THE BEHAVIOR OF HEAT SINK-IMPINGEMENT COOLING WITH FLAT PLATE AND ARCED FINS MODELS

: In this paper, a statistical analysis was applied to the numerical predictions of temperature distribution for the heat sinks. There are two types of heat sink with an array of impingement. The first type is a flat plate heat sink, and the second type is arcs-fins heat sinks. The second type category considers five models (A, B, C, D, and E). The shapes of fins were changed, but the thickness, distance between fins, and radius were held fixed for comparing and analyzing them depending upon the improvement of the fin geometry of heat sink. The heat sinks of the two types are subjected to multi impinging flow at different Reynolds numbers (7000-11000). Thermodynamic and hydraulic results were collected. The best model was calculated through a statistical analysis. The efficiency of an arcs-fin heat sink was superior to that of the flat plate heat sink. The findings of Model D were more appropriate than those of the other models. The concave arc near the heat sink's exit (model D) created better effect than the convex arc (model E), despite the fact that the (model D) shape fins being identical to (model E) shape fins (only rotated 180° at the same location). However, Descriptive Statistics manifested that in all situations, the mean temperature for (model D) is better than (model E). The results of comparison between the flat plate heat sink and models (D and E) evinced that the average heat sink temperature in the suggested design reduced via 12%, 8%, while the (model E) decreased by 12%, 7% for Re (7000, 9000), respectively. In addition, the two models maintained the same percentage of (8% and 7%) improvement at Re (11000). The correlation coefficient between the flat plate and the arcs-fins heat sink for model B has the highest value (0.809), while model A has the lowest value of correlation (0.673).


Introduction
The increasing of the flow rate, the surface area of heat sinks, or improving the flow distribution through the use of baffle barriers and other techniques, like parallel flow or impingement flow are the all ways that can help increase the electronic modules and packages cooling.All of these strategies have benefits, but they come at a cost.Raising the rate of flow is easy to do, but it necessitates greater and more efficient (air)moving equipment, which increases the acoustic noise in addition to the total expense, weight, and volume of system.Due to the relatively high friction effects, this issue of enhancing the rate of heat transfer via raising the rate of flow is specially leading to cooling.This has a much smaller impact in liquids, where an improvement in the rate of flow causes a perfect heat transfer at a low expense in friction.The coefficient of heat transfer per unit area is obtained to differ as the ratio of velocity (v) to the power (P) is around (0.7).The viscous influences, otherwise, are a function of (v) to (P) of (2 to 3), a much stronger function [1].
Generally, increasing the surface area, while lowering the velocity (v), is more efficient [2].CPU cooling, audio amplifier cooling and power LED cooling are examples of passive cooling.In contrast to electronic devices, however, the method of passive heat sink hasn't advanced significantly.Most of the traditionally obtainable passive heat sinks being yet bulky and made of a sole material, like graphite or metal or.Only a few extrusion designs of fin have been investigated, and there has rarely been a requirement for further effectual module designs since the modules have historically been comparatively big.Savithri Subramanyam and Keith E. Crowe [3] identified how to use thermal finite element analysis (FEA) and (CFD) to test the designs of the electronic cooling heat sinks.Sathe and Sammakia studied a unique high-performance impingement heat sink.[1].S. Zu and Yan [4] looked at how well seven turbulent models predicted the thermal and flow characteristics of a confined impinging jet.S. Manivannan S. et al. [5] proposed a Taguchi design of experiments-based Grey relational analysis method for multi-objective optimization of the flat plate heat sink.ANOVA test was used to determine the contribution and effect of each heat sink design factor on the heat sink's multiple responses.Mathias Ekpu et al.
[6] improved the thermal management and microelectronics package efficiency.M. Beriache et al. 2012 [7] investigated the numerical simulation of the plate-fin heat sinks with confined impingement cooling.Simple model was developed to predict the thermal and hydraulic efficacies of the plate fin heat sink for impingement air cooling.Finite difference method (FDM) was utilized for converting the governing equations to algebraic formulas.
Multiple grid sizes were used, then a (42 × 37 × 66) grid was chosen to show that the solution became nearly independent of the size of grid, as well as more increment in the grids wouldn't possess an important influence upon the solution.Also, the outcomes of this preparation were satisfactory leading to infer that the computational correctness of the field parameters was independent of the nodes' number while having (102,564) or further.The effect of base thickness and fin height upon the thermal efficacy of heat sinks made from aluminum and copper being investigated using a steady-state thermal conduction analysis.Lemos and Dorea provided numerical results for a a turbulent jet impinging on a flat plane covered with a sheet of permeable and thermally conducting material.Kucaba-Pietal, 2014 [11] used an array of (6) impingement jets.Chamfer and countersunk nozzle type were used to study the numerical analysis of a flow characteristic, the coefficient of heat transfer (h), (Nu) distribution and pressure drop (ΔP).Results manifested that using an array of cooling jets gave a uniform (ΔP) distribution.Also, the biggest deflection angle was observed in the chamfer nozzle configuration.Where, the lowest (ΔP) takes place through the analysis with the nozzles countersunk kind.The presented analysis showed that (h) relies upon the flow direction whilst air entering the nozzle.Roaad K. Mohammed A. [12] examined experimentally the local distribution of heat transfer coefficients between the impinging jets from a circular orifice on a flat plate.Jet-to-plate spacing was varied from (2 to 8) orifice diameters, and (Re) was varied between (7100 and 44400).P. Chandramohan et al. [13] investigated the temperature, Nusselt number, and heat transfer coefficient of a hot plate that were exposed to multi-jet air impingement cooling in an experimental environment and by using ANOVA analysis found that the important participations upon the responses were owing to the ratio of (H/D) ratio as well as the Re no.influence.
Xiaoming Huang et al. [14] examined three various dimple designs: convex, concave and mixed).The exterior faces alongside the model channel were presumed to be adiabatic and considered the geometric and boundary symmetry of the micro channel heat sink with impinging jets (MIJ) with dimples alongside the X and Y axes and simulated its model.The (MIJ) having dimples being compared with the MIJ having no dimples.Result showed that the use of convex dimples to (MIJs) improved the flow of fluid and the heat transfer, comparative to the other kinds.Gao Apeng et al. [15] used a computational simulation to analyze the features of impingement cooling before evaluating and improving the structure.Archibald Allswell Amoako [16] developed a numerical technique to test thirteen various heat sink geometries employing CFD program, as well as simple and exotic heat sink fin designs which improved the thermal efficiency of heat sink.Hassan Khurshid et al. [17] identified an empirical approach to the design and construction of a passive heat sink for an ABB communication board that was used in it.Based on the natural convection, two traditional fin geometries, rectangular plate fins, and rectangular pins fins were considered.Patrick McInturff et al. 2018 [18] improved the efficiency and the rise levels of the surface heat transfer of impingement cooling by adding special patterns of surface roughness to the impingement target surfaces.Circle, racetrack, and triangle were the (3) various impingement hole configurations that utilized inside a jet array.Each of the three hole shapes had the similar hydraulic diameter.Data were presented at (Re = 900, 1500, 5000, and 11,000).Result depicted that the shape of racetrack hole gives the similar rise of heat transfer as a circle hole shape, with somewhat better efficiency, at certain circumstances.Differently, the triangle hole shape gives lower rising in the heat transfer, comparably with the racetrack hole and circle hole shapes.The swirl jet impingement effect was studied experimentally and numerically by N. V. S. Shankar and H. Ravi Shankar [19], by using swirl generators, it was possible to raise the turbulence of the impinging plane.On a flat plate, 33 swirl jets were impinged.Ammar A. Hussain et al. [20] searched and improved the convective heat transfer of the plate-fin heat sinks.Two geometries were investigated: platefin heat sinks without fillet profile and plate-fin heat sinks with fillet profile.Impinging (traditional design) and parallel flow were added to the investigation.The computational grid was developed using ANSYS Fluent for discretizing and solving the governing equations.Mohamed L. Elsayed et al. [21] investigated the efficiency of a partial shield heat sink for various open area ratios, as well as the effect of inserting the guide plate at various inclination angles.Paweł Gil and Joanna Wilk, [22] used a synthetic jet to investigate the heat transfer phenomenon that occurs during the impingement cooling.
In this article, ANOVA was used in two ways, based on the numerical results of using ANSYS Fluent (2019-R1).The aims of the study are to determine the best heat sink configuration and the connection between the flat plate and the arcs-fin heat sinks using a new fin-heat sink arrangement with different geometries.The use of an impingement jet in combination with a heat sink can also assist in the dissipation of heat from an electronic device.Finally, the thermal and flow fields of a modern heat sink as a result of new multi jet impingement characteristics will be analyzed.According to a review of the literature, there has not been a statistical analysis work on a multi-jet impingement over the finned-heat sink arrays in arcs shapes.Arcs were designed in a range of ways, including fins with the same number of fins arrayed, and exposure to air from jets arrayed.The first model has the same form of concave arcs at a constant radius.This model has changed to have two concave arcs and two convex arcs in different locations at the same radius.The focus of the study is on the effect of arcs types and the location of it on heat dissipation by new impingement jet array.To get an enhancement for electronic cooling, one needs the best alternative model for the flat plate heat sink.A suitably modified version of the three-dimensional impingement jets over the arcs-fins heat sink has been used.Computational fluid dynamic model is created depending on the test description and by the software package Fluent examined using ANSYS Fluent (2019-R1).Then, the numerical results were used in a statistical analysis in twoway (ANOVA).

Physical Model
The forced convection and conduction heat transfer from a 60 mm× 60 mm discrete heat source (8333.33 w/m 2 ) using an arcs-fin heat sink were investigated.The heated part was flush mounted on the enclosure base, and the arcs-fin array was connected to it.The heat sink was cooled using a multi jet impingement.The parameters of jet impingement and heat sink used in this study are shown in Where: The computational domain is bounded by solid (heat sink) and fluid (air).The solution domain is filled with stagnant air.By supposing that the heat being produced in the heat sink at an even rate and can be denoted via (q°=c) from the bottom.To simplify the proposed model solution, the following assumptions are used:  The working fluid is air, which has constant properties. The conditions are steady state. The heat sink's sides are insulated, only the fin surfaces and top surface of heat sink are exposed to convection.
 The comparative pressure being zero Pa, and the working temperature is 300 K, with (5%) turbulence. The air temperature is at (300 K).  The model case is turbulence, and the standard k-ε model is used. The wall surface was in no-slip condition. Thermal conductivity is constant with the exception of variations in air density in the momentum equation's buoyancy term. There is no gravitational effect during impingement. The term of viscous dissipation is negligible. The heat sink is made of aluminum, which has a density of 2702 kg/m 3 , a specific heat capacity of 903 J/kg.K, and (K) thermal conductivity (237 W/m.°C). The value of constant heat flux (8333.33W/m 2 ).

Analysis of Data Using SPSS Software
Analysis of variance (ANOVA analysis in the SPSS software) is a statistical models group and it is related estimation proceedings (like the "variation" between groups) utilized for analyzing the variation between group means in specimen.ANOVA has been developed by the statistician Ronald Fisher.It has been based on the total variance law, in which the observed difference in a special changeable is divided into components attributable to various variation sources.In its simplest shape, ANOVA provides a statistical test of whether two or more population means have been equal, so it generalizes the T-test beyond the two means.
The temperature results obtained from these tests may utilize to study the difference between specimen and the significant influence of treatment and factors [24].
(SPSS) has been used for these considerations using two ways ANOVA, and Table (5) shows the summary of two ways ANOVA.[25].
While, figure (3) evinces the legends of numerical study that used in analysis.SPSS is a statistical software package used for statistical analysis.The data for the numerical distribution temperatures were analyzed with SPSS program, those data were collected from a numerical work for temperature distribution with the variation of the effect of Reynolds number with a two-way variation analysis.The level of significance adopted during the analysis of the empirical results data for the research is a 95%.So, the accepted error ratio is 0.05.To test the effectiveness of factors, the calculated significance was compared with 0.05.If the calculated value is lower than (0.05), this means rejecting the hypothesis of non-absence and accepting the alternative hypothesis, which indicates that the variables are effective in the model.The opposite state (if the calculated value is greater than the value (0.05), which means that the variables are not affecting in the model [24].

ANOVA Tables Resulting From Data Analysis
The legend of the solid that resulted by using ANSYS Fluent (2019-R1) at Re (7000-9000-11000) for the two types of heat sink, were presented in (figure 1).Temperature distribution values represent the data entered in the statistical analysis.Because the significance value is more than 0.05.

Results
In figure (4), the profile plot between the estimated marginal of the temperature and Re clarifies the effect of the arcs fins heat sink to dissipate the heat comparative with the flat plate heat sink.While in figure (5), the profile plot between the estimated marginal of the temperature and Re gives the models sort from the best to the worst (D, C, A, B, and E) (4, 3, 1, 2, and 5).Although the models (B, C, D, and E) are concave-convex arcs, but the model A is a concave arc, the models of the concave-convex arcs split into two groups: one group that provided better heat dissipation than model A.
As for the second group, it performed below the A model and represented by the models B and E. The explanation for this case is the location of the concave arc, which generates large eddies.They are in viscid and interaction with flow, hence extracting energy from it.That leads to increase the rotation of large eddies and produce small eddies.The presence of a concave tail towards the edges of the heat sink is better.
The cooling improvement of the electronic modules and packages can be completed via a diversity of methods, like raising the flow rate of air, improving the air flow distribution, but maximizing the surface area of heat sinks may be increased or not if and only if the air flow distribution was improved.The numerical results of comparison between flat plate heat sink and the model D demonstrated that the average heat sink temperature in the suggested design reduces via 12% and 8% for Re (7000 and 9000), respectively.After the best model was determined, the five models were correlated with the flat plate heat sink.The results illustrated that there is a difference between the new model that will be manufactured and the basic one (flat plate).The relationship is not strong as the correlation value is closer to its value 1, the better it can be.
In other words, reaching a value of 1 means that the new model matches the basic model 0 ≤ correlation ≤ 1.This state did not show through the results any mismatch, see figure (6). All state fin-heat sinks are in safety for uses and are better than the flat plate heat sinks. Model C is nearer to model D than the other models. Model B is nearer to model E than the other models. Improvement of the electronic modules and packages cooling can be talented if the air flow distribution was improved. Having a concave arc near the exit of heat sink (model D) gives better effect than having a convex arc (model E).

Validation
A validation case was recognized based on the research published in 2020 belongs to Basim Freegah, carried out for confirming that the outcomes got from the run of simulation being true, and the suppositions and the employed models being usable.By utilizing the numerical outcomes from Basim Freegah et al. [26] work on numerical analysis by using Plate-fin of Heat Sinks (PFHS) without fillet profile using the type of parallel flow.Across the z-axis, the coolant moves inside the heat sink.This state was taken to establish and prove the accuracy of the result.Table (8) views the geometry that taken in the validation.(m° = 0.0092 kg/s) that obeys to parallel flow shows a good correspondence between both models, as shown in figure (7).The temperature distribution of freegah is (from 345.3 to 351.6) K, while in the present study, it is (from 347.1 to 352.8) K.The comparion between Basim Freage results and results

Conclusion
The increasing of Re for flat plate heat sink (conventional) enhances the dissipations of heat by 6% and 5% at Re (9000 and 11000), respectively.The new models of fins and the shapes that were chosen at the same thickness, distance between fins, length, height of fins, no. of fins, array of jets and its diameter were kept constant to be compared and analyzed depending on the geometry improvement of the heat sink fin.Under the same flow rate, the heat transfer performance of the arcs shape fin for model D appeared better among the other shapes of arcs fin (figure 4).However, the reflected shape (model E) leads to weaker performance.The results of comparison between flat plate heat sink and model (D, E) manifested that the average temperature of heat sink in the suggested design reduced via 12%, 8%, while the model E decreased by 12% and 7% for Re (7000 and 9000), respectively.The two models maintained the same percentage of (8% and 7%) improvement at Re (11000).The disadvantage with flow through the heat sinks is the rise in air temperature caused by upstream power dissipation.The heat sink design for a particular rate of flow and the air temperature inlet can finish up in a device, where the air comes in the heat sink at a slightly more temperature and can even bypass the heat sink.
Careful study or testing is essential to the actual system in order to confirm that the design is successful.Air impingement, in which the air being ducted straight to the heat sink as well as pushed into it, is one way to solve these challenges.Then, the flow rate and the air inlet temperature being further exactly understood.Such method being expensive since each implementation necessitates unique manifold, stiffener, heat sink, and the overall device of mechanical designs.Also, the impingement needs further space in the dimension vertical to the boards; to permit for the ducts and the manifolds directing the flow.But, the benefits are too important mainly for applications in great power by employing the air cooling.

Performance of an
[8].Yang et al. [9] studied the turbulent fluid flow and the heat transfer characteristics of the air jet impingement onto rotating and stationary heat sinks using numerical simulations.The effects of impingement cross-flows on reducing the local surface Nusselt numbers as the impingement jets were deflected and became less coherent were shown by Junsik Lee et al [10].K. Marzec and A.

Figure 1 .
Figure 1.The tested design of the present study

Figure 3 .
Figure 3.The legends of the numerical study input in analysis

Figure 4 .
Figure 4. Profile plot between the estimated marginal of temperature and Re (7000, 9000, and 11000) for flat plate with five models of AFHS

Figure 5 .Figure 6 .
Figure 5. Profile plot between the estimated marginal of temperature and Re (7000, 9000, and 11000) for (A-B-C-D-E) models

Figure 7 .
Figure 7.Comparison of the validation results of Freegah and present study

Figure 8 .
Figure 8.The comparative result between (Basim Freage) and present research

Table 1 .
Table (1) and Table (2).While, Table (3) views the comparison of the arcs-fins heat sink geometry specifications, and figure (1) manifests the design models of the present study.Description modeled of the multi air jet

Table 2 .
Description modeled of heat sink

Table 3 .
Comparison of the arcs-fins Heat sink

Table 4 .
The effect of the amount of grid element on

Table 5 .
Two-way ANOVA summary

Table (
no. having the higher value.The table also elucidates that the Re.no intersection with the model is not significance at value (0.985).

Table 7 .
Tests of Between-Subjects Effects.