement and ingestion occurred by determining the hotness motion and stream of pseudo-plastic non-Newtonian nanofluid over the entry surface. By combining Newtonian and non-Newtonian nanofluids, non-Newtonian nanofluids exhibit superior hotness move execution as compared to Newtonian nanofluids. In any event, changing the kind of nanoparticles has a significant effect on the heat transfer process during maintenance [23].

Second-grade fluids are a subtype of non-Newtonian fluids in which the speed field has up to two auxiliaries in the pressure strain tensor connection. In contrast, Newtonian fluids have up to two subordinates. The investigators evaluated the stream of second-grade fluid augmentations in various breaking point layer streams and found them to be viable in a variety of streams. Nowadays, researchers are particularly interested in the movement of heat in non-Newtonian fluids. The properties of a second-grade fluid are altered by the impact of temperature-dependent thickness. When the temperature increases, the thickness of gaseous substances increases, while the thickness of liquids decreases. Thus, many researchers focused their attention on the impact of variable consistency models. A study by Fetecau [24,25,26] focused on two winding movements for a subsequent grade and Oldroyd-B fluids in tube modeled areas. Real restrictions were explored to see how they affected smooth growth by introducing a time-dependent demand at a certain moment in time. Additionally, Jamil and Khan [27] used a comparative approach to determine Burger’s fluid speed and sheer pressure. Considering the fluid stream’s meaning in barrel modeled space, specialists concentrated on the smooth development of chambers by considering various fluids and their breaking point circumstances. In an indirect part, Barnes et al. [28,29] used pulsatile Air Plethysmography to evaluate the polymer stream, while Davies et al. [30] and Lin et al. [31] focused on a comparative problem for White-Metzner fluid. The formation of a fractionalized second-grade fluid as a result of longitudinal and torsional motions of an infinite round chamber governed by Laplace and restricted Hankel changes was discovered by Jamil et al. [32]. A study by Fetecau et al. [33] found that, in the presence of longitudinal movements of an infinite indirect chamber and those connected to an influencing pressure point, the solutions to the faltering development of a summarized Burgers fluid are set up as Fourier–Bessel series to the extent that some proper eigenfunctions are present. An incompressible second-grade fluid was studied by Fetecau et al. [34] to create a heatwave inside the limits of a possible vortex. One of the streams studied by Hayat et al. [35] was a second-grade fluid stream formed by a non-coaxial rotation of a penetrable plate. Using a two-chamber rheometer, Huang et al. [36] established a numerical method in the middle of the range for the constitutive relationship model of second-grade fluid.

Various examinations have discovered a propensity for the investigation of the magnetoconvection stream in contemporary centuries attributable to its many solicitations in design fields, for example, the cooling of atomic reactors, electronic bundles, microelectronic gadgets, and solar-centered innovation [37,38,39,40]. Numerous studies have explored the effect of attractive fields on convective hotness movement in 2D and 3D cavities. Thermal convection in a moving square enclosure was studied by Pirmohammadi and Ghassemi [41]. They found that the attractive field and the propensity point had a significant impact on the hotness movement system and stream features within the walled-in zone. In a pit filled with alumina–water nanofluid, Malvandi and Ganji [42] evaluated the influence of an attractive field on free convection. As a result, the speed angle at the divider increases and the rate of heat transmission reduces. According to Chamkha et al. [43], regarding the vented cavities exposed to attractive fields, heat transfer was focused in a cover-driven permeable nook with Cu–water nanofluid when MHD consolidated convection heat transfer was applied. The results showed that raising Hartman number improves the neighborhood Nusselt number while increasing the nanofluid volume part reduces the normal Nusselt number for all Richardson number ups. Attractive fields were utilized in a vented T-shaped pit to drive a convection flow of Cu–water nanofluid via adiabatically warmed base dividers in Kasaeipoor et al. [44] study. The low-temperature nanofluid enters the bottom and exits at the top of the chamber. With a rise in Hartmann numbers, they found that the pace at which hotness moves rises marginally. In any event, the rate increases as the Hartmann number rises, despite the substantial advantages of the Reynolds number [45]. It was found that the outer attractive field of three bearings affects the stream design and regular convection heat transfer in a cubic depression at various Rayleigh and Hartmann values. When comparing the appealing field’s upward heading to the corresponding dynamic divider bearing, the findings show that this is the most incorrect. An attractive field-induced normal convection of water–Al2O3 in a cubic cavity was studied by Sheikholeslami and Ellahi [46] using the Lattice Boltzmann Method (LBM) and the benefits of Hartmann number, nanoparticle volume fraction, and Rayleigh number were investigated. Successful thermal conductivity and nanofluid thickness are modeled using the Koo–Kleinstreuer–Li (KKL) model for a 4% concentration of the KKL model. However, they observed that the Nusselt number boosts Rayleigh’s number capacity but reduces Hartmann’s number capacity. Al2O3–water nanofluid was studied Zhou et al. [47] using the LBM in a variably warmed cubical nook with attractive powers. This study found a strong correlation between the smothering hotness move and the Nusselt number, with the normal Nusselt number showing the most severe effects of an attracting field with a flat bearing.

Slips fall into two main categories. First, the no-slip limit condition and then the slip limit condition are alluded to. One definition of the no-slip boundary condition (BC) is that it is one in which the liquid layer that is directly in contact with the limit travels at a constant pace with the boundary. There is no slip since there is no overall movement between them [48]. Limit slip situations are created when there is an overlap between the limit and the layer; as a result, slip is present. The occurrence of a slip limit in microfluidics is exceedingly unusual [49]. The equilibrium of surface energy can attain the convection limit condition, which is linked to convection warming. An incompressible and sticky liquid stream was tested for the influence of the divider’s slip condition on a slope divider temperature and hotness move [50]. Using convective limit conditions and inclining and topsy-turvy passages, Sayed et al. [51] studied the peristaltic movement of an exaggerated digression nanofluid. When it comes to incompressible liquids, speed slip and convective heating have been shown to affect the development of an early polar age [52]. Acharya et al. [53] used a penetrable expanding surface to study the effect of a second request slip mechanism on the development of a nanofluid.

The introduction of entropy establishes the first and second laws of thermodynamics to work on thermodynamics. The investigation of entropy idea has not introduced the examinations in designing; however, it is demonstrated in other fields like physical science, software engineering, and insights. The warm exchange emerges through vanishing energy and its development. With such realities, the entropy idea is focused on outlining such frameworks. The entropy idea characterizes the measures of energy misfortunes. The hypothesis and the properties of entropy can advance the show of assembling game plans. This increase and minimization are known as limited-time thermodynamics. The assets of various elements on entropy are researched to resistor the entropy in various media. Digression exaggerated crossover nanofluid is assessed by entropy [54]. A mathematical review for peristalsis of Sisko nanomaterial with entropy companions is discussed in ref. [55], and the entropy of non-Newtonian material introduces advancement which can be found in ref. [56]. Streamlining by the entropy for pressing progression of gooey liquid is given in ref. [57]. Nonlinear radiation and slip conditions by entropy are found in ref. [58]. Following that, a slew of other studies begins to emerge, each focusing on a different aspect of the problem [59,60,61,62,63,64,65,66], to name a few.

To the best of creators’ information, no mathematical or exploratory examination is directed to concentrate on the joined impacts of second-grade nanofluid stream, hotness move over a level moving surface with Lorentz powers warm radiation and entropy rate analysis utilizing the KKL nanofluid model. This examination work aims to explore the elements of entropy age and improvement of hotness move rate in warm frameworks by portraying the progression of nanofluids through a non-Newtonian numerical model.

2 Mathematical formulation

The flat horizontal stretching sheet’s linear velocity U w and temperature T w are stated as follows:

(2.1) U w ( x , 0 ) = b x ,

(2.2) T w ( x , 0 ) = T ∞ + b x ,

where b is a positive constant that is only true when x > 0 , and T ∞ is the temperature at a distance from the sheet.

2.1 The graphical model of fluid flow

Figure 1 shows a model of fluid flow. The following is a list of the model’s limitations:

  • steady-state and laminar flow in two-dimensional Cartesian coordinates;

  • nanofluid of second grade with a KKL model;

  • slip BCs;

  • Joule heating, thermal radiation, viscous dissipation, and MHDs, are all concepts that may be applied to a porous sheet;

  • copper oxide (CuO) nanoparticles;

  • engine oil (EO) as a base fluid.

Figure 1 The visual depiction of a fluid flow model.
Figure 1

The visual depiction of a fluid flow model.

2.2 Stress tensor in a second-grade fluid

Second-grade fluid’s Cauchy stress tensor [67] is cited by Shah et al.

S ⁎ = μ A ς 1 + α 1 A ς 2 + α 1 A ς 1 2 − p I ,

A ς 1 = ( grad V ) + ( grad V ) T ,

A ς 2 =   d A ς 1 d t + A ς 1 ( grad V ) + A ς 1 ( grad V ) T ,

where α 1 and α 2   are the substance parameters, A ς 1 and A ς 2 are the Rivlin–Ericksen tensors previously designated, dynamic viscosity μ , identity tensor I , pressure p , fluid velocity V , and the substance time derivative d/dt are all present. This model supports the Clausius–Duhem inequality. In addition, Helmholtz’s free energy is at its lowest point at equilibrium.

μ ≥ 0 , α 1 ≥ 0 , α 1 + α 2 = 0 .

In the second-grade fluid situation, if α 1 + α 2 = 0 , we are left with only the viscous fluid.

2.3 Model equations

Viscoelastic nanofluid, second-grade nanofluid, joule heating, and MHD impact are only some of the improvements to ref. [67] that have been included:

(2.3) u x + v y = 0 ,

(2.4) u u x + v u y = α 1 ρ n f [ u x u y y + u u x y y + u y v y y + v u y y y ] + μ n f ρ n f u y y − σ n f B 2 u ρ n f ,

(2.5) u T x + v T y = k n f ( ρ C p ) n f T y y − 1 ( ρ C p ) n f ( q r ) y + μ n f ( ρ C p ) n f ( u y ) 2 + σ n f B 2 u 2 ( ρ C p ) n f .

Boundary circumstances identical to those described in control – (2.3)–(2.5):

(2.6) u ( x , 0 ) = U w + N w ( u y ) , v ( x , 0 ) = V w , − k 0 ( T y ) = h f ( T w − T ) ,

(2.7) u → 0 , u y → 0 , T → T ∞ as y → ∞ .

Vector of flow velocity is defined as v ← = [ u ( x , y , 0 ) , v ( x , y , 0 ) , 0 ] . T presents the temperature of the fluid. B and N w are the magnetic field and slip length, respectively. V w is representing the porosity of the extending plate, while k symbolizes the porousness of material.

2.4 Primary properties of the KKL nanofluid model

To assess the impact of nanoparticles in the field of velocity and temperature profiles, nanofluid properties must be identified. The frequency, dilute suspensions, certain thermal conductivity, and electrical flow are as follows [68]:

(2.8) ρ n f = ( 1 − ϕ ) ρ f + ϕ ρ s , ( ρ C p ) n f = ( 1 − ϕ ) ( ρ C p ) f + ϕ ( ρ C p ) s , σ n f σ f = 1 + 3 σ s σ f − 1 ϕ σ s σ f + 2 − σ s σ f − 1 ϕ .

Here, κ n f and μ n f can be estimated via the KKL model [69]:

(2.9) κ n f = κ static + κ Brownian , μ n f = μ static + μ Brownian κ n f = 1 + 3 κ s κ f − 1 ϕ κ s κ f + 2 − κ s κ f − 1 ϕ ︸ static + 5 × 10 4 g ′ ( T , ϕ , d p ) ρ f ( C p ) f k b T ρ p d p ϕ , ︸ Brownian g ′ ( T , ϕ , d p ) = ln ( T ) ( a 1 + a 2 ln ( d p ) + a 3 ln ( ϕ ) + a 4 ln ( d p ) ln( ϕ ) + a 5 ln ( d p ) 2 ) + ( a 6 + a 7 ln ( d p ) + a 8 ln ( ϕ ) + a 9 ln ( d p ) ln ( ϕ ) + a 10 ln ( d p ) 2 ) μ n f = μ f ( 1 − ϕ ) 2.5 + κ Brownian μ f κ f ( Pr ) f , 300 K ≤ T ≤ 325 K .

ϕ is the coefficient of the fraction of the volumetric nanoparticles. μ f , ρ f , ( C p ) f , and κ f are flexible viscosity, density, active heat capacity, and thermal conductivity of the base fluid, respectively. Other properties ρ s , ( C p ) s , κ s , κ b , and d p are densities, active heat dissipation, the thermal conductivity of nanoparticles, a constant Boltzmann, and a wide range of nanoparticles, respectively.

2.5 Nanoparticles and base fluid features

Basic EO materials and nanoparticles used in the current study are given in Table 1, and coefficient values of CuO and aluminum oxide are shown in Table 2.

Table 1

Factual possessions [70] of nanoparticles at 293 K and base fluid

Property ρ ( kg / m 3 ) C p ( J / kgK ) k ( W/mK ) σ ( S/m ) d p ( nm )
CuO 6,500 540.0 18.00 1 × 10−10 47
EO 884 1910 0.144 5.5 × 10−6 —
Table 2

Values of coefficients [70] for CuO nanoparticle

Coefficient values CuO
a 1 −26.593310846
a 2 −0.403818333
a 3 −33.3516805
a 4 −1.915825591
a 5 6.42185 × 10−2
a 6 48.40336955
a 7 −9.787756683
a 8 190.245610009
a 9 10.9285386565
a 10 −0.7200998366

2.6 Rosseland approximations

The Rosseland approximation [71,72,73,74,75] is utilized to incorporate the thermal radiation impact into the current regulating equations (2.3)–(2.5).

(2.10) q r = − 4 σ ⁎ 3 k ⁎ ∂ T 4 ∂ y .

The Stefan–Boltzmann number is denoted by σ*, while the absorption coefficient is denoted by k*.

3 Final equations

Converting equations (2.3)–(2.5) into the new form solves the mathematical model presented in this article (ODEs). Equation (2.3) ought to be fulfilled by stream functions before moving on to the next phase (3.1). Using the formula (3.1) and similarity variables, the conversion step is completed (3.2) (for instance, refs. [76,77,78,79]) (Figure 2)

(3.1) u = ψ y , v = − ψ x .

(3.2) η ( x , y ) = b ν f y , ψ ( x , y ) = ν f b x f ( χ ) , θ ( η ) = T − T ∞ T w − T ∞ .

Figure 2 Mathematical model’s flowchart structure.
Figure 2

Mathematical model’s flowchart structure.

The following ODEs are obtained by substituting (3.1)–(3.2) into each of the governing equations (2.3)–(2.5).

(3.3) f ‴ + ϕ 1 ϕ 2 ( f f ″ − f ′ 2 ) + α ( 2 f ′ f ‴ − f ″ 2 − f f iv ) − ϕ 4 ϕ 2 M f ′ = 0 ,

(3.4) θ ″ 1 + 1 ϕ 5 PrNr + Pr ϕ 3 ϕ 5 f θ ′ − f ′ θ + E c ϕ 1 ϕ 3 f ″ 2 + ϕ 4 ϕ 3 MEc f ′ 2 = 0 ,

through

(3.5) f ( 0 ) = S , f ′ ( 0 ) = 1 + Λ f ″ ( 0 ) ,      θ ′ ( 0 ) = − B s ( 1 − θ ( 0 ) ) f ′ ( η ) → 0 , f ″ ( η ) → 0 , θ ( η ) → 0 ,    as    η → ∞ .

In the following equations (3.3)–(3.4), the nanofluid’s thermophysical characteristics are represented by ϕ ' i s , which is 1 ≤ i ≤ 5 [80,81,82,83]:

(3.6) ϕ 1 = ( 1 − ϕ ) 2.5 , ϕ 2 = 1 − ϕ + ϕ ρ s ρ f , ϕ 3 = 1 − ϕ + ϕ ( ρ C p ) s ( ρ C p ) f , ϕ 4 = 1 + 3 σ s σ f − 1 ϕ σ s σ f + 2 − σ s σ f − 1 ϕ , ϕ 5 = ( k s + 2 k f ) − 2 ϕ ( k f − k s ) ( k s + 2 k f ) + ϕ ( k f − k s ) .

3.1 Parameter expression

ODE parameters and their associated BCs are listed together in Table 3.

Table 3

The existing ODEs and their governing parameter BCs

Governing parameters Appearance
Non-Newtonian second grade α = α 1 b μ f
MHD M = σ f B 0 2 b ρ f
Prandtl number Pr = ν f α f
Thermal diffusivity α f = κ f ( ρ C p ) f
Suction/injection S = − V w 1 ν f   b
Thermal radiation Nr = 16 3 σ ⁎ T ∞ 3 κ ⁎ ν f ( ρ C p ) f
Velocity slip Λ = b ν f N w
Eckert number Ec = U w 2 ( C p ) f ( T w − T ∞ )
Biot number B s = h f k 0 ν f b

3.2 Quantities for engineering interest

(C f ) and (Nu x ) are the physical quantities that have been measured in this present model [84,85].

(3.7) C f = τ w ρ f U w 2 , Nu x = x q w k f ( T w − T ∞ ) .

The symbols for τ w and q w are shown below:

(3.8) τ w = [ μ n f u y + α 1 ( u u x y + 2 u y u x + v u y y ) ] y = 0 , q w = − k n f 1 + 16 3 σ ⁎ T ∞ 3 κ ⁎ ν f ( ρ C p ) f ( T y ) y = 0 .

It is possible to get the following result by substituting equations (3.2) and (3.8):

(3.9) C f Re x 1 2 = f ″ ( 0 ) ( 1 − ϕ ) 2.5 + α [ 3 f ″ ( 0 ) f ′ ( 0 ) − f ‴ ( 0 ) f ( 0 ) ] , Nu x Re x − 1 2 = − k n f k f ( 1 + Nr ) θ ′ ( 0 ) .

Using equation (3.9), the Nusselt number Nu x and the decreased skin friction C f may be found. Meanwhile, Re x = U w x ν f is used to express the local Rayleigh number.

3.3 Entropy generation analysis

The entropy generation for the above mentioned suppositions is [76]:

(3.10) E G = k n f T ∞ 2 ( T y ) 2 + 16 3 σ ⁎ T ∞ 3 κ ⁎ ν f ( ρ C p ) f ( T y ) 2 + μ n f T ∞ ( u y ) 2 + σ n f B 2 u 2 T ∞ .

The dimensionless form of entropy equation is acquired as follows:

(3.11) N G = T ∞ 2 b 2 E G k f ( T w − T ∞ ) 2 .

From equation (3.10), the dimensionless entropy equation is as follows:

(3.12) N G = Re ϕ 4 ( 1 + Nr ) θ ′ 2 + 1 ϕ 1 Br ω ( f ″ 2 + ϕ 1 ϕ 4 M f ′ 2 f ′ 2 ) .

Here, Re  is the Reynolds number, Br is the Brinkman number, and ω is the dimensionless temperature gradient.

4 Numerical procedure: Shooting method

The shooting method [86] is used to compute the numerical solutions, which adapts the fourth-order Runge–Kutta (RK4) technique. The shooting method’s mathematical modeling (3.3–3.5) is being disclosed and adorned in Figure 3.

Figure 3 The shooting method’s methodological framework.
Figure 3

The shooting method’s methodological framework.

The subsequent phases of the shooting technique need the conversion of (3.3)–(3.5) into a first-order system. The results of the first-order system are displayed in the following way:

(4.1) z 1 = f ′ ,

(4.2) z 2 = z 1 ′ ,

(4.3) z 3 = z 2 ′ ,

(4.4) z 4 = θ ′ ,

(4.5) z 2 ′ + ϕ 1 ϕ 2 ( f z 2 − z 1 2 ) + α ( 2 z 1 z 2 ′ − z 2 2 − f z 3 ′ ) − ϕ 4 ϕ 2 M z 1 = 0 ,

(4.6) z 4 ′ 1 + 1 ϕ 4 PrNr + Pr ϕ 3 ϕ 5 f z 4 − z 1 θ + Ec ϕ 1 ϕ 3 z 2 2 + + ϕ 4 ϕ 3 MEc z 1 2 = 0 ,

(4.7) f ( 0 ) = S , z 1 ( 0 ) = 1 + Λ z 2 ( 0 ) , z 3 ( 0 ) = − B s ( 1 − θ ( 0 ) ) , z 1 ( ∞ ) → 0 , z 2 ( ∞ ) → 0 , θ ( ∞ ) → 0 .

5 Validity of code

The computed outcomes are verified by comparing with the previous proclaimed results in the literature [87,88]. Every value in Table 4 has been validated for consistency. By contrast, the present results are in good agreement and accepted.

Table 4

Comparison of − θ ′ ( 0 ) for various Pr , where ϕ = 0 , Λ = 0 , Nr = 0 , M = 0 , Ec = 0, S = 0 , and B s → 0

Prandtl number Pr Ref. [87] Ref. [88] Present results
0.20 0.1691 0.1691 0.1691
0.70 0.4539 0.4537 0.4537
2.00 0.9114 0.9114 0.9114
7.00 1.8954 1.8958 1.8958

6 Numerical results and discussion

Viscosity dissipation and shifting BCs were studied in MHD radiation-level nanofluid experiments. The mathematical modeling is done using the KKL model. Table 1 lists the thermophysical properties of one nanoparticle (CuO) and the principal liquid (EO). Table 2 illustrates the coefficient value of CuO for KKL model, and Table 3 demonstrates the parameters of the nanoparticles and the primary fluid, respectively. In this experiment, nanoparticles and a base liquid are employed. Non-dimensional components will be discussed in this section (Table 4). Consequently, several features are taken into account, such as second-grade, nanoparticle volume friction and magnetic, Eckert number, thermal radiation, Biot number, velocity slip, suction/injection, and velocity slip. The skin friction and Nusselt numbers CuO–EO nanofluids have also been computed numerically.

Figure 4 shows the velocity distribution as the second-grade parameter α augmented. Fluid velocity is shown to have risen significantly on this graph. This will result in an upsurge in momentum boundary layer thickness. Growth causes viscosity to fall owing to the fluid escalation speed and the height at which it is disturbed, according to a statistical representation. The second-grade parameter is also well-known for revamping fluid behavior to reduce fluid viscosity and hence improve liquid velocity.

Figure 4 Nature of f ′ f^{\prime} over α \alpha .
Figure 4

Nature of f ′ over α .

The difference in heat distribution across α is shown in Figure 5. According to this graph, thermal distribution is decreasing as a result of rising α . As a result, the thermal boundary layer’s thickness has dwindled. The results showed the heat from the surface is being actively transferred to fluid and released to the far-field. The phenomenon happens due to the velocity of the liquid is enlarged with increasing α in the system.

Figure 5 Nature of θ \theta over α \alpha .
Figure 5

Nature of θ over α .

According to Figure 6, M is growing with f ′ ( η ) diminished. When contrast to the high M values, the movement of the liquid particles is negligible. The occurrence is due to M generating Lorentz force, acting as retarded force in the flow. The Lorentz force will be forcing the molecules of the fluid to flow oppositely from the original flow. It has the opposite impact on particle mobility if a constant magnetic field is provided in the normal flow direction across a vast area.

Figure 6 Nature of f ′ f^{\prime} over M M .
Figure 6

Nature of f ′ over M .

The heat boundary layer thickness intensifies, leading to an escalation in thermal dispersion, as shown in Figure 7. The system releases thermal energy by exerting more effort than necessary to bring a nanofluid closer to a magnetic field. This occurrence will cause increases in the temperature of the fluid. M instantly amplified the temperature of the surface as it acted on the system. There will be more heat transferred to flow since there are more molecules in the fluid, and this will result in a higher temperature for the flow.

Figure 7 Nature of θ \theta over M M .
Figure 7

Nature of θ over M .

Figure 8 depicts the change f ′ ( η ) across various solid volume fractions ϕ . Because of this consequence, Figure 8 shows that the rising ϕ causes fluid particles to slow down. This occurrence is due to the particles occupied at each phase having less space between each particle in the flow. Hence, the molecules of the fluid have difficulties moving in the flow and the liquid velocity is diminished.

Figure 8 Nature of f ′ f^{\prime} over ϕ \phi .
Figure 8

Nature of f ′ over ϕ .

In addition, the improved thermal distribution may be noticed through the action of the heat-injection system (Figure 9). The physical definition of the phrase “thermal boundary layer” shows that the solid volume percentage increases the fluid concentration, tumbling momentum thickness, and the thermal boundary layer thickness. This phenomenon has a similar physical explanation as in the discussion of Figure 8.

Figure 9 Nature of θ \theta over ϕ \phi .
Figure 9

Nature of θ over ϕ .

Figure 10 shows a growth in the velocity slip parameter Λ . The diminution f ′ ( η ) is the result of velocity slip Λ . The flow slows down as a result of a higher acceleration element height, which creates a friction force that allows more fluid to flow through the sheet. On the other hand, the slip parameter indicates a different distribution of temperatures.

Figure 10 Nature of f ′ f^{\prime} over Λ \text{Λ} .
Figure 10

Nature of f ′ over Λ .

When the slip parameter improves, the thermal distribution diminishes at the beginning (for η < 4 ), but opposite observation is observed when the data are η > 4 , as shown in Figure 11. Since there is friction between the flow and the sheet’s surface, the heat will be created on the surface and transported to the fluid flow. Then, the temperature of the flow will consequently double up.

Figure 11 Nature of θ \theta over Λ \text{&#x039B;} .
Figure 11

Nature of θ over Λ .

An illustration of the relationship between thermal distribution and Biot number B s is shown in Figure 12. The plotted figure makes it clear that intensifying the amount of heat transferred affects B s. This incident is due to the creation of a thicker layer of the thermal boundary layer in the region as a result of varying temperature changes in the surrounding area. Compared to the permanent circumstances of water temperature, a nanofluid with a convective BC is a more accurate model.

Figure 12 Nature of θ \theta over B s.
Figure 12

Nature of θ over B s.

Figure 13 examines θ ( η ) over η changes as a result of Nr . Figure 13 shows that heat transfer is abridged without the use of a heat shield. In addition, the heat distribution improves Nr as the temperature rises. As Rosseland radiation absorption decreases, so does the luminous temperature change variability. As a result, the liquid’s radiation temperature rises, helping to raise its temperature.

Figure 13 Nature of θ \theta over Nr \text{Nr} .
Figure 13

Nature of θ over Nr .

Figure 14 shows the temperature distribution that is affected by the Eckert number. The rise in thermal variation is shown in Figure 14. Liquids generate heat as the value Ec grows owing to temperature collisions. When it comes to the physical aspects of the Eckert number, it measures the amount of energy that may be transferred from one object to another. As a result, increasing the Eckert numbers leads to the conversion of kinetic energy into internal energy through effort against viscous fluid pressures. As a result, a rise in Ec raises the liquid’s temperature.

Figure 14 Nature of θ \theta over Ec \text{Ec} .
Figure 14

Nature of θ over Ec .

Figures 15 and 16 illustrate the suction/injection increment for the velocity and temperature distributions separately. When the injection rate becomes hikes, as S negative, but when the suction rate becomes favorable, as S escalations. While a minor proliferation in the suction parameter declines the fluid velocity, the injection parameter contributes the opposite behavior (Figure 15). Figure 16 illustrates the thermal distribution variance for different. When the injection parameter is improved, the thermal distribution grows; the thermal dispersion shrinks when the suction parameter has dwindled. Because vigorous ventilation surges the temperature of the hot border, and with the proper liquid flow to the wall, absorption may be employed as a surface scraper.

Figure 15 Nature of f ′ f^{\prime} over S S .
Figure 15

Nature of f ′ over S .

Figure 16 Nature of θ \theta over S S .
Figure 16

Nature of θ over S .

In the stretched boundary layer regime, the response in Reynolds number Re on the entropy generation profiles is shown in Figure 17. It can be shown that the higher the Reynolds number Re , the stronger the entropy impact. Due to higher values of Reynolds number Re , retrogression of frictional forces tends to gasify entropy profiles. Figure 18 shows the change in entropy generation number N G versus Brinkman number Br values, indicating that increasing Brinkman number Br increases entropy generation. Br investigates the fluid’s viscous influence because of reality and such behavior. As a result, large Br values indicate that fluid friction is the major cause of entropy formation (Table 5).

Figure 17 Nature of N G {N}_{G} over Re \text{Re} .
Figure 17

Nature of N G over Re .

Figure 18 Nature of N G {N}_{G} over Br \text{Br} .
Figure 18

Nature of N G over Br .

Table 5

Values of skin friction = C f Re x 1 2 and Nusselt number = Nu Re x − 1 2 for Pr = 6450

α M ϕ Λ B s Nr Ec S C f Re x 1 2 NuRe x − 1 / 2
0.1 0.5 0.01 0.5 0.5 2 3 0.5 0.86494 0.46768
0.5 1.36079 0.49521
1.1 1.92112 0.51589
0.5 0.86494 0.46768
1.5 0.94812 0.35546
2.5 1.0417 0.23367
0.01 0.86494 0.46768
0.03 0.85894 0.46291
0.05 0.81491 0.42592
0.1 0.86494 0.46768
0.5 0.33894 0.62242
1.1 0.07528 0.69001
0.1 0.86494 0.46768
0.5 0.86494 0.64776
1.1 0.86494 0.70595
0.1 0.86494 0.46768
1.5 0.86494 0.50131
2.5 0.86494 0.53138
1 0.86494 0.46768
3 0.86494 0.38086
5 0.86494 0.29403
−0.6 0.42107 0.12815
−0.4 0.44588 0.17523
0.4 0.85029 0.43435
0.6 0.87869 0.50026

7 Final remarks

Using a liquid model, the effects of MHD in a second-grade flow of nanoliquid along with heat transfer and entropy generation are investigated in this study. The model is based on the KKL framework. The RKF45 scheme and shooting approach are used to solve the ODEs. The graphs show second-grade nanofluid velocity and temperature, while the comparative values for physical parameters are shown in the table (Nusselt number and skin friction coefficient). A variety of non-dimensional parameter values are used to measure these representations (graphs and tables). Its best results may be found in the following summary:

  1. α intensification velocity while declining heat distribution and local Nusselt numbers (in both nanofluids). Nanofluid CuO–EO has a higher skin friction coefficient as a result of this characteristic.

  2. Solid volume fraction and the MHD parameter escalation heat distribution, while velocity shrinkages; MHD parameter amplifications of the skin friction coefficient and reductions in the Nusselt number. On the other hand, the solid volume fraction is responsible for the decrease in physical characteristics.

  3. Temperature distribution growing with Nr and Ec augmented Nusselt number. This decrease in velocity and temperature is accompanied by an increase in the Nusselt number of other physical measures (temperature is reduced only at the location close to the sheet).

  4. Skin friction coefficient can be reduced by using Λ . However, the Nusselt number rises as a result of Λ .

  5. Biot number amplified the temperature distributions in the flow due to the thickness of the boundary layer getting swollen.

  6. Entropy rate of the thermal system is enhanced with the boost in the values of Reynolds number Re due to the effect of dominant inertial forces.

  7. System entropy rate is boosted with Brinkman number Br increment results in the growth in the surface heat dissipation.

  8. Injection parameter affects temperature and velocity enhancements, as well as Nusselt number and temperature rise. When suction rises, they become repressed. Physical properties can be improved by increasing the suction rate. In the meantime, both physical characteristics decrease when the injection rate grows.

Acknowledgments

The authors express their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a research groups program under grant number R.G.P.2/43/40. Also, the authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education, in Saudi Arabia, for funding this research work through the project no.IFP-KKU-2020/9. Also, this study was supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R132), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

  1. Funding information: This work received funding from King Khalid University, Ministry of Education, Saudi Arabia. Also, this study was supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R132), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

  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: 2021-12-18
Revised: 2022-02-23
Accepted: 2022-04-27
Published Online: 2022-06-01

© 2022 Faisal Shahzad et al., published by De Gruyter

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

Articles in the same Issue

  1. Research Articles
  2. Theoretical and experimental investigation of MWCNT dispersion effect on the elastic modulus of flexible PDMS/MWCNT nanocomposites
  3. Mechanical, morphological, and fracture-deformation behavior of MWCNTs-reinforced (Al–Cu–Mg–T351) alloy cast nanocomposites fabricated by optimized mechanical milling and powder metallurgy techniques
  4. Flammability and physical stability of sugar palm crystalline nanocellulose reinforced thermoplastic sugar palm starch/poly(lactic acid) blend bionanocomposites
  5. Glutathione-loaded non-ionic surfactant niosomes: A new approach to improve oral bioavailability and hepatoprotective efficacy of glutathione
  6. Relationship between mechano-bactericidal activity and nanoblades density on chemically strengthened glass
  7. In situ regulation of microstructure and microwave-absorbing properties of FeSiAl through HNO3 oxidation
  8. Research on a mechanical model of magnetorheological fluid different diameter particles
  9. Nanomechanical and dynamic mechanical properties of rubber–wood–plastic composites
  10. Investigative properties of CeO2 doped with niobium: A combined characterization and DFT studies
  11. Miniaturized peptidomimetics and nano-vesiculation in endothelin types through probable nano-disk formation and structure property relationships of endothelins’ fragments
  12. N/S co-doped CoSe/C nanocubes as anode materials for Li-ion batteries
  13. Synergistic effects of halloysite nanotubes with metal and phosphorus additives on the optimal design of eco-friendly sandwich panels with maximum flame resistance and minimum weight
  14. Octreotide-conjugated silver nanoparticles for active targeting of somatostatin receptors and their application in a nebulized rat model
  15. Controllable morphology of Bi2S3 nanostructures formed via hydrothermal vulcanization of Bi2O3 thin-film layer and their photoelectrocatalytic performances
  16. Development of (−)-epigallocatechin-3-gallate-loaded folate receptor-targeted nanoparticles for prostate cancer treatment
  17. Enhancement of the mechanical properties of HDPE mineral nanocomposites by filler particles modulation of the matrix plastic/elastic behavior
  18. Effect of plasticizers on the properties of sugar palm nanocellulose/cinnamon essential oil reinforced starch bionanocomposite films
  19. Optimization of nano coating to reduce the thermal deformation of ball screws
  20. Preparation of efficient piezoelectric PVDF–HFP/Ni composite films by high electric field poling
  21. MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon
  22. Effects of nano-SiO2 modification on rubberised mortar and concrete with recycled coarse aggregates
  23. Mechanical and microscopic properties of fiber-reinforced coal gangue-based geopolymer concrete
  24. Effect of morphology and size on the thermodynamic stability of cerium oxide nanoparticles: Experiment and molecular dynamics calculation
  25. Mechanical performance of a CFRP composite reinforced via gelatin-CNTs: A study on fiber interfacial enhancement and matrix enhancement
  26. A practical review over surface modification, nanopatterns, emerging materials, drug delivery systems, and their biophysiochemical properties for dental implants: Recent progresses and advances
  27. HTR: An ultra-high speed algorithm for cage recognition of clathrate hydrates
  28. Effects of microalloying elements added by in situ synthesis on the microstructure of WCu composites
  29. A highly sensitive nanobiosensor based on aptamer-conjugated graphene-decorated rhodium nanoparticles for detection of HER2-positive circulating tumor cells
  30. Progressive collapse performance of shear strengthened RC frames by nano CFRP
  31. Core–shell heterostructured composites of carbon nanotubes and imine-linked hyperbranched polymers as metal-free Li-ion anodes
  32. A Galerkin strategy for tri-hybridized mixture in ethylene glycol comprising variable diffusion and thermal conductivity using non-Fourier’s theory
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  36. Electrospun nanofibers of Co3O4 nanocrystals encapsulated in cyclized-polyacrylonitrile for lithium storage
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  38. Formulation of polymeric nanoparticles loaded sorafenib; evaluation of cytotoxicity, molecular evaluation, and gene expression studies in lung and breast cancer cell lines
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https://doi.org/10.1515/ntrev-2022-0123
Keywords for this article
Koo–Kleinstreuer–Li model; second-grade nanofluid; thermal radiations; entropy generation; shooting method
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Theoretical and experimental investigation of MWCNT dispersion effect on the elastic modulus of flexible PDMS/MWCNT nanocomposites
  3. Mechanical, morphological, and fracture-deformation behavior of MWCNTs-reinforced (Al–Cu–Mg–T351) alloy cast nanocomposites fabricated by optimized mechanical milling and powder metallurgy techniques
  4. Flammability and physical stability of sugar palm crystalline nanocellulose reinforced thermoplastic sugar palm starch/poly(lactic acid) blend bionanocomposites
  5. Glutathione-loaded non-ionic surfactant niosomes: A new approach to improve oral bioavailability and hepatoprotective efficacy of glutathione
  6. Relationship between mechano-bactericidal activity and nanoblades density on chemically strengthened glass
  7. In situ regulation of microstructure and microwave-absorbing properties of FeSiAl through HNO3 oxidation
  8. Research on a mechanical model of magnetorheological fluid different diameter particles
  9. Nanomechanical and dynamic mechanical properties of rubber–wood–plastic composites
  10. Investigative properties of CeO2 doped with niobium: A combined characterization and DFT studies
  11. Miniaturized peptidomimetics and nano-vesiculation in endothelin types through probable nano-disk formation and structure property relationships of endothelins’ fragments
  12. N/S co-doped CoSe/C nanocubes as anode materials for Li-ion batteries
  13. Synergistic effects of halloysite nanotubes with metal and phosphorus additives on the optimal design of eco-friendly sandwich panels with maximum flame resistance and minimum weight
  14. Octreotide-conjugated silver nanoparticles for active targeting of somatostatin receptors and their application in a nebulized rat model
  15. Controllable morphology of Bi2S3 nanostructures formed via hydrothermal vulcanization of Bi2O3 thin-film layer and their photoelectrocatalytic performances
  16. Development of (−)-epigallocatechin-3-gallate-loaded folate receptor-targeted nanoparticles for prostate cancer treatment
  17. Enhancement of the mechanical properties of HDPE mineral nanocomposites by filler particles modulation of the matrix plastic/elastic behavior
  18. Effect of plasticizers on the properties of sugar palm nanocellulose/cinnamon essential oil reinforced starch bionanocomposite films
  19. Optimization of nano coating to reduce the thermal deformation of ball screws
  20. Preparation of efficient piezoelectric PVDF–HFP/Ni composite films by high electric field poling
  21. MHD dissipative Casson nanofluid liquid film flow due to an unsteady stretching sheet with radiation influence and slip velocity phenomenon
  22. Effects of nano-SiO2 modification on rubberised mortar and concrete with recycled coarse aggregates
  23. Mechanical and microscopic properties of fiber-reinforced coal gangue-based geopolymer concrete
  24. Effect of morphology and size on the thermodynamic stability of cerium oxide nanoparticles: Experiment and molecular dynamics calculation
  25. Mechanical performance of a CFRP composite reinforced via gelatin-CNTs: A study on fiber interfacial enhancement and matrix enhancement
  26. A practical review over surface modification, nanopatterns, emerging materials, drug delivery systems, and their biophysiochemical properties for dental implants: Recent progresses and advances
  27. HTR: An ultra-high speed algorithm for cage recognition of clathrate hydrates
  28. Effects of microalloying elements added by in situ synthesis on the microstructure of WCu composites
  29. A highly sensitive nanobiosensor based on aptamer-conjugated graphene-decorated rhodium nanoparticles for detection of HER2-positive circulating tumor cells
  30. Progressive collapse performance of shear strengthened RC frames by nano CFRP
  31. Core–shell heterostructured composites of carbon nanotubes and imine-linked hyperbranched polymers as metal-free Li-ion anodes
  32. A Galerkin strategy for tri-hybridized mixture in ethylene glycol comprising variable diffusion and thermal conductivity using non-Fourier’s theory
  33. Simple models for tensile modulus of shape memory polymer nanocomposites at ambient temperature
  34. Preparation and morphological studies of tin sulfide nanoparticles and use as efficient photocatalysts for the degradation of rhodamine B and phenol
  35. Polyethyleneimine-impregnated activated carbon nanofiber composited graphene-derived rice husk char for efficient post-combustion CO2 capture
  36. Electrospun nanofibers of Co3O4 nanocrystals encapsulated in cyclized-polyacrylonitrile for lithium storage
  37. Pitting corrosion induced on high-strength high carbon steel wire in high alkaline deaerated chloride electrolyte
  38. Formulation of polymeric nanoparticles loaded sorafenib; evaluation of cytotoxicity, molecular evaluation, and gene expression studies in lung and breast cancer cell lines
  39. Engineered nanocomposites in asphalt binders
  40. Influence of loading voltage, domain ratio, and additional load on the actuation of dielectric elastomer
  41. Thermally induced hex-graphene transitions in 2D carbon crystals
  42. The surface modification effect on the interfacial properties of glass fiber-reinforced epoxy: A molecular dynamics study
  43. Molecular dynamics study of deformation mechanism of interfacial microzone of Cu/Al2Cu/Al composites under tension
  44. Nanocolloid simulators of luminescent solar concentrator photovoltaic windows
  45. Compressive strength and anti-chloride ion penetration assessment of geopolymer mortar merging PVA fiber and nano-SiO2 using RBF–BP composite neural network
  46. Effect of 3-mercapto-1-propane sulfonate sulfonic acid and polyvinylpyrrolidone on the growth of cobalt pillar by electrodeposition
  47. Dynamics of convective slippery constraints on hybrid radiative Sutterby nanofluid flow by Galerkin finite element simulation
  48. Preparation of vanadium by the magnesiothermic self-propagating reduction and process control
  49. Microstructure-dependent photoelectrocatalytic activity of heterogeneous ZnO–ZnS nanosheets
  50. Cytotoxic and pro-inflammatory effects of molybdenum and tungsten disulphide on human bronchial cells
  51. Improving recycled aggregate concrete by compression casting and nano-silica
  52. Chemically reactive Maxwell nanoliquid flow by a stretching surface in the frames of Newtonian heating, nonlinear convection and radiative flux: Nanopolymer flow processing simulation
  53. Nonlinear dynamic and crack behaviors of carbon nanotubes-reinforced composites with various geometries
  54. Biosynthesis of copper oxide nanoparticles and its therapeutic efficacy against colon cancer
  55. Synthesis and characterization of smart stimuli-responsive herbal drug-encapsulated nanoniosome particles for efficient treatment of breast cancer
  56. Homotopic simulation for heat transport phenomenon of the Burgers nanofluids flow over a stretching cylinder with thermal convective and zero mass flux conditions
  57. Incorporation of copper and strontium ions in TiO2 nanotubes via dopamine to enhance hemocompatibility and cytocompatibility
  58. Mechanical, thermal, and barrier properties of starch films incorporated with chitosan nanoparticles
  59. Mechanical properties and microstructure of nano-strengthened recycled aggregate concrete
  60. Glucose-responsive nanogels efficiently maintain the stability and activity of therapeutic enzymes
  61. Tunning matrix rheology and mechanical performance of ultra-high performance concrete using cellulose nanofibers
  62. Flexible MXene/copper/cellulose nanofiber heat spreader films with enhanced thermal conductivity
  63. Promoted charge separation and specific surface area via interlacing of N-doped titanium dioxide nanotubes on carbon nitride nanosheets for photocatalytic degradation of Rhodamine B
  64. Elucidating the role of silicon dioxide and titanium dioxide nanoparticles in mitigating the disease of the eggplant caused by Phomopsis vexans, Ralstonia solanacearum, and root-knot nematode Meloidogyne incognita
  65. An implication of magnetic dipole in Carreau Yasuda liquid influenced by engine oil using ternary hybrid nanomaterial
  66. Robust synthesis of a composite phase of copper vanadium oxide with enhanced performance for durable aqueous Zn-ion batteries
  67. Tunning self-assembled phases of bovine serum albumin via hydrothermal process to synthesize novel functional hydrogel for skin protection against UVB
  68. A comparative experimental study on damping properties of epoxy nanocomposite beams reinforced with carbon nanotubes and graphene nanoplatelets
  69. Lightweight and hydrophobic Ni/GO/PVA composite aerogels for ultrahigh performance electromagnetic interference shielding
  70. Research on the auxetic behavior and mechanical properties of periodically rotating graphene nanostructures
  71. Repairing performances of novel cement mortar modified with graphene oxide and polyacrylate polymer
  72. Closed-loop recycling and fabrication of hydrophilic CNT films with high performance
  73. Design of thin-film configuration of SnO2–Ag2O composites for NO2 gas-sensing applications
  74. Study on stress distribution of SiC/Al composites based on microstructure models with microns and nanoparticles
  75. PVDF green nanofibers as potential carriers for improving self-healing and mechanical properties of carbon fiber/epoxy prepregs
  76. Osteogenesis capability of three-dimensionally printed poly(lactic acid)-halloysite nanotube scaffolds containing strontium ranelate
  77. Silver nanoparticles induce mitochondria-dependent apoptosis and late non-canonical autophagy in HT-29 colon cancer cells
  78. Preparation and bonding mechanisms of polymer/metal hybrid composite by nano molding technology
  79. Damage self-sensing and strain monitoring of glass-reinforced epoxy composite impregnated with graphene nanoplatelet and multiwalled carbon nanotubes
  80. Thermal analysis characterisation of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: An optimal thermal application
  81. Pyrene-functionalized halloysite nanotubes for simultaneously detecting and separating Hg(ii) in aqueous media: A comprehensive comparison on interparticle and intraparticle excimers
  82. Fabrication of self-assembly CNT flexible film and its piezoresistive sensing behaviors
  83. Thermal valuation and entropy inspection of second-grade nanoscale fluid flow over a stretching surface by applying Koo–Kleinstreuer–Li relation
  84. Mechanical properties and microstructure of nano-SiO2 and basalt-fiber-reinforced recycled aggregate concrete
  85. Characterization and tribology performance of polyaniline-coated nanodiamond lubricant additives
  86. Combined impact of Marangoni convection and thermophoretic particle deposition on chemically reactive transport of nanofluid flow over a stretching surface
  87. Spark plasma extrusion of binder free hydroxyapatite powder
  88. An investigation on thermo-mechanical performance of graphene-oxide-reinforced shape memory polymer
  89. Effect of nanoadditives on the novel leather fiber/recycled poly(ethylene-vinyl-acetate) polymer composites for multifunctional applications: Fabrication, characterizations, and multiobjective optimization using central composite design
  90. Design selection for a hemispherical dimple core sandwich panel using hybrid multi-criteria decision-making methods
  91. Improving tensile strength and impact toughness of plasticized poly(lactic acid) biocomposites by incorporating nanofibrillated cellulose
  92. Green synthesis of spinel copper ferrite (CuFe2O4) nanoparticles and their toxicity
  93. The effect of TaC and NbC hybrid and mono-nanoparticles on AA2024 nanocomposites: Microstructure, strengthening, and artificial aging
  94. Excited-state geometry relaxation of pyrene-modified cellulose nanocrystals under UV-light excitation for detecting Fe3+
  95. Effect of CNTs and MEA on the creep of face-slab concrete at an early age
  96. Effect of deformation conditions on compression phase transformation of AZ31
  97. Application of MXene as a new generation of highly conductive coating materials for electromembrane-surrounded solid-phase microextraction
  98. A comparative study of the elasto-plastic properties for ceramic nanocomposites filled by graphene or graphene oxide nanoplates
  99. Encapsulation strategies for improving the biological behavior of CdS@ZIF-8 nanocomposites
  100. Biosynthesis of ZnO NPs from pumpkin seeds’ extract and elucidation of its anticancer potential against breast cancer
  101. Preliminary trials of the gold nanoparticles conjugated chrysin: An assessment of anti-oxidant, anti-microbial, and in vitro cytotoxic activities of a nanoformulated flavonoid
  102. Effect of micron-scale pores increased by nano-SiO2 sol modification on the strength of cement mortar
  103. Fractional simulations for thermal flow of hybrid nanofluid with aluminum oxide and titanium oxide nanoparticles with water and blood base fluids
  104. The effect of graphene nano-powder on the viscosity of water: An experimental study and artificial neural network modeling
  105. Development of a novel heat- and shear-resistant nano-silica gelling agent
  106. Characterization, biocompatibility and in vivo of nominal MnO2-containing wollastonite glass-ceramic
  107. Entropy production simulation of second-grade magnetic nanomaterials flowing across an expanding surface with viscidness dissipative flux
  108. Enhancement in structural, morphological, and optical properties of copper oxide for optoelectronic device applications
  109. Aptamer-functionalized chitosan-coated gold nanoparticle complex as a suitable targeted drug carrier for improved breast cancer treatment
  110. Performance and overall evaluation of nano-alumina-modified asphalt mixture
  111. Analysis of pure nanofluid (GO/engine oil) and hybrid nanofluid (GO–Fe3O4/engine oil): Novel thermal and magnetic features
  112. Synthesis of Ag@AgCl modified anatase/rutile/brookite mixed phase TiO2 and their photocatalytic property
  113. Mechanisms and influential variables on the abrasion resistance hydraulic concrete
  114. Synergistic reinforcement mechanism of basalt fiber/cellulose nanocrystals/polypropylene composites
  115. Achieving excellent oxidation resistance and mechanical properties of TiB2–B4C/carbon aerogel composites by quick-gelation and mechanical mixing
  116. Microwave-assisted sol–gel template-free synthesis and characterization of silica nanoparticles obtained from South African coal fly ash
  117. Pulsed laser-assisted synthesis of nano nickel(ii) oxide-anchored graphitic carbon nitride: Characterizations and their potential antibacterial/anti-biofilm applications
  118. Effects of nano-ZrSi2 on thermal stability of phenolic resin and thermal reusability of quartz–phenolic composites
  119. Benzaldehyde derivatives on tin electroplating as corrosion resistance for fabricating copper circuit
  120. Mechanical and heat transfer properties of 4D-printed shape memory graphene oxide/epoxy acrylate composites
  121. Coupling the vanadium-induced amorphous/crystalline NiFe2O4 with phosphide heterojunction toward active oxygen evolution reaction catalysts
  122. Graphene-oxide-reinforced cement composites mechanical and microstructural characteristics at elevated temperatures
  123. Gray correlation analysis of factors influencing compressive strength and durability of nano-SiO2 and PVA fiber reinforced geopolymer mortar
  124. Preparation of layered gradient Cu–Cr–Ti alloy with excellent mechanical properties, thermal stability, and electrical conductivity
  125. Recovery of Cr from chrome-containing leather wastes to develop aluminum-based composite material along with Al2O3 ceramic particles: An ingenious approach
  126. Mechanisms of the improved stiffness of flexible polymers under impact loading
  127. Anticancer potential of gold nanoparticles (AuNPs) using a battery of in vitro tests
  128. Review Articles
  129. Proposed approaches for coronaviruses elimination from wastewater: Membrane techniques and nanotechnology solutions
  130. Application of Pickering emulsion in oil drilling and production
  131. The contribution of microfluidics to the fight against tuberculosis
  132. Graphene-based biosensors for disease theranostics: Development, applications, and recent advancements
  133. Synthesis and encapsulation of iron oxide nanorods for application in magnetic hyperthermia and photothermal therapy
  134. Contemporary nano-architectured drugs and leads for ανβ3 integrin-based chemotherapy: Rationale and retrospect
  135. State-of-the-art review of fabrication, application, and mechanical properties of functionally graded porous nanocomposite materials
  136. Insights on magnetic spinel ferrites for targeted drug delivery and hyperthermia applications
  137. A review on heterogeneous oxidation of acetaminophen based on micro and nanoparticles catalyzed by different activators
  138. Early diagnosis of lung cancer using magnetic nanoparticles-integrated systems
  139. Advances in ZnO: Manipulation of defects for enhancing their technological potentials
  140. Efficacious nanomedicine track toward combating COVID-19
  141. A review of the design, processes, and properties of Mg-based composites
  142. Green synthesis of nanoparticles for varied applications: Green renewable resources and energy-efficient synthetic routes
  143. Two-dimensional nanomaterial-based polymer composites: Fundamentals and applications
  144. Recent progress and challenges in plasmonic nanomaterials
  145. Apoptotic cell-derived micro/nanosized extracellular vesicles in tissue regeneration
  146. Electronic noses based on metal oxide nanowires: A review
  147. Framework materials for supercapacitors
  148. An overview on the reproductive toxicity of graphene derivatives: Highlighting the importance
  149. Antibacterial nanomaterials: Upcoming hope to overcome antibiotic resistance crisis
  150. Research progress of carbon materials in the field of three-dimensional printing polymer nanocomposites
  151. A review of atomic layer deposition modelling and simulation methodologies: Density functional theory and molecular dynamics
  152. Recent advances in the preparation of PVDF-based piezoelectric materials
  153. Recent developments in tensile properties of friction welding of carbon fiber-reinforced composite: A review
  154. Comprehensive review of the properties of fly ash-based geopolymer with additive of nano-SiO2
  155. Perspectives in biopolymer/graphene-based composite application: Advances, challenges, and recommendations
  156. Graphene-based nanocomposite using new modeling molecular dynamic simulations for proposed neutralizing mechanism and real-time sensing of COVID-19
  157. Nanotechnology application on bamboo materials: A review
  158. Recent developments and future perspectives of biorenewable nanocomposites for advanced applications
  159. Nanostructured lipid carrier system: A compendium of their formulation development approaches, optimization strategies by quality by design, and recent applications in drug delivery
  160. 3D printing customized design of human bone tissue implant and its application
  161. Design, preparation, and functionalization of nanobiomaterials for enhanced efficacy in current and future biomedical applications
  162. A brief review of nanoparticles-doped PEDOT:PSS nanocomposite for OLED and OPV
  163. Nanotechnology interventions as a putative tool for the treatment of dental afflictions
  164. Recent advancements in metal–organic frameworks integrating quantum dots (QDs@MOF) and their potential applications
  165. A focused review of short electrospun nanofiber preparation techniques for composite reinforcement
  166. Microstructural characteristics and nano-modification of interfacial transition zone in concrete: A review
  167. Latest developments in the upconversion nanotechnology for the rapid detection of food safety: A review
  168. Strategic applications of nano-fertilizers for sustainable agriculture: Benefits and bottlenecks
  169. Molecular dynamics application of cocrystal energetic materials: A review
  170. Synthesis and application of nanometer hydroxyapatite in biomedicine
  171. Cutting-edge development in waste-recycled nanomaterials for energy storage and conversion applications
  172. Biological applications of ternary quantum dots: A review
  173. Nanotherapeutics for hydrogen sulfide-involved treatment: An emerging approach for cancer therapy
  174. Application of antibacterial nanoparticles in orthodontic materials
  175. Effect of natural-based biological hydrogels combined with growth factors on skin wound healing
  176. Nanozymes – A route to overcome microbial resistance: A viewpoint
  177. Recent developments and applications of smart nanoparticles in biomedicine
  178. Contemporary review on carbon nanotube (CNT) composites and their impact on multifarious applications
  179. Interfacial interactions and reinforcing mechanisms of cellulose and chitin nanomaterials and starch derivatives for cement and concrete strength and durability enhancement: A review
  180. Diamond-like carbon films for tribological modification of rubber
  181. Layered double hydroxides (LDHs) modified cement-based materials: A systematic review
  182. Recent research progress and advanced applications of silica/polymer nanocomposites
  183. Modeling of supramolecular biopolymers: Leading the in silico revolution of tissue engineering and nanomedicine
  184. Recent advances in perovskites-based optoelectronics
  185. Biogenic synthesis of palladium nanoparticles: New production methods and applications
  186. A comprehensive review of nanofluids with fractional derivatives: Modeling and application
  187. Electrospinning of marine polysaccharides: Processing and chemical aspects, challenges, and future prospects
  188. Electrohydrodynamic printing for demanding devices: A review of processing and applications
  189. Rapid Communications
  190. Structural material with designed thermal twist for a simple actuation
  191. Recent advances in photothermal materials for solar-driven crude oil adsorption
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