Numerical analysis of mono and hybrid nanofluids-cooled micro finned heat sink for electronics cooling-(Part-I)

This study explores the thermohydraulic performance of metallic-oxide and carbon-additives-based mono and hybrid nanofluids-cooled micro pin-fin heat sink by adopting the multiphase Eulerian model. The circular configuration is adopted for micro pin-fins, with the staggered arrangement and constant heat flux applied at the base of the heat sink. The mono and hybrid nanofluids are based on an aqueous solution of Ag, MgO, GNP, MWCNT, Ag-MgO, and GNP-MWCNT mono and hybrid nanoparticles, and a pressure drop ( Δ p ) range is applied across the heat sink. The heat transfer and fluid flow performance are evaluated in terms of temperature difference ( Δ T ), thermal resistance ( R th ) of the heat sink, average heat transfer coefficient ( h avg ), average Nusselt number ( Nu avg ), pumping power ( PP ), overall performance ( OP ), and performance evaluation criteria ( PEC ), whereas the velocity, temperature, pressure coefficient, and flow streamline contours present the qualitative depiction of flow distributions across the heat sink. The results revealed that under certain Δ p conditions, the GNP dispersed mono nanofluid showed the highest thermal performance of the micro pin-fin heat sink compared to the water as a coolant. The optimal nanoparticle loading ( φ ) is found between 0.50 % and 0.75 % of GNP nanoparticles. The maximum enhancement in PEC is achieved at 60 % for φ of 0.50 % and 0.75 % for both Δ p of 1120 Pa and 1470 Pa, respectively. At an optimum Δ p , the higher average h avg , Nu avg , and lower R th are achieved.


Introduction
The rapid advancement of the electronics industry is increasingly challenged by overheating issues, particularly due to the compactness of modern circuitry.This miniaturization trend leads to higher heat generation within limited spaces, posing significant challenges to thermal management.Data centres, a critical component of the global digital infrastructure, consume approximately 1.31 % of global electricity, with a substantial 33 % dedicated to cooling systems [1].The operational reliability of integrated circuits (ICs) is notably affected by temperature, as a mere 2 • C increase can reduce their reliability by 10 %.Overheating is a major cause of electronic component failure, accounting for 55 % of such incidents, while other factors like vibration, humidity, and dust contribute to the remaining 45 % [2].Traditional cooling methods often struggle to meet advanced thermal management demands, partly due to the use of coolants with inherently low thermal conductivity.Additionally, the effectiveness of these cooling methods is influenced by the geometric configuration and operating parameters.
In response, a variety of innovative cooling strategies have been explored in recent research.These include optimizing heat sink geometry [3,4] employing advanced coolants such as metal-based nanofluids [5][6][7], carbon-additives based nanofluids [8,9], supercritical CO 2 [10,11], and hybrid nanofluids [12,13].These approaches are driven by the need for cooling technologies that offer superior thermal conductivity and convective heat transfer rates to keep pace with the demanding thermal requirements of high-tech electronics.Nanofluids, particularly those combining metal or carbon nanoparticles with conventional fluids, demonstrate enhanced thermal properties.These fluids boast a high surface-to-volume ratio and an increased solid-liquid interface, which can lead to improved interphase heat exchange [14,15].However, it is important to note that achieving excellent suspension stability remains a significant challenge in many applications of nanofluids, potentially limiting their effectiveness.Recent advancements in heat sink technology focus on the use of pin-fins and nanofluids for enhanced cooling.The below review presents a detailed analysis of recent studies, each offering unique insights into heat sink design and optimization.
Yan et al. [16] employed numerical simulations to analyze alumina/water nanofluid flow in heat sinks with pin-fins.Key findings include the reduction of maximum and average heat sink temperatures with increased Reynolds number, lower outlet temperature, and higher pressure drop.Square pin-fins were found to generate more entropy compared to rhombic pin-fins.Dey et al. [13] focused on the cooling performance of Highly Concentrating Photovoltaic/Thermal (HCPV/T) systems using nanofluids and pin-finned heat sinks.Significant temperature reduction in solar cells was achieved using MWCNT nanofluid, with staggered arrangements of pin-fins showing higher heat transfer characteristics.The study highlighted the influence of MWCNT volume concentration and pin-fin arrangements on thermal performance.Ambreen et al. [17] conducted a numerical research by employing the circular pin-fin heat sink with Al 2 O 3 dispersed aqueous nanofluid with volume fraction from 0 % to 1 % as a coolant.They studied the heat and flow dynamics of nanofluid at varying operating conditions for cooling of for the purpose of thermal management.Their study concluded that with the addition of Al 2 O 3 into water demonstrated an enhancement of 16 % in average heat transfer coefficient.In another study [18], they explored the effects of hybrid nanoparticles of Cu and Al 2 O 3 into water with volume of 1 % flowing through the diamond, circular and elliptical configured pin-fin heat sinks.They found that average Nusselt number was enhanced of 19.65 %, 24 %, and 25.14 % for circular, elliptical, and diamond fins, respectively.Shahsavar et al. [19] studied the fluid position of a single-phase flow at inlet and outlet of a micro pin-fin heat sink numerically at Reynolds number range of 500 to 2000.They found that input and output at opposite side along the longitudinal length gave the higher performance evaluation criteria value of 1.131.Similarly, Shahsavar et al. [20] numerically investigated the effect of perforation angle of perforated pin-fin heat sink under single-phase flow at various Reynolds numbers of 500-2000.They found the highest performance evaluation criteria of 11.06 % to 16.63 % with perforation angle of 45 • compared to the 0 • Wang and Hai [21] conducted research on optimizing the performance of pin-fin heat sinks with splitters, using water and water-Al 2 O 3 nanofluids as coolants.Their study focused on improving the hydrothermal performance of heat sinks, which is essential for cooling CPU systems.The introduction of splitters increased the heat transfer surface area and improved fluid mixing, leading to enhanced heat transfer efficiency.Furthermore, the use of nanofluids boosted thermal conductivity, contributing to more effective heat dissipation.These modifications resulted in a significant reduction in CPU temperatures, thereby improving the overall performance of the cooling system.
In another study, Shahsvar et al. [22] conducted an investigation on analyzing thermal and frictional irreversibility in heatsinks and the use of splitters in heat sinks, but with variations in coolant types or heat sink configurations.They highlighted different aspects of splitter technology, focusing on different operational conditions or electronic devices, offering a broader perspective on the application of this technology.Their methodology included a combination of computational fluid dynamics simulations and experimental tests, similar to Wang and Hai [21], but with a focus on different performance metrics such as pressure drop and flow turbulence.Both studies underscored the value of splitters in enhancing heat transfer efficiencies.However, differences emerged in terms of the types of coolants used, the specific applications targeted, and the detailed outcomes related to thermal and fluid dynamics.For example, Shahsvar et al. used synthetic coolants targeting applications like automotive cooling systems, in contrast to Wang and Hai's use of water-based nanofluids for CPU cooling.Ahsaee et al. [23] investigated the effect of ultrasound waves on pin-fin heat sinks, revealing that certain configurations can significantly reduce thermal entropy generation while increasing frictional entropy generation.In another study, Ahsaee et al. [24] investigated the effect of inlet velocity profiles on a pin-fin heat sink.Results indicated that non-uniform velocity profiles offer better hydrothermal performance and lower frictional entropy generation compared to uniform profiles.
Zhu et al. [25] designed and simulated a circular heat sink with cylindrical pin-fins, studying the effects of pin-fin dimensions and inlet velocity profiles on heat transfer characteristics.Haque et al. [26] conducted a numerical analysis of water/silver nanofluid flow in a perforated pin-fin heat sink, focusing on the impact of perforation inclination angles on heat transfer and entropy generation.Haghighi et al. [27] carried out an experimental investigation exploring the forced convection heat transfer performance of different Plate Pin-Fin Heat Sink (PPFHS) models with varying fin-pin spacing using air as the coolant.The study found that optimal fin-pin spacing enhances heat transfer efficiency and airflow management, with empirical correlations developed to predict performance.Heatsinks with conical pins and 7-fin configurations exhibited the best thermal performance.These findings are crucial for designing efficient PPFHS heatsinks, emphasizing the importance of fin-pin spacing in thermal management systems.Wang et al. [28] conducted an experimental investigation comparing forced convection heat transfer across different heat sink models, identifying optimal fin-pin spacing and heat sink configurations.Liu et al. [29] investigated flow and heat transfer of nanofluid in pin-fin heat sinks, assessing the impact of Reynolds number, nanoparticle concentration, and splitters on entropy generation and heat dissipation.Harris et al. [30] conducted a numerical analysis of biomorphic pin-fin heat sinks and studied the heat transfer and flow characteristics under Reynolds number 5500-13,500.They found that plain hexagon top design pin-fin revealed the higher heat transfer coefficient and Nusselt number.This novel design enhanced the heat transfer performance 1.5 to 1.7 times compared to the rectangular and square fin designs.
The reviewed studies collectively enhance the understanding of heat sink design and optimization.The reviewed studies can be categorized based on the type of coolant used, heat sink geometry, and optimization methods as listed in Table 1.Studies using water/synthetic coolants, such as those by Shahsavari et al. [22], found that arched splitters minimize entropy generation.Research utilizing silver/water nanofluids, like that by Shahsavari et al. [22] and Ghazizade-Ahsaee et al. [24], revealed that perforations and varying inlet velocities can improve heat transfer.Studies with nanofluids, including work by Dey et al. [13], Haque et al. [26], and Wang et al. [28], demonstrated enhanced cooling performance with different geometries, such as pin fins and elliptical fins.Hai et al.'s [31] research on Fe 3 O 4 ferrofluid showed that magnetic fields can further improve cooling efficiency.In terms of geometry, pin fin designs were widely used and optimized across several studies, while elliptical and circular fins, explored by Haque et al. [26] and Zhu et al. [25] respectively, offered high thermal performance.Optimization methods varied, with numerical techniques used in most studies, showing significant improvements in thermal efficiency.AI-based approaches, highlighted by Yan et al. [16], Zhu et al. [25], and Liu et al. [29], were particularly effective in reducing maximum temperatures and identifying key factors influencing thermal efficiency.Overall, both numerical and AI-based optimization methods have proven to significantly enhance heatsink performance.Following pints were deducted from the above-mentioned studies.
Key insights include.
• Reynolds Number and Flow Rate: Higher Reynolds numbers and flow rates generally lead to lower heat sink temperatures but increase pressure drops.• Pin-Fin Geometry: Square pin-fins often generate more entropy than rhombic pin-fins, and specific shapes like elliptical pin-fins can significantly enhance hydro-thermal performance.• Nanofluids and Magnetic Fields: The use of nanofluids, particularly MWCNT and alumina/water, significantly improves cooling performance.Magnetic fields further enhance this effect, especially in microchannel heat sinks with ferrofluid.• Inlet Velocity Profiles: Non-uniform velocity profiles yield better hydrothermal performance and lower frictional entropy generation compared to uniform profiles.• Ultrasound Waves and Splitters: The application of ultrasound waves and the use of splitters in heat sinks can optimize heat transfer and reduce entropy generation.
Hence the literature review demonstrates the effectiveness of various strategies in enhancing heat sink performance.Future research should continue exploring innovative materials, geometries, and external influences like magnetic fields and ultrasound waves to further improve cooling systems in diverse applications.However, the use of nanofluids, especially hybrid variants, in conjunction with micro pin-fin heat sinks has been explored by only a few researchers [32][33][34].In this context, the current study delves into the thermohydraulic performance of mono and hybrid nanofluids in an aqueous solution, circulating through a micro pin-fin heat sink with a circular configuration.It focuses on various pressure drop (Δp) ranges, employing a multiphase Eulerian model for numerical analysis with a constant and varying volume fraction.It also provides valuable insights into the design and optimization of heat sink systems, highlighting the potential of various pin-fin configurations and nanofluids to enhance cooling efficiency in modern electronic applications.

Problem description and numerical formulation
An aluminum-made and circular geometry of micro pin-fins heat sink with the staggered arrangement was modelled, as shown in Fig. 1.A constant heat flux ( q˙) of 300 kW/m 2 was applied at circular micro pinfins (CMPFs) heat sink base and Δp was varied in the range of 570 Pa ≤ Δp ≤ 2760 Pa.The detailed dimensions of used CMPFs heat sink are mentioned in Table 2.The mono and hybrid nanoparticles of Ag, MgO, GNP, MWCNT, Ag-MgO, and GNP-MWCNT of volume fraction (φ) of 1.0 % were considered with water and later varying φ of 0 %, 0.25 %, 0.50 %, 0.75 %, and 1.0 % of GNP nanoparticles were further investigated as mono nanofluid.The multiphase Eulerian approach is considered under laminar, steady-state, and incompressible flow conditions.The continuity, momentum, and energy equations for p th phases and mixture quantities are defined as follows: Mixture continuity: Mixture conservation of momentum: The shear stress tensor, velocity, and volume fraction in the above equation are denoted by τ m , V → m , and α respectively.V → km is the drift velocity and can be estimated using the Eq. ( 3).
The drift velocity can then be utilized to estimate the mixture velocity and density using Eqs.( 4) and (5), respectively.
The relative/slip velocity can relate to drift velocity using Eq. ( 6), this equation is valid for the flow field of a two-component fluid but can be extended for the higher number phases.
α c and ρ c are the volume fraction and fluid density for the continuous phase or the primary phase which is water in the present case.To complete the mixture model, constitutive equations are needed, and then the slip velocity can be obtained with the help of an algebraic equation defined by Manninen et al. [35].
The drag coefficient (C D ) can be utilized to evaluate the drag function (in Eq. ( 7)) using Eq. ( 8) [36].The particle-particle interaction is neglected in the study which is why the agglomeration and collation of nanoparticles is not considered.These interactions are important when conducting the molecular dynamics simulation [37,38].
Mixture conservation of energy: Eq. ( 9) presents the energy conservation equation of the mixture.

∇⋅
( The heat flux due to conduction and the mixture enthalpy are denoted by q m and H m .The volume fraction equation can be used to estimate the particle distribution in the primary phase, the continuity derived for the particle phase using a constant density method can be used as mentioned in Eq. (10).
The relative velocity between fluid phase and particle phase can be Fig. 1.Schematic heat sink with boundary conditions.
) , the fluid density, particle diameter and viscosity are denoted by ρ c , d p , and µ c , respectively.The thermophysical properties of the base fluid and nanoparticles used in the current study are listed in Table 3.
Steady-state 3D Eulerian-Eulerian multiphase simulations were conducted, the schematic diagram of the computational domain is shown in Fig. 1 [37,38].The present conjugate heat transfer problem has been simulated using the Finite Volume Method (FVM) by utilizing commercial software (Ansys-FLUENT).The coupling of pressure and velocity has been estimated using the coupled scheme.The pressure terms have been discretized using the standard scheme, while the interpolation of the remaining parameters has been carried out using the second-order upwind scheme.The total mass of the injected particles (secondary phase) has been calculated considering the Reynolds number, viscosity, density, and nanoparticle volume fraction of the nanofluid.The velocity and temperature of the nanoparticles are assumed to be equivalent to the base fluid.To reduce the maximum mass residuals of the grid control volume, the convergence criteria for all parameters (continuity, momentum, energy) have been restricted to 10 -05 [40].The heat sink base is exposed to constant heat flux, the pressure inlet boundary condition is applied at the inlet of the heat sink, and the pressure outlet is defined at the outlet of the heat sink.All walls, except for the interfaces, have been treated as adiabatic, and a no-slip boundary condition has been imposed.The inlet fluid temperature is considered as the ambient temperature, and the outlet pressure is considered as the ambient pressure.The escape boundary condition has been implemented for the discrete phase at the heat sink inlet and outlet, while the walls of the heat sink have been assigned the reflect boundary condition.
Where, Δp and Q represent the pressure drop across the test section and volumetric flow rate, respectively.A grid convergence study is conducted before obtaining any results and validated by utilising a Grid Convergence Index (GCI) method [43].Later, results were validated against the single-phase benchmark numerical [17] and experimental data [44], as shown in Fig. 2. It can be seen that the flow rate across the pressure drop gives quite accurate values, but some deviation can be observed for the thermal resistance of the heat sink with respect to the pressure drop but still with an acceptable limit.The trend quite matches that thermal resistance decreases with an increase in pressure drop.

Results and discussion
This section discusses the results of CMPFs heat sink cooled with mono and hybrid nanofluids based on metallic-oxide and carbon additives nanoparticles under different Δp across the inlet and outlet.Fig. 3a represents the variations of thermal resistance (R th ) in case of water and nanofluids under different Δp conditions as result of augmented flow velocity.A decreasing trend in R th is observed with the increase of Δp for all flowing fluids through the heat sink which means a uniform heat transfer occurs along with mild heat sink temperature.The higher decrease in R th is obtained in case of mono Ag and GNP nanoparticles dispersed nanofluids in comparison of their respective hybrid nanoparticles (i.e., Ag-MgO or GNP-MWCNT) based nanofluids.Along with that, Fig. 3a shows the carbon additives (GNP, MWCNT and GNP-MWCNT) dispersed mono and hybrid nanofluids have lower R th in comparison to metallic-oxide (Ag, MgO and Ag-MgO) dispersed nanofluids because of higher thermal conductivity of carbon additives.The decrease in the case of Ag and GNP nanoparticles dispersed mono nanofluids in R th is 25.20 % and 40.71 %, respectively, at Δp of 570 Pa compared to the water-cooled CMPFs heat sink.Similarly, a decrease of 30.74 % and 44.26 % in R th is obtained in case the of Ag and GNP nanoparticles dispersed mono nanofluids at Δp of 2760 Pa compared to the water-cooled CMPFs heat sink which is because of increasing fluid velocity.
Contrarily to the R th , an increasing trend was obtained in average Nusselt number (Nu avg ) with the increase of Δp because of enhanced heat transfer rate at higher flow velocity, shown in Fig. 3b.The higher Nu avg shows that there is a higher heat transfer rate with higher convective heat transfer coefficient with the variation of Δp.The increase in Nu avg is higher in case of GNP dispersed mono nanofluid follow on GNP-MWCNT, MWCNT, Ag, Ag-MgO and MgO dispersed nanofluids.Again, it is revealed that the nanoparticles which exhibit higher thermal conductivity such as GNP, MWCNT, Ag and MgO show the higher Nu avg .The enhancement in Nu avg is achieved of 45.06 % and 54.26 % at Δp of 570 Pa and 2760 Pa, respectively, in case of GNP dispersed mono nanofluid compared to the water cooled CMPFs heat sink.The lesser enhancement in Nu avg is obtained with GNP-MWCNT and followed on MWCNT based hybrid and mono nanofluids, respectively, against each Δp in case of carbon additives nanoparticles.Similarly, in case of Ag, MgO and Ag-MgO based mono and hybrid nanoparticles, the higher increase in Nu avg of 15.62 % and 24.23 % is obtained at Δp of 570 Pa and 2760 Pa, respectively, in case of Ag dispersed mono nanofluid compared to the water cooled CMPFs heat sink.It is revealed from Fig. 3a and b that the combination of hybrid nanoparticles of Ag-MgO and GNP-MWCNT show the higher R th and lower Nu avg of because of the addition of MgO and MWCNT which have the lower thermal conductivity compared to GNP and Ag, keeping a constant volume fraction.
The results of volumetric flow rate (Q) of water, mono, and hybrid nanofluids flowing through the heat sink as a function of Δp is shown in

Table 3
Thermophysical properties of base fluid and nanoparticles [20,[39][40][41].Fig. 3c.The higher Q is achieved with the increase of Δp because of the increase in velocity which reveals the same trend reported experimental studies [44].At lower Δp, there is no significant variation in Q for both in mono and hybrid nanofluids cases flowing through the CMPFs heat sink.The maximum decrease of 2 % in case of Ag nanoparticles dispersed mono nanofluid compared to the water-cooled heat sink.The slight variation in Q of nanofluids is because of highly fluid viscosity which causes the higher flow resistance and slight shear thickening effects by the suspension of nanoparticles.
The similar increasing trend in pumping power (PP) as a function of Δp in cases of all mono and hybrid nanofluids.The dispersion of nanoparticles increases the viscosity of nanofluids which is associated with the shear thickening effect.The slight variation of 1.87 % at Δp = 1470 Pa is obtained in case of MWCNT dispersed mono nanofluids in comparison with water cooled heat sink.The amplified viscosity of nanofluids certainly requires higher pumping power to achieve the higher flow velocity for enhanced heat transfer rate resulting in a higher cost.
The overall performance (OP) of CMPFs heat sink cooled with water, mono, and hybrid nanofluids is represented in Fig. 3d.The OP is evaluated based on supplied input power ( Q˙) and required pumping power (PP) to circular the coolant, which act simultaneously to draw the comprehensive performance of heat sink under different coolants.Since, the OP parameter considers both parameters because it is the ratio of heat transfer to PP.It is revealed that there is no significant difference observed in OP comparing all mono and hybrid nanofluids, as shown in Fig. 3e.The decrease in OP with the increase of Δp is observed because of the increase of PP, as shown in Fig. 3d.The slight variation in OP of 1.95 % is achieved in case of Ag dispersed nanoparticles which is because of individual thermophysical properties since the volume fraction of both mono and hybrid nanoparticles is constant.Furthermore, heating power for all case is constant, therefore the OP is higher at lower Δp or lower fluid flow velocity which requires lower PP.Further, the hydraulic thermal performance of CMPFs heat sink cooled with mono and hybrid nanofluids is analyzed using performance evaluation criteria  (PEC) which is the ratio heat transfer enhancement to pressure drop.The PEC simultaneously evaluates the effect of two parameters Nusselt number (positive parameter) and pressure drop (negative parameter).The results of PEC as a function of Δp are shown in Fig. 1f for all mono and hybrid nanofluids used as coolant flowing through the CMPFs heat sink by keeping the water as a reference coolant.The higher value of PEC is observed in the case of nanofluids, and the highest enhancement of 57 % and 56 % is obtained at Δp of 1120 Pa and 2280 Pa, respectively, in case of GNP nanoparticles dispersed mono nanofluid compared to the water-cooled CMPFs heat sink.In the case MgO nanoparticles dispersed mono nanofluid, the PEC is less than unity at lower Δp = 570 Pa or inlet velocity flow rate because of slightly lower heat transfer and high pumping power.
The results shown in Fig. 3, reveal that there is not a huge significance in hydraulic thermal performance of mono and hybrid nanofluid having constant volume fraction flowing through the CMPFs heat sink at varying Δp.The results of R th , Nu avg , and PEC reveal that GNP dispersed mono nanofluid has the lowest thermal resistance, higher convective heat transfer performance exhibiting highest Nu avg and optimum PP.Furthermore, it is suggested to flow the nanofluids at lower PP resulting in lower flow velocity.
Further the hydraulic thermal performance is explored by considering only GNP dispersed mono nanofluid by varying the volume fraction (φ) from 0 % to 1 % of GNP because GNP-based mono nanofluid exhibited the better cooling performance among other mono and hybrid nanoparticles at varying Δp across the inlet and outlet.It can be seen from Fig. 4a that with the increase of GNP volume fraction, the R th decreases, as expected.The decrease in thermal resistance (R th ) is achieved of 32.82 %, 37.0 %, 39.25%, and 41.0 % at φ of 0.25 %, 0.50 %, 0.75 %, and 1.0 %, respectively, at Δp = 570 Pa.In a similar manner, the reduction of 37.1 %, 41.22 %, 43.24 %, and 45.27 % at φ = 0.25 %, 0.50 %, 0.75 %, and 1.0 %, respectively, is achieved in R th at Δp = 2760 Pa.
The heat transfer enhancement in terms of average Nusselt number (Nu avg ) as a function of Δp is presented in Fig. 4b for all cases of φ.The Nu avg increases with the increase of φ which shows that addition of nanoparticles augments the heat transfer.Apart from the higher thermal conductivity of nanoparticles, there are some other factors such as thermal-viscous boundary layer, specific heat transfer enhancement mechanisms, Brownian motion of nanoparticles, thermophoresis and molecular interactions of two different types of nanoparticles in the case of hybrid nanoparticles dispersed hybrid nanofluids with base fluid [37,40] which are not considered and captured in this study.
The increasing trend in volumetric flow rate (Q) and pumping power (PP) is obtained by changing the Δp from 570 Pa to 2760 Pa, as shown in Fig. 4c and Fig. 4d, respectively.Moreover, there is no significant variations observed with the change of φ from 0 % to 1 % of GNP nanoparticles.The maximum enhancement in Q and PP is obtained at 1.15 % and 1.05 %, respectively, at φ = 0.25 % and Δp = 1470 Pa compared to the φ = 0 %.However, there is no significant enhancement in Q and PP observed by the addition of more quantity of nanoparticles.
The combined effect of supplied input power ( Q˙) and pumping power (PP) is illustrated in Fig. 4e in terms of overall performance (OP) as a function of Δp and it can be seen that OP decreases exponentially with the increase of Δp as a consequence of higher PP at a constant Q˙.Similar to Q and PP, there is no significant variation observed in OP of varying φ.A maximum decrease of 1.24 % is achieved atΔp = 1120 Pa and φ = 1.0 % compared to the φ = 0 %.
The comparison of performance evaluation criteria (PEC) of all selected φ of GNP nanoparticles dispersed mono nanofluid cooled CMPFs heat sink is presented in Fig. 4f.It is revealed that the PEC increases from φ = 0.25 % to 0.75 %, however it decreases at 1.0 % especially at lower pressure boundary conditions or velocity flow rates.The maximum enhancement in PEC is achieved of 60 % for φ of 0.  5a and Fb that flow field in both cases are very much similar which is also reflected from the quantitative results of pumping power and volumetric flow rate, shown in Fig. 3c and Fig. 3d, respectively.In both cases, higher velocities exhibit in the inlet header side, with noticeable recirculation zones and flow separations near the inlet, indicating inefficient flow distribution.The streamlines of both coolants show complex and turbulent flow patterns with prominent recirculation zones and vortices, accelerating effective heat transfer depending on the type of coolant, i.e. water or GNP nanofluid, in present study.These observations validate the findings from Fig. 2, where accurate flow rate predictions and acceptable thermal resistance values were reported for varying pressure drops.Fig. 6 illustrates the temperature distribution across the x-y and x-z planes for both water-cooled and GNP nanofluid-cooled, having φ of 1.0 % of GNP nanoparticles, CMPFs heat sinks at a Δp of 570 Pa.The temperature gradient is highest from the upstream to the downstream.The temperature zone is high downstream as nanofluid flows through the fins which illustrates the optimal heat transfer.Similarly, the temperature gradient change from the bottom to the top of the heat sink.The temperature gradient is higher at the bottom of the heat sink and around the fins, increasing from the upstream to the downstream.The temperature gradient across the heat sink surface is noticeably lower, due to the reduced temperature range, in case of GNP nanofluid-cooled heat sink, indicating enhanced heat transfer capabilities due to the higher thermal conductivity of the GNP nanoparticles.Whereas, in case of water-cooled heat sink exhibits high-temperature localization at the fins, indicating lower heat transfer values.This enhanced heat transfer is supported by Fig. 3a, which shows a significant reduction in thermal resistance (R th ) for the GNP nanofluid compared to water, and by Fig. 3b, which depicts a higher avergage Nusselt number (Nu avg ) for the nanofluid.The enhancment in heat transfer is expected that GNP-nanofluid can maintain the fins and the heated base at a lower temperature, which is noticeable in the Fig. 6b.The performance evaluation criterion (PEC) results, shown in Fig. 3f, further quantifies the superior cooling performance of the GNP nanofluid under varying Δp.The augmentation of heat transfer is higher when compared to the water-cooled because of the dispersion of nanoparticles, which exhibit the enhanced surface area with the interaction between particle-particle and particle-liquid phases [37,40,[45][46][47].
A qualitative analysis of temperature field and velocity streamlines flow field cumulatively is illustrated in Fig. 7 as an isometic view of CMPFs heat sink for (a) water-cooled and (b) GNP nanofluid-cooled, having φ of 1.0 % of GNP nanoparticles at Δp = 570 Pa.The threedimensional view of both cases reflects the real-time picutre of flow regime and temperature distribution across the heat sink sufraces with effect of water and GNP dispersed nanofluid as coolants.The comparison between water-cooled and GNP nanofluid-cooled CMPFs heat sink highlights the superior cooling performance of the GNP nanofluid in terms of reduced temperature distribution.This uniform temperature distribution, indicating efficient heat dissipation, is because of higher thermal conductivity exhibiting GNP nanofluid with uniformly flow field at a certain pressure boundary conditions.The smoother flow pattern improves heat transfer performance which can be observed with the data presented in Fig. 3a and b, where the R th is significantly reduced, and the Nu avg is increased for the GNP nanofluid compared to water.In contrast, the water-cooled heat sink, shown in Fig. 7a, presents higher temperature localization around the fins, signifying lower heat transfer efficiency.In summary, the combined data from the resutls clearly demonstrate that GNP nanofluid significantly enhances the thermal management capabilities of CMPFs heat sinks compared to water, corroborating the study's conclusion that GNP nanofluid is more effective in improving the overall performance of these cooling systems.

Conclusion
The current numerical study presents the heat and fluid flow phenomenon of Ag, MgO, GNP and MWCNT dispersed mono and hybrid water-based nanofluid-cooled circular micro pin-fins (CMPFs) heat sink at varying volume fraction (φ) and pressure drop (Δp).The results revealed that the addition of Ag, MgO, GNP and MWCNT nanoparticles in base fluid enhance the heat transfer rate.The higher average Nusselt number (Nu avg ) and lower thermal resistance (R th ) are achieved with the increase of Δp.The highest Nu avg and lowest R th are obtained with GNP added water-based nanofluid because of the higher thermal conductivity of GNP nanoparticles.This improvement is primarily due to the substantial reduction in thermal resistance, which exceeds one third, without a significant increase in friction losses.Consequently, the electronic components can operate at lower temperatures with the same pumping power, leading to a more efficient and reliable cooling system.• While the incorporation of mono and hybrid nanofluids at a constant volume fraction into the CMPFs heat sink does not lead to a significant change in hydraulic performance across varying Δp, it does notably enhance the thermal performance.Specifically, the results indicate that the GNP dispersed mono nanofluid provides the lowest R th , the highest Nu avg , and optimal PP among the tested configurations.These findings demonstrate that the use of GNP dispersed mono nanofluid in a staggered arrangement significantly improves the convective heat transfer performance, thereby enhancing the overall thermal performance of the nanofluid-cooled heat sink. A. Arshad et al.

Fig. 2 .
Fig. 2. Validation with experimental and numerical data for different pressure drops across the heat sink, (a) flow rate and (b) thermal resistance.

Table 1
Summary of key studies on heatsink optimization based on coolant, geometry, and method of analysis.

Table 2
Dimensions of CMPFs heat sink.
used to calculate the particle Reynolds number