The Behavior of Variable Zone for Concave Arcs -Fin of Heat Sink with Multi Air Jet Impingement

Novel array arcs- fin heat sink 7×2 with 6×2 multi air jet impingement are presented in this paper by using numerical simulation. Temperature distribution of jets diameter of 5mm and arcs- fin heat sink with variety shapes at constant radius of 45mm are evaluated. Reynolds number ranges from 7000 – 11000. The study has been done at constant Z/d= 6 and constant heat flux =8333.33 W/m 2 . The best shapes of fins has an effective role in improving the rate of heat transfer .In this paper, the design concerned in arcs ships to construct fin geometry. Four concave arcs constricted the shape of fins heat sink for model A. This model has been changed to construct models (B-C-D-E) by reflect two concave arc from it to be convex arc. All five models at the same radius. The five configurations were comparative between each other and the best model comparative with flat plate heat sink. It is observed that model D of heat sink showed best temperature dissipation than the others. The results of this paper can help to select heat sink that meets a design's thermal, Power, packaging and cost requirements (specialized in arcs fins) with array of impingement jet, which is a popular used in cooling electronic devices.

arrangement was 4 to 5% more. Rıdvan Yakut, et. al. [8] determined the experimental and numerical analytic by ANSYS -Fluent CFD program. Impingement air jet was used with hexagonal-fins heat sink. Experiments were performed for jet diameter (d) =50mm at constant heat flux. The results showed that the maximum Nusselt values and Pressure coefficients were found for Y/d=1 and fin height=100 mm. Sk. Esub Basha et. al. [9] determined the most effective heat transfer parameters by using taguchi's optimization method where the orthogonal array L 16 (4 2 2 9) for the cooling applications. CFD model performed after optimizing technique by considering results of taguchi method. Experiments were performed for nozzle diameter= (20) mm, at z/d= (4, 6, 8 and 10). The two different velocity values = (8,9) m/sec were used. The result showed that the highest Nusselt number were obtained for Z/d=6 and U=8m/sec. Furthermore the highest heat flux and heat transfer rate were obtained at Z/d=6 for both numerical and experimental results. Zhipeng Duan et. al. [10] investigated the pressure drop (Δp) of the plate -fin heat sink subjected to rectangular impinging of air flow. Widths, fin heights, and the shapes of flow were run in the numerical simulations in different inlet. Reynolds number was in laminar flow. The numerical results showed that, at the same flow rate, (Δp) reductions with the rise of the impingement inlet width and growths significantly with the increase of the fin height. Besides (Δp) for an impinging plate-fin heat sink without elliptic bottom profiles was larger than that with elliptic bottom profiles.
However from vast literature survey it is observed that array of air impingement jet at new distribution jets on 5 models of (concave, concave -convex) arcs-fin heat sink (AFHS) is still interesting. The current study depends on (7×2) array at variety distributed of (concave -convex) arcs for fin heat sink with (60×60) base are chosen to enhance the dissipation of heat from a heat target surface by multi air jets (6×2) of (5) mm dia. The arrangement of the nozzle as shown in (Fig 1) and the arrangement of fins with its five models are shown in (Fig  2). The objective of this study is to determine the rate local temperature with fins to local temperature without fins for five models in order to understand the fins characteristics. The influence of Reynolds number and the velocity distribution are examined in detail.

Governing equation
Conservation of mass equation [2] ………. (1) Conservation of linear momentum equation [ The fluctuating terms appearing in Eq. (2) to (4) represent the components of the "turbulent momentum flux" and they are usually referred to as additional "apparent stresses" or "Reynolds stresses" resulting from the turbulent fluctuations. The fluctuating terms appearing in Eq. (5) represent the components of "the turbulent energy flux". [2] 3. Physical problem A physical model of a multi-jet impinging on (AFHS) are analyzed, show (Fig 3). The jet is discharged with length (l) and diameter (d) is directed towards the (AFHS) with base (60mm×60mm×6mm) vertically. Constant value of heat flux was subjected from bottom. All other walls are adiabatic except top surface. After impingement, the flow (air) exit from four side from opening with (minimum cross flow).

Fig 3. Physical model of 6×2 multi jet with 7×2 arcs-fin heat sink
Fin array consist of high (H), radius (R) and transverse pitch of arc fin array is S T , longitudinal pitch of arc fin array is S L , the thickness of the fin is t. nozzle plate consist of (n-1× n) array with (d)diameter. Heat sink material is aluminum.

Mesh -boundary conditions
Meshing of all models of (AFHS) and computation domain are shown in (Fig 4). The domain of interest is rectangular geometry, the fin height in (Z-direction).

Result and discussion 5.1 Temperature distribution for impingement-heat sink
The comparative of temperature distribution for jet impingement with heat sink in Y-Z plane at fin region and between it, has founded it similarity. Also the temperature distribution in Y-X plane is similar with temperature distribution at Y-Z plane. The plot of comparative between three states is shown in (Fig 5.) give us improvement for the uniform state of our study and the advantage of the multi jet impingement.

Effect of Reynolds number on velocity distribution
The effects of Reynolds number (Re) on the heat transfer performance of (flat plate) heat sink and (AFHS) under multi-jet (6×2 nozzle arrays) impingement are studied at 7000 ≤ Re ≤ 11000 for z/d=6 by taking cutting in Y-X plane (7 fins with 6 jets) as shown in the ( Fig 6) . The second plane was taking in Y-Z plane.

A. Velocity distribution in Y-X plane
The average velocity vector on 7 fins in Y-X plane is shown in the (Fig 6). All fins in difference cases have thickness in that plane =3mm. The momentum has not reduced with constant Z/d. the potential core zone is predominant.

Fig.6 Average velocity vector on7 fins in Y-X plane at
Re (7000-9000-11000) B. Velocity distribution in Y-Z plane Two planes in Y-Z plane are taken for fin region as shown in (Fig 7) and for the region between fins as shown in (Fig 8). The flow velocity is variables because the effect of fins walls appears in first plane.
It is most important to know the movement of fluid (air) in the space between the fins in array that give as indicate for enhancing the heat transfer [11].
The Comparative plot of average velocity vector for models (A-B-C-D-E), in Y-X plane and Y-Z plane at Re (7000-9000-11000) can show in (Fig 9) ) ( g )   (Figs 15 and 16).  (Fig 17). In spite the shape fins of (model D) are similar to shapes fins of (model E) (only rotated 180° at same location). But the average temperature for (model D) is better than (model E) in all cases. At Re =7000, the average temperature of (case1-D) = 316.15K, but the value of (case1-E) = 317.229 K. At Re =9000, the average temperature of (case2-D) = 313.91K, and the value of (case2-E) = 314. 91 K. While at Re =11000, the average temperature of (case3-D) and (case3-E) =312.4K and 313.15K respectively.
The influences of geometric shape with jets impingement gave different indicate to heat transfer. The reflection of its fins gave different result in temperature distribution to dissipate the heat for all values of Reynolds number show (Fig 18). have (convex-concave) tail in X-direction only in two sides of fins array near the edge of heat sink. When comparing the results of (models B, C, and D), we founded that at all state of Reynolds number (model B) has the low performance than the other models, besides each of (model C) and (model D) have the same performance. Show (Figs 19) and (Fig 20) Re=7000-9000-11000). (7000-9000-11000). E. Average temperature of the solid with concave ended of fins array near the edges of heat sink (Model C) have concave end for its fins array at one side of heat sink in X-direction. (Model D) have concave end in its fins array near from the edge of heat sink for two side of heat sink. While (model A), have concave end in its fins array near from the edge of heat sink at four side of heat sink. Concave end for the fins array whether in X or Z direction provided they are close to the edges of heat sink, enhanced the performance. Only at Re=9000, the value of average temperature for (case2-A) have low performance than (case2-C) and (case2-D). Each of (case2-C) and (case2-D) have average temperature = 313.98K and 313.91K respectively, while (case2-A) have average temperature = 314.43K. The behavior of the three models at Re= 7000-11000 are similarity. Show (Fig 21).  (7000, 9000, 11000). F. Average temperature with same number of (concave-convex) arcs. Each of Models (B, C, D and E) have the same number of concave arc and convex arc. But it gave different temperature distribution with difference average temperature. Show (Fig 22). g p ( g ) (7000-9000-11000). (Table 4) give the summery results of average temperature of the solid for the two types of heat sink (flat plate-fined heat sink). While (Table 5) show the summery of temperature distribution for the solid.  3-E 311.3-315 Through the paragraphs that have been presented, we reach conclusions as follows:-In multi-jet impingement, for middle nozzles, the heat transfer peak was directly on the jet centerline. The cross-flow is still minor. As the cross flow developed, the peak position of the outer nozzles is observed to shift slightly downstream to rise cross flow moved the jets effect. The comparison of temperature distribution between the models have concave end and the others. The concave end of fin array at one side or two side of heat sink is the better state. Reveals that these results are in tune with our latter discussed results. Through this comparison it was confirmed that:-However model A have the smaller surface area but it has better dissipation the temperature than (model B) and (model E) All state fin-heat sink are safety to use and all are better than flat plate heat sink. Models (B, C, D and E) have the same numbers of (concave -convex) arcs and have the same surface area, although model D has the same of model E except it reflected, but the result showed that model E is the worst, and model D is the best. Model C is nearest to model D than the other models. Model B is nearest to model E than the other models.

Fig 22. Comparative plot between average temperatures of the solid for models (B -C-D-E) at Re
Having concave arc near the exit of the heat sink models (C-D) give better effect than having convex arcs near the exit (model E). a validation case was recognized based on the research published in 2020 belongs to Basim Freegah, conducted to confirm results obtained from the simulation run were true and the assumptions and models used were valid. By using numerical results from Basim Freegah et. al. [12] work on numerical analysis by using Plate-fin of heat sinks (PFHS) without fillet profile using the parallel flow type. Across the z-axis, coolant flows into the heat sink. This state was taken to establish and prove the accurate of it result. (Table .6) view the geometry that taken in validation. 3.3mm This model builds to numerically solve by using ANSYS Fluent (version 2019-R1) program with the same operation conditions. The result of validation of temperature of the (PFHS) at mass flow rate (m°) = 0.0092 kg/s obey to parallel flow shows good correspondence between both models as show in (Fig 23).

Fig. 23. Comparison of the validation results of Basim Freegah and present study
Comparison with [12] of diverse designs in impinging flow to examine the thermal performance of proposal designs when offer to impinging flow, the base temperature at m°= 0.0092 kg/s have been presented for models (a-b-c-d-e-f). All that models were Compared to the base temperature counter for models (A-B-C-D-E) for present study at Re (7000-9000-11000) correspond mass flow rate (0.005183kg/s-0.006597Kg/s-0.008011Kg/s) respectively. Anywhere temperature display more active heat distribution.
At q° (18750) W/m 2 , A (40mm× 39.7mm), and m° (0.0092) Kg/s were used in (Basim Freege) study. The present study was presented in q°(8333.33) W/m 2 , A (60mm×60mm), and m° (0.005183kg/s-0.006597Kg/s-0.008011Kg/s) By changing the geometry and parameters of fins-heat sink with changing the mass flow rate, the improvement in the cooling of the dispersion base is achieved. All state of arcs-fin heat sink have better result by comparative with the research view. Show the (Fig 24).

Conclusions
The focus of our study are investigation of heat transfer and fluid flow characteristics. New distribution of array jets impingement at different values of (Re) at constant Z/d with two types of heat sink (flat plate, arcs-fins) heat sink. The new model of array jets give: High saturated convection heat transfer coefficient in the core region and multi stagnation points. In multi jet impingement, the temperature distribution are more uniform. The average temperature for the solid of the flat plate heat sink and five new models were presented too. The first model with configure from four concave arc at same radius, this model was change to consist from two concave arcs -two convex arcs that result the models (B-C-D-E). The optimized structure was obtained for minimum average temperature. By comparing the average temperature for the optimized (AFHS) with flat plate we find that the optimized (AFHS) possess lower average temperature.
The counter map is expected to be practically used as a guideline in the design of heat sink.