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Abstract

Traditional strategies for improving heat transmission in industrial systems include nanofluids and porous inserts. In these kinds of systems, increasing the rate of thermal transmission can also be accomplished by utilizing porous materials that have a higher thermal conductance. Al₂O₃, CuO, and ZnO in engine oil (20w50) nanofluid are studied numerically in three dimensions to see how they affect forced convection in a porous media oil cooler. Within the oil cooler, the porous medium was placed. A two-phase mixture model was used in conjunction with the Darcy–Brinkman–Forchheimer equation indicating the drag forces to simulate nanofluid flow in porous media. In addition, utilizing temperature laboratory data, a more specific thermophysical feature of the fluid was identified and characterized. ANSYS-FLUENT, a commercial computational fluid dynamics (CFD) software, is used to partition the governing equations using the finite volume method. In addition, the thermal boundary parameters of the oil cooler walls were made to be temporally constant and spatially uniform. The effects of varying volume fractions (ranging from 0% to 5%), Darcy number (ranging from 10⁻² to 10²), overall Nusselt number, pressure reduction, and the performance evaluation criteria (PEC) were analyzed and compared for a variety of distinct nanoparticles. The increased Darcy number (10⁻² to 10²) had a significant effect on the enhanced heat transfer coefficient, according to the data. In light of the findings, it can be deduced that the high-volume percentage of the nanoparticles will improve thermal transmission and, more significantly, the PEC factor. Furthermore, the given variables were compared, leading to the creation of diagrams for different variables.

Keywords

CFD heat transfer nanofluid oil cooler porous media

Introduction

One of the most innovative technologies of the 21st century, nanotechnology is applied in a variety of industries. In the field of surface engineering, numerous hypotheses and predictions have been developed concerning the behavior of lubricants that include a variety of nanoparticles as additives. The addition of nanoparticles has been shown in several experiments to have the effect of lowering the coefficient of friction and wear.¹ One of the most significant factors contributing to mechanical components’ loss of energy, the severe erosion and early failure of machines are caused by a lack of sufficient and regular machinery lubrication, which also reduces effectiveness. In addition, the operation of the machines is uniquely influenced by the selection of the proper lubricant. On friction surfaces, lubricants form a thin layer that keeps them apart from one another and disperses heat and abrasive particles. In recent years, a significant amount of investigation has been carried out into various strategies for enhancing the lubricating capabilities of base oils. Utilizing a variety of additives, each of which possesses its own set of qualities, is one method for enhancing the physical, chemical, and mechanical characteristics of base lubricants. In this context, nanotechnology has been applied with the goal of improving and boosting the overall lubricants effectiveness. In other terms, the type and amount of additive employed in the base oil greatly influence lubricant efficiency.^2–4

When employing nanofluid media, it is possible to significantly reduce the effectiveness of thermal transmission. The thermal conductivity of nanofluid is a major factor for many various energy conversion applications, including energy storage, solar equipment, heat exchangers, radiators, nuclear reactors, automobiles, and different medical settings.^5–9 Recently, a lot of focus has also been put on hybrid convective thermal transmission. Consequently, numerical and experimental research has been substantially conducted on thermal transmission, nanofluids flow, and hybrid nanofluids flow.^8,10,11–19 Akbari et al.²⁰ used a two-phase approach to conduct a numerical investigation on the thermal transmission that occurred when CuO nanofluid was introduced into a micro-tube. They discovered that increasing the content of nanoparticles might decrease the Nusselt number and the friction factor.

By numerically computing the Navier–Stokes equations, Tahir and Mital²¹ studied the forced convection thermal transmission inside the laminar nanofluid flow of water–aluminum oxide in a channel containing a round cross-section. The Reynolds number was shown to be the most effective when compared to the effects of nanoparticles’ volume fraction, size, and Reynolds number on enhancing nanofluids’ thermal transmission. In addition, they discovered that a decline in the thermal transmission function took place as the size of the particles increased.

Al₂O₃-water nanofluid's pressure drop and thermal transmission in a tube subjected to constant heat flux were evaluated by Moshizi et al. As a consequence of the increased slip velocity along the tube walls, they discovered an improvement in the proportion of pressure gradient to thermal transmission coefficient. At the moment, a unique group of fluids has been representing exceptional thermo-physical properties (hybrid nanofluids). As prospective fluids, hybrid-nanofluids offer superior thermo-physical characteristics and thermal performance compared to the usual thermal transfer fluids.²² Numerous empirical and numerical investigations have looked into hybrid nanofluids.^23–26 Suresh et al.²⁷ investigated the thermal conductance and viscosity of a hybrid nanofluid composed of a mixture of Al₂O₃ and Cu/H₂O. They discovered that raising the volume concentrations of the nanoparticles led to improvements in the two variables in question. Aminian et al.²⁸ made a comparison between the nanofluid (water-based Al₂O₃) and the hybrid nanofluid (Al₂O₃-Cu). They found that the thermal transmission coefficient of the utilized hybrid nanofluid was significantly higher than the value obtained for the water-based Al₂O₃ nanofluid. Over the course of the past decade, a great deal of attention has been focused on the use of nanofluids in conjunction with porous medium to improve thermal transmission. Hajipour and Dehkordi²⁹ analytically and numerically demonstrated the mixed-convection entirely produced in a nanofluid flowing into a channel partially filled by a porous medium concerning the forced convection within a porous medium. They tackled the thermal energy equations and the momentum equations, respectively, by making use of a variety of viscous dissipation models and the Darcy–Brinkman–Forchheimer model.

In their study on the flow of nanofluids through a porous medium, Uphill et al.³⁰ found that nanofluids with particles smaller than 60 nm exhibited superior flow in timber. Sundar et al.³¹ explored the impacts of volume fraction and temperature on hybrid nanofluids containing multi-walled carbon nanotubes, iron oxide nanoparticles, and water-based fluid. They carried out the experiments at temperatures ranging from 20 to 60 °C. and volume fractions of more than 3%. At a temperature of 60 °C and a volume fraction of 3%, their results indicated an increase in the thermal conduction coefficient by 31%. Copper content and temperature, titanium oxide nanoparticles at 30–60 °C, and volume fractions of more than 2% were experimentally examined by Esfe et al.³² As a pure fluid, a hybrid combination of water and ethylene glycol was chosen as the best option. Under conditions of volume fraction and temperature of 2% and 60 °C, they found a 44% increase in the material's thermal conductance. Targui and Kahalerras³³ evaluated the performance of a heat exchanger of the double-pipe type filled with nanofluids and porous baffles.³³ Ganesh Kumar et al.³⁴ investigate the effects of thermal radiation on the flow and heat transfer of carbon nanotubes in a convergent and divergent channel. The rate of heat transfer in the divergent channel was higher than that in the convergent channel. Gnaneswara Reddy et al.³⁵ mathematically considered the steady and incompressible two-dimensional boundary layer flow of Rainer–Philippoff's non-Newtonian flow on a stretched surface with a porous medium. If the permeability is lower, the fluid velocity decreases, so the thickness of the hydrodynamic boundary layer decreases. Nanoparticles derived from metal oxides are the most typical type found in petroleum oils. About 26% of the nanoparticles utilized in lubricating oils are comprised of metal oxides.³⁶

Mineral oil-based cutting oils were used by Saouti et al.³⁷ to introduce SiO₂ nanoparticles and investigate their effects on wear and surface characteristics. The size of the SiO₂ nanoparticles ranges from 5 to 15 nm, and they are combined in various concentrations (0 to 1 wt%). It has been shown that the optimal concentration of 0.5 wt% SiO₂ results in the least amount of tool wear while simultaneously providing the greatest amount of improvement in surface roughness. Shear forces at opposite surfaces are increased as the concentration of nanoparticles in the material is raised to higher levels. The thermal conductivity of engine oil with varying particle concentrations was explored by Farbod et al.³⁸ for the influence of CuO nanostructure shape and concentration. CuO nanoparticles, CuO nanotubes, and medium-sized nanorods with dimensions of 61 nm, 91 nm, and 78 nm are all examples of nanostructures. With nanorods, the highest percentage improvement in thermal conductance was seen at a concentration of 6% by weight or 8.3%. The surface area of the nano additives has a role in the difference in the thermal conductivity of their various shapes. Surface area variations influence the surface layer and surface tension, resulting in a variation in heat conductance.

The impact of adjusting the content of copper nanoparticles (0.1–1 wt%) on the thermal conductance of engine oil was explored by Abroumand and Jafari Moghaddam.³⁹ The one-step process is used to prepare nano-copper, and the nanoparticles produced by this technique have a size equal to 20 nm. The engine oil's thermal conductivity and nanoparticle concentration are directly correlated, meaning that as nanoparticle concentration rises, so does oil thermal conductance. The engine's thermal conductance increases from 27% by 0.2 wt% to 49% by 1 wt% over the course of the experiment. The Brownian motion of the nanomaterials is thought to be the cause of the rise in thermal conductance seen in engine oil. CuO nanoparticles were synthesized by Agarwal et al.⁴⁰ using a wet chemical process. After preparation, the nanoparticles were combined with distilled water, ethylene glycol, and engine oil in various quantities ranging from 0.25% to 2% by volume fraction. Nanofluids are subjected to various concentrations and temperatures (ranging from 10 °C to 70 °C) to determine their thermal conductivity. There is a 19% increase in the thermal conductivity of the oil when nanoparticles are added.

In earlier investigations, it was established that an improvement in thermal transmission might be significant, whether it was brought about by a porous media, nanofluids, or both alone or in combination. Nevertheless, the forced convection in nanoparticles with base fluid engine oil flowing inside an oil cooler in a porous medium has received less attention, according to our understanding. The numerical research of incorporating Al₂O₃CuO and ZnO nanoparticles with a volume percentage of 1–5 in engine oil 20w50 in the geometry of the oil cooler (3D) was carried out in the current research. The modality with the best performance evaluation criteria (PEC) was subsequently chosen. In this instance, three different varieties of Nickel, Copper, and Aluminum metal foams were numerically simulated as porous metal foam with the Darsi number of 0.1-0.01-1-10-100. Further research is done on temperature profiles, volume fractions, pressure drops, Darcy numbers, and PEC.

Problem statement

Geometry

The geometry depicted in Figure 1 is the issue at hand in this research. $D_{o u t} = 14.7 mm$ and $D_{i n} = 14.7 mm$ represent the outer and inner diameters, respectively. $T_{w} = 300 K$ is the constant temperature of the channel walls. There is thermal equilibrium between the 38 nm-diameter nanoparticles. $T_{i n} = 390 K$ is the nanofluid's inlet temperature. The volume fraction and Darcy number ranges are $0 % \leq φ \leq 5 % and 10^{- 2} \leq D a \leq 10^{2}$ . To anticipate the behavior of the fluid and the laminar flow thermal transmission of Newtonian fluids, it was considered that the speed at the inlet was 1 m/s.

Figure 1.

Geometry of the problem under consideration.

It was anticipated that the porous media would be completely saturated with fluid (ε = 0.9). In addition, the selected fluid did not exhibit any signs of compressibility while the flow remained constant. The porous media and the working fluid maintained their thermo-physical characteristics throughout the experiment. The porous medium and working fluid achieved a local thermal equilibrium.

Mathematical formulation

The equation of mass, momentum, and energy in vector form is as follows^18,41:

\nabla . (ρ_{m} \vec{v_{m}}) = 0

(1)

\frac{ρ_{m}}{ε^{2}} [(\vec{v_{m}} . \nabla) \vec{v_{m}})] = - \nabla p + \frac{μ_{m}}{ε} \nabla^{2} \vec{v_{m}} - \frac{μ_{m} \vec{v_{m}}}{K} - \frac{ρ_{m} C_{d}}{\sqrt{K}} \vec{v_{m}} | \vec{v_{m}} |

(2)

\nabla . ((ρ C_{P})_{m} \vec{v_{m}} T) = \nabla . (k_{e f f} \nabla T)

(3)

The following are the mathematical formulations of the equations for the conservation of mass, energy, and momentum in a three-dimensional steady-state flow⁴²:

\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y} + \frac{\partial w}{\partial z} = 0

(4)

\frac{1}{ε^{2}} (u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} + w \frac{\partial u}{\partial y}) = - \frac{1}{ρ_{m}} \frac{\partial p}{\partial x} + \frac{ϑ_{m}}{ε} (\frac{\partial^{2} u}{\partial x^{2}} + \frac{\partial^{2} u}{\partial y^{2}} + \frac{\partial^{2} u}{\partial z^{2}}) - \frac{ϑ_{m} u}{K} - \frac{ϑ_{m} C_{d} | u |}{\sqrt{K}} u

(5)

\frac{1}{ε^{2}} (u \frac{\partial v}{\partial x} + v \frac{\partial v}{\partial y} + w \frac{\partial v}{\partial z}) = - \frac{1}{ρ_{m}} \frac{\partial p}{\partial y} + \frac{ϑ_{m}}{ε} (\frac{\partial^{2} v}{\partial x^{2}} + \frac{\partial^{2} v}{\partial y^{2}} + \frac{\partial^{2} v}{\partial y z^{2}}) - \frac{ϑ_{m} v}{K} - \frac{ϑ_{m} C_{d} | v |}{\sqrt{K}} v

(6)

\frac{1}{ε^{2}} (u \frac{\partial w}{\partial x} + v \frac{\partial w}{\partial y} + w \frac{\partial w}{\partial z}) = - \frac{1}{ρ_{m}} \frac{\partial p}{\partial z} + \frac{ϑ_{m}}{ε} (\frac{\partial^{2} w}{\partial x^{2}} + \frac{\partial^{2} w}{\partial y^{2}} + \frac{\partial^{2} w}{\partial z^{2}}) - \frac{ϑ_{m} w}{K} - \frac{ϑ_{m} C_{d} | w |}{\sqrt{K}} w

(7)

u \frac{\partial T}{\partial x} + v \frac{\partial T}{\partial y} + w \frac{\partial T}{\partial z} = α_{e f f} (\frac{\partial^{2} T}{\partial x^{2}} + \frac{\partial^{2} T}{\partial y^{2}} + \frac{\partial^{2} T}{\partial z^{2}})

(8)

The following equations can be expressed in dimensionless pattern^43–45:

\begin{aligned} X = \frac{x}{D_{h}}, Y = \frac{y}{D_{h}}, Z = \frac{z}{D_{h}}, U = \frac{u}{U_{i n}}, V = \frac{v}{U_{i n}}, \\ W = \frac{w}{U_{i n}}, θ = \frac{T - T_{i n}}{T_{w} - T_{i n}} \end{aligned}

\begin{aligned} α_{e f f} = \frac{k_{e f f}}{{(ρ C_{p})}_{m}}, P = \frac{p}{ρ_{f} U_{i n}^{2}}, C_{d} = \frac{1.75}{\sqrt{150} ε^{\frac{3}{2}}}, \\ T_{b} = \frac{\int_{0}^{D_{h}} u T d y}{\int_{0}^{D_{h}} u d y} \end{aligned}

(9)

\begin{aligned} R e = \frac{ρ_{f} U_{i n} D_{h}}{μ_{f}}, N u = \frac{D_{h} {(\frac{\partial T}{\partial y})}_{w a l l}}{T_{w a l l} - T_{b}}, D a = \frac{K}{D_{h}^{2}}, \\ P r = \frac{ϑ_{f}}{α_{f}} \end{aligned}

(10)

Equation (10),

N u, R e, D a,

and

P r

are Nusselt, Reynolds, Darcy, and Prandtl numbers, respectively. The following equation is used to determine the efficient thermal conductance of the fluid being applied in porous media:

k_{m} = (1 - φ) k_{f} + φ k_{n p}

(11)

k_{e f f} = (1 - ε) k_{p} + ε k_{m}

(12)

It is possible to derive the equations in a non-dimensional form by substituting non-dimensional variables into equations (4)–(8).

\frac{\partial U}{\partial X} + \frac{\partial V}{\partial Y} + \frac{\partial W}{\partial Z} = 0

(13)

\frac{1}{ε^{2}} (U \frac{\partial U}{\partial X} + V \frac{\partial U}{\partial Y} + W \frac{\partial U}{\partial Y}) = - \frac{\partial P}{\partial X} + \frac{1}{R e . ε} (\frac{\partial^{2} U}{\partial X^{2}} + \frac{\partial^{2} U}{\partial Y^{2}} + \frac{\partial^{2} U}{\partial Z^{2}}) - \frac{U}{R e D a} - \frac{ε C_{d} | U |}{\sqrt{D a}} U

(14)

\frac{1}{ε^{2}} (U \frac{\partial V}{\partial X} + V \frac{\partial V}{\partial Y} + W \frac{\partial V}{\partial Y}) = - \frac{\partial P}{\partial Y} + \frac{1}{R e . ε} (\frac{\partial^{2} V}{\partial X^{2}} + \frac{\partial^{2} V}{\partial Y^{2}} + \frac{\partial^{2} V}{\partial Z^{2}}) - \frac{V}{R e D a} - \frac{ε C_{d} | V |}{\sqrt{D a}} V

(15)

\frac{1}{ε^{2}} (U \frac{\partial W}{\partial X} + V \frac{\partial W}{\partial Y} + W \frac{\partial W}{\partial Y}) = - \frac{\partial P}{\partial Z} + \frac{1}{R e . ε} (\frac{\partial^{2} W}{\partial X^{2}} + \frac{\partial^{2} W}{\partial Y^{2}} + \frac{\partial^{2} W}{\partial Z^{2}}) - \frac{W}{R e D a} - \frac{ε C_{d} | W |}{\sqrt{D a}} W

(16)

(U \frac{\partial θ}{\partial X} + V \frac{\partial θ}{\partial Y} + W \frac{\partial θ}{\partial Z}) = - \frac{1}{R e . P r} \frac{{(ρ c_{p})}_{f}}{{(ρ c_{p})}_{m}} (\frac{\partial^{2} θ}{\partial X^{2}} + \frac{\partial^{2} θ}{\partial Y^{2}} + \frac{\partial^{2} θ}{\partial Z^{2}})

(17)

The nanofluids’ thermo-physical features

At a range of temperatures, the laboratory was able to extract the thermophysical characteristics of the base fluid used in engine oils, as well as nanoparticles containing a variety of volume fractions. The thermophysical characteristics of engine oil, nanofluid containing Al₂O₃, CuO, and ZnO are depicted in Figures 2–4, respectively. The thermophysical characteristics of the nanofluid, particularly density, viscosity, and thermal conductance, reduce as the temperature rises. The nanofluid's thermophysical characteristics, such as density, viscosity, and thermal conductivity, increase in correlation with an elevation in the nanoparticle volume fraction. The nanofluid will become less viscous and more dilute as the temperature increases. The thermal conductance of nanofluids rises with enhanced volume fraction owing to the high thermal conductance of nanoparticles.

Figure 2.

Thermophysical property of nanofluid engine oil and $C u O$ (a) thermal conductivity, (b) density, (c) specific heat capacity, and (d) viscosity.

Figure 3.

Thermophysical property of nanofluid engine oil and $A l_{2} O_{3}$ (a) thermal conductivity, (b) density, (c) specific heat capacity, and (d) viscosity.

Figure 4.

Thermophysical property of nanofluid engine oil and $Z n O$ (a) thermal conductivity, (b) density, (c) specific heat capacity, and (d) viscosity.

Boundary conditions

The oil cooler maintains a constant flow with a consistent profile at all times (300 K). When the entrance temperature is known, Equation (6) can be used to calculate the inlet velocity (1 m/s). In the thermal boundary situation for the walls, a constant temperature (390 K) was incorporated. It was anticipated that the pressure at the boundary condition output was 30 psi.

Numerical solution

As a finite volume-based computational fluid dynamics (CFD) solver, ANSYS-FLUENT was employed in the process of discretizing the equations that were presented. It was anticipated to solve the algebraic equations in an iterative manner by using the line-by-line method. To address the pressure-velocity coupling problem, the pressure-linked equations (SIMPLE) algorithm utilized the semi-implicit method. The convective and diffusive terms were expressed in the upwind and central techniques of the second order. Over the course of the convergence of the velocity field, the equation for the segregated energy was solved, derived from the equations for momentum and continuity. The fundamental variables of the momentum, energy, and pressure equations under relaxation were 0.7, 1, and 0.3, respectively. The solution's stability was preserved through the application of these parameters. The momentum conservation, the energy, and the mass equations all had their divergence criteria set at 10⁻⁶.

Grid sensitivity analysis

The development of the grid is one of the more important steps of the simulation technique. It has an effect on the convergence as well as the amount of time and the solution. These characteristics are more susceptible to change when applied to a regular gridding pattern as opposed to an irregular one. It is important to note that sufficiently fine grids are required to resolve the steep gradient in the physical characteristics located adjacent to the wall grids. The thermal transmission coefficient for each of the five distinct meshes is displayed in Figure 5. From mesh 4 onwards and beyond, the error decreases to less than 1% as the number of cells grows. The proper number of numerical flaws and the suitable number of grids for calculating the Nusselt number are among the parameters taken into consideration in this study as part of the investigation into the number of grids (Table 1). A Newtonian fluid (engine oil) and a solid nanoparticle with a diameter of dp = 38 nm are both taken into consideration when analyzing grid independence in Table 1. The error for the Nusselt number is proportionate to the additional accurate answers (number of cells 3,200,000) when considering the grid independence. Fewer cells would be needed with a <1% error, requiring less computing power and memory.

Figure 5.

Graph of the heat transfer coefficient against the number of cells.

Table 1.

Grid-independence for this study.

Number of cells	Heat transfer coefficient $W / m^{2} . K$
$800, 000$	$408.26$
$1, 600, 000$	$502.85$
$2, 400, 000$	$550.34$
$3, 200, 000 (M a i n g r i d)$	$578.75$
$4, 000, 000$	$578.46$

Model validation

After running the simulation, the next step was to determine the converged mesh configuration and then apply the boundary situations and nanofluid equations provided by the software. The validity of the proposed scheme was evaluated by contrasting the simulation findings with the values obtained through experimentation. The findings were evaluated in light of the findings presented by Akhavan-Behabadi et al.⁴³ With a steady heat flux of 5 KW/m², these empirical findings are based on engine oil 20w50 in a tube. The adequate consistency between current and Akhavan-Behabadi et al. data demonstrate that the present model's projections are precise within the range of employed variables, as can be seen in Figure 6.

Figure 6.

Validating the present numerical solution with the results of Akhavan-Behabadi et al.⁴⁶

Result and discussion

To assess the enhanced thermal transmission characteristics and ideal fluid flow conditions, the impacts of incorporating nanoparticles into the base design are evaluated based on the pressure drop, Nusselt number, PEC, and volume fraction. After determining the optimum model for a porous metal foam, including a variety of Darcy and Nickel alloys, Copper and Aluminum are incorporated into the foam, and a simulation is run.

The impacts of volume fraction and porous media on heat transfer

The diagram of the total Nusselt number (Nu) versus the kind of nanoparticles in different volume fractions is shown in Figure 7(a). The effects of three distinct nanoparticles in the base engine oil (20w50) in volume fractions of $0 % \leq φ \leq 5 %$ are depicted here: Al₂O₃, CuO, and ZnO.

Figure 7.

Total Nusselt number versus the type of nanoparticles for different volume fraction (a) and total Nusselt number versus porous kind of media for different Darcy number $A l_{2} O_{3} φ = 5 %$ . (a) The impacts of volume fraction, (b) the impact Darcy number on optimum case (a).

The Al₂O₃ nanoparticles with a volume fraction of 5% have the highest possible Nusselt number. The rate of improvement is 20% when compared to the base engine oil. In Figure 4(b), the impacts of the porous medium containing Aluminum, Copper, and Nickel materials in varied Darcy numbers are explored in the ideal situation (a). Permeability diminishes when Darcy's number drops, as shown in Figure 7(b). In this condition, thermal transmission increases. The effect of the total Nusselt number on the volume fraction of nanoparticles was also investigated, as shown in Figure 4. The convection thermal transmission coefficient is significantly influenced favorably by the thermal transmission coefficient of increments for greater nanoparticle concentrations. It is important to keep in mind that reduced permeability results in a more concentrated fluid toward the walls. Enhanced velocity gradient and higher thermal transmission are additional effects of this phenomenon. Furthermore, the thermal conductivity coefficient increases noticeably once the nanoparticles have been incorporated into the base fluid and the volume fraction has been increased.

The impacts of volume fraction and porous media on pressure drop

The influence of the volume fraction of the nanoparticles and the type of nanoparticles on the pressure drop is illustrated in Figure 8(a). When the volume fraction was increased from 1% to 5%, there was a discernible upward trend detected for the pressure drop. This was because there was a greater amount of viscosity. In addition, $φ = 5 %$ corresponded to the maximum pressure drop value for nanoparticle type, as seen in Figure 8(a).

Figure 8.

Pressure drop versus the type of nanoparticles for different volume fractions (a) and pressure drop versus porous media for different Darcy numbers ( $A l_{2} O_{3}, φ = 5 %$ ).

The influence of Darcy number and porous metal foam on pressure drop was explored in Figure 8(b). The minimum Darcy number resulted in the greatest drop in pressure. This is due to the limited permeability and the fluid's subsequent confinement.

The impacts of volume fraction and porous media on the performance evaluation and criteria

At a certain nanoparticle concentration, the dimensionless variable ( $N u / N u_{b}$ ) indicates the proportion of the Nusselt number regarded to the Nusselt number used for the nominal configuration when the Reynolds number is identical. The addition of nanoparticles to the base fluid results in an increase in the rate of thermal transmission. On the other hand, the pressure drop is enhanced, which results in an increase in the amount of power consumed. The performance evaluation criterion (PEC) variable can be determined by using pressure drop and the proportion of the Nusselt numbers for an improved physical explanation as follows¹¹:

P E C = \frac{N u / N u_{b}}{Δ P / Δ P_{b}^{1 / 3}},

(18)

Where PEC is enhanced by raising the Nusselt number, and also PEC is decreased by enhancing the pressure decline. In Supplementary Figure 9(a), the PEC values were determined for different volume fractions ranging from 0% to 5% as a function of the type of nanoparticles. In Supplementary Figure 9(b), a type of porous metal foam with various permeability was incorporated for the maximal PEC form of Supplementary Figure 9(a). The porous metal foam made of copper, with a Da = 100, has the greatest PEC value (38.24).

Temperature contours

The temperature profiles with and without the inclusion of solid particles—Al₂O₃CuO and ZnO (φ = 5%) to the engine oil (20w50) are depicted in Supplementary Figure 10(a–d), respectively. As shown in Supplementary Figure 10, the utilization of the nanofluid resulted in an improvement in thermal transmission. On the other hand, because there are no porous media present, there are reduced fluctuations in temperature and negligible thermal efficiency.

Conclusion

To promote forced convection in an oil cooler, engine oil (20w50) containing three nanoparticles (Al₂O₃, CuO, and ZnO) was numerically applied. After selecting the optimal case, porous metal foam exhibited $10^{- 2} \leq D a \leq 10^{2}$ . Additionally, the behavior of three distinct materials was modeled. The temperature encountered by the oil cooler was consistent and unchanging. To describe the fluid flow in the porous medium, the Darcy–Brinkman–Forchheimer formulation, along with a two-phase method, was used to simulate the nanofluid flow. To solve the governing equations and investigate the effect of various key variables (including volume fraction and Darcy number) on the thermal transmission and pressure decline, a CFD code based on the finite volume approach was utilized. In addition, to conduct additional research on the thermal performance of systems, PEC were presented as a novel variable in this investigation. The following conclusions can be drawn:

Enhancing the volume fraction of nanoparticles to oil results in a 20% increase in thermal transmission. The optimal state is for $φ = 5 %, A l_{2} O_{3}$ .

Enhancing the volume fraction increases the pressure decline. The increase in pressure declines for ( $A l_{2} O_{3}$ , $C u O$ , and $Z n O$ ) is 38%, 48%, and 46%, respectively.

Reducing the Darcy number from 100 to 0.01 decreases the permeability. The pressure decline enhances by 84%. The thermal transmission coefficient enhances by 2%.

Increasing the volume fraction of oil increases PEC. The maximum effect is 8%, 5%, and 6% for $A l_{2} O_{3} C u O$ and $Z n O$ , respectively.

Increasing the Darcy number increases PEC. The most PEC-containing porous metal foams are Copper, Aluminum, and Nickel.

The thermal transmission coefficient and total Nusselt number could be enhanced by incorporating the metal nanoparticles into the base fluid.

Supplemental Material

sj-docx-1-pie-10.1177_09544089221143895 - Supplemental material for Numerical investigation on forced convection enhancement within an oil cooler through the simultaneous use of porous media and nanofluid

Supplemental material, sj-docx-1-pie-10.1177_09544089221143895 for Numerical investigation on forced convection enhancement within an oil cooler through the simultaneous use of porous media and nanofluid by Mohamad Sedighi, Ahmadreza Ayoobi and Ehsan Aminian in Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Ahmadreza Ayoobi

Ehsan Aminian

Supplemental material

Supplemental material for this article is available online.

Nomenclature

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