1. Introduction
The nanofluids are engineered colloidal suspensions of nano-sized particles in conventional fluids (water, EG, or oil) [
1,
2,
3,
4,
5,
6,
7,
8,
9,
10]. Mostly, nanoparticles of carbides, oxides, and metals are used to synthesize the nanofluids. The nanofluids are usually used as coolants in various heat transfer equipment, such as electronic cooling systems, heat exchangers, radiation, etc., due to their improved thermophysical properties [
11,
12,
13,
14,
15,
16,
17,
18].
Many investigations have been carried out to see the behavior of thermophysical properties of nanofluids for different applications by using different types of nanoparticles [
19,
20,
21,
22,
23]. In the list of thermophysical properties, viscosity plays an important role in the transport of mass and convective heat transfer. The viscosity of nanofluid is affected not only by shear rate but also by operating temperature, nanoparticle concentration, type of nanoparticles and their sizes, etc. Numerous studies have been conducted on the behavior of viscosity of nanofluids. Moghaddam et al. [
24] studied the viscosity of graphene/glycerol nanofluids at a 6.32 shear rate, 20 °C temperature, and different particle concentrations. It increases by increasing nanoparticle concentration and decreases by enhancing temperature. Chen et al. [
25] described the rheological properties of TiO2/EG nanofluids. The results exhibit the Newtonian at a 0.5–10
4 shear rate and found that viscosity is independent of the temperature. Rashin and Hemalatha [
26] investigated the viscosity of CuO/coconut oil nanofluids. Their experiments showed the non-Newtonian behavior at a low shear rate (0–2.5%) concentration under different temperatures. Khedkar et al. [
27] studied the viscosity of Fe
3O
4/paraffin at 0.01–0.1% concentration. Their experimental results showed that the viscosity is enhanced by increasing nanoparticle concentration whereas it shows Newtonian behavior at a high shear rate and non-Newtonian at a lower. Halelfadl et al. [
28] studied the viscosity of CNT/water nanofluids at a high shear rate under different temperature conditions. The results showed that the nanofluids performed a non-Newtonian behavior at high nanoparticle concentration and Newtonian at lower nanoparticle concentration. Later, Chen et al. [
29] studied the rheological properties of TiO
2/EG nanofluids at different nanoparticle concentrations and temperatures. The nanofluids show a non-Newtonian property at 2% particle concentration under different temperatures. Numburu et al. [
30] investigated the rhetorical property of SiO
2/EG and SiO
2/water nanofluids at −35–50 °C temperature. It is found that the nanofluid exhibited Newtonian properties at high temperatures and non-Newtonian properties at low temperatures. Kulkarni et al. [
31] reported the viscosity of Al
2O
3/EG, CuO/EG, and SiO
2/EG nanofluids under −35–50 °C temperature ranges. It is reported that viscosity reduces exponentially by increasing temperature. Yu et al. [
32] observed the effects of the viscosity of ZnO/EG nanofluids. The results detected Newtonian behaviors at low particle concentrations and non-Newtonian behaviors at higher particle concentrations under different temperature conditions.
In the literature related to nanofluids, the behavior of thermal conductivity is investigated widely due to heat transfer’s applications, and found that the behavior of conduction depends on various factors such as temperature, nanoparticle shape, size, and type [
33,
34]. Teng et al. [
35] investigated the impact of a particle’s size and temperature on the thermal conductivity of Al
2O
3/H
2O nanofluids. The results exhibit that the thermal conductivity is increased with increasing nanoparticles concentration and temperature. Chandrasekar et al. [
36] observed that the thermal conductivity of Al
2O
3/water nanofluids increased by increasing nanoparticle concentration under room temperature. Sundar et al. [
37] predicted the behavior of thermal conductivity and viscosity of Al
2O
3/EG-Water nanofluids on different particle concentrations (0.3–1.5%) at temperatures range (20–60 °C). The results specified that the thermal conductivity of nanofluids improves with increasing nanoparticle concentrations and temperatures. Mahbubul et al. [
38] studied the behavior of the thermal conductivity of Al
2O
3/R141b nano-refrigerant and found an enhancement in thermal conduction by increasing nanoparticle concentration and temperature. Mostafizur et al. [
39] investigated the thermal conductivities of SiO
2/methanol, Al
2O
3/methanol, and TiO
2/methanol nanofluids. It was concluded that the thermal conductivity is increased for all nanofluids but found higher for Al
2O
3/methanol nanofluids as compared to the other two nanofluids. Das et al. [
40] studied the thermal conductivity in different ranges of temperature for five distinct nanofluids which are prepared by dispersion of SiO
2, Al
2O
3, TiO
2, CuO, and ZnO nanoparticles in propylene glycol-water. The improvement in thermal conductivity of all nanofluids by enhancing temperature and nanoparticle concentration is found. Murshed et al. [
41] investigated the thermal conductivity of TiO
2/DI H
2O nanofluids. Their experiments show the enhancement in thermal conductivity by increasing particle concentration (0.5–5%) at room temperature. Duangthongsuk and Wong wises [
42] detected the behavior of thermal conductivity of TiO
2/H
2O nanofluids. The thermal conductivity of nanofluids increased by nanoparticle concentration as well as increased temperature.
In the above studies, it is found that the nature of fluid whether it is Newtonian or non-Newtonian depends on the behavior of viscosity. The behavior of viscosity is not only changed by nanoparticles but also depends on operating temperature. Similarly, the thermal conductivity of the nanofluid not only increased by nanoparticle concentration but also increased by increasing temperature. Keeping in mind these facts, the rheological properties of four different nanofluids such as SiO
2/DIW, Al
2O
3/DIW, PEG-TGr/DIW, and PEG-GnP/DIW are modeled as a function of nanoparticle concentration and operating temperature in the current study. For modeling, experimental data is picked at 0.025%, 0.05%, 0.075%, and 0.1% nanoparticle concentration under 30 °C, 40 °C, and 50 °C temperature range [
1]. Further, these models are used in transport equations to see the boundary layer flow over two different geometries such as wedge and plate. The whole investigation is divided into different sections. After introductions in
Section 1, the mathematical models are established based on experimental data to discuss the thermophysical properties and parameters of schematic nanofluids in the form of graphs and tables respectively in
Section 2. In
Section 3, the mathematical problem for flow is developed by using continuity, momentum, and energy equations. In
Section 4, physical parameters such as momentum and thermal boundary layers thickness, momentum and displacement thicknesses, coefficient of skin friction, and Nusselt number are modeled. The numerical solution of the problem is obtained using the RK method and gets the solutions in the form of velocity and temperature functions. In next
Section 6, attained results are displayed in graphical and tabular form for discussion. In last
Section 7, the significant outcomes are concluded.
3. Heat and Mass Flow Modeling
Consider the steady state and an incompressible boundary layer fluid flow propagating over two different geometries (Plate and Wedge). The fluid at the wall flowed with
velocity and flowed with
velocity in the free stream region as seen in
Figure 19. The relationship between the Falkner-Skan power law parameter
and the wedge’s angle
is stated as
Geometry exhibited plate-shaped when and wedge when . The temperature at the wall and away from the wall is maintained with constant and i.e., respectively.
Under the boundary layer approximation, the continuity, momentum, and energy equations can be written as
with the boundary conditions
For simplicity, introduced the similarity transformations [
43] as
After the substitution of Equation (11) into Equation (6)–(8), we obtain the following non-dimensional equations
Here, is Prandtl Number, is Reynold number, is the mixed convection parameter, is the local Grashof number, and is the Eckert number.