Introduction he most significant hindrances to the technological advances in power electronics, plasma-facing components, high load optical components, laser diode arrays, X-ray medical devices, power electronics for hybrid vehicles as well as for toys and appliances, high-power computers, power generation, optoelectronic equipment, leading edges/nose caps of supersonic/hypersonic cruise vehicles, advanced gas turbines, and new directed energy based weapon systems has always been the issue of effective thermal management. Microelectronic chips which power the system or subsystems of these devices dissipate heat fluxes as high as 10 W through a 5 mm x 5 mm side (400 W/cm2 ) and heat fluxes over 1,000 W/cm2 have been projected [1], [2]. The attendant rise in temperature in these devices which as results from the waste heat dissipation of the chips is the cause of failure in these devices. Such that the failure rate of these systems themselves increases exponentially with temperature [3]. An effective thermal management system must find a solution to high heat flux as well as the non-uniform system temperature or heat flux distribution across the surfaces. Efforts are actively ongoing to develop better solutions to this problem. Cao and Gao [4][5] and Cao et al. [6] conceived, designed and tested a novel solenoid and bellows-type Reciprocating-Mechanism Driven Heat Loops (RMDHL).The RMDHL shown in Fig 1 uses a reciprocating flow of the working fluid inside the heat transfer device for cooling of the cold plate/evaporator. In addition to the hollow loop, other components include a reciprocating driver, an evaporator section, a condenser section, and a liquid reservoir. The reciprocating driver is integrated with a liquid reservoir and facilitates a reciprocating flow of the working fluid within the heat loop. There is a partial vacuum within the loop and the working fluid hermetically sealed within the loop is under a substantially saturated condition. Experimental results for bellows based heat loop indicated that using a 5 W rated driver, the heat loop could handle a heat loads of more than 550 W in the evaporator section. Additional studies are required to extend the device to substantially increase the cooling load while simultaneously optimizing material and energy utilization. Furthermore, in the selection of thermal management solution, there are quite a number possible options available and for each approach there is a large number of process variables. As a result, it is essential that each cooling system be investigated on a case by case basis. Even when all the factors are investigated, it is also essential to create a schedule of preference of ideal combinations for proper selection. Computer simulation has become an invaluable tool for greatly improving thermal management for particular applications [7]. Developing a CFD model For the RMDHL is not a simple one as the model will involve generating the oscillating flow in the channel using fluid structure interaction, numerous fluid properties such as density, viscosity, thermal conductivity and specific heat, as well as the geometry and the flow conditions [8], [9]. The geometry for the bellows type RMDHL is a challenge as it involves a continuous interchange between the rectangular channels of the evaporator and the circular channels in the connecting piping. Furthermore, a review of literature [9]- [19] showed that the study into heat transfer in oscillating pipe flow has been mostly experimental and analytical studies focused on pulsating pipe flow, Stirling engines and Vuilleumier heat pumps type systems, high Reynolds number open channel applications and gravity-wave induced boundary layer in biological systems like arteries and airways. For the RMDHL, the requirement for the numerical for the inlet and outlet boundary conditions is a challenge, as it involves specifying the inlet and outlet in the same geometric position. Depending on the flow direction, inlet and outlet interchange. The outlet and the inlet in the forward direction become the inlet and outlet in the reverse direction. Additionally, the fluid conditions at the outlet and inlet of the model are interdependent for both the forward and reverse flow; the outlet flow conditions determine the value of the inlet flow conditions. The numerical studies reviewed failed to provide details on how to resolve the inlet and outlet boundary condition of the oscillating flow or simply modelled the loop driver using a fluid structure interaction (FSI) model. FSI modelling for the RMDHL requires costly computational resources because the number of mesh node in the driver is more than double the number of nodes in the rest of the RMDHL loop. This study aims to empirically compare the performance of RMDHL to that of an existing liquid cooling systems, a dynamic pumps driven heat loop (DPDHL). This experimental and numerical study looks into the heat transfer and fluid flow aspects of the (RMDHL). Using a commercial CFD software and a novel numerical code, this study proposes an open loop configuration of the reciprocating flow. The proposed open loop configuration is developed based on the laminar model of T. S. Zhao and Cheng [20] and it seeks to reduces the computational cost of the numerical study by eliminating the need for fluid structure interaction study. It is expected that for future studies, the open loop configuration will reduce computational cost at the same time provided the accuracy required. To establish the accuracy of the Numerical codes, the results of the simulation were validated with appropriate experimental data. The study will also present the results of the validation of the CFD model and then compare the performance of a RMDHL with the DPDHL in terms of temperature, uniformity and heat removal from the surface of the heat source. For the current study a 3D, turbulent flow setup of continuous and RMDHL cooling loops with liquid water as the cooling fluid is provided. The setup and its results will be the foundation for the turbulent two phase model for various cooling fluids. It is expected that the completed model will be used to effectively evaluate the general concepts of RMDHL for future development and optimization of a standard industrial product. # II. Conceptual Design of the Bellow-Type RMDHL The construction of the RMDHL and the specification of the design parameters remain as specified by [6]. For the schematic of the RMDHL represented in Fig. 1b, the most important relation that describes the critical requirement for the operation of the heat loop is given as [6]: # ???????????????+2????????+???????? (1) The length and average interior cross-sectional area of the evaporator are denoted by Le and Ae, respectively, the length and average interior crosssectional area of the connection tubing between the evaporator and the condenser are Lt and At, the length and interior cross-sectional area of each condenser section are Lc and Ac. The piston cross-sectional area and reciprocating stroke are Ap and S, respectively. From the geometry of the heat loop Fig 1b and consideration of all the components of the RMDHL designed in equation ( 1), the critical S was calculated as 7 cm. A value of 7.62 cm was used for the reciprocating driver. # III. Performance Evaluation of the Model Bellow-Type RMDHL The experimental setup for the bellows-type RMDHL demonstration model is similar to the setup shown in Fig. 2a. The setup includes electric heaters for supplying heat to the cold plate of the heat loop, a DC power supply to the reciprocating driver, a control circuit board to control the reciprocating frequency of the driver, a constant temperature circulator to maintain a constant coolant inlet temperature of 10oC to the condenser, which would also control the operating temperature level of the heat loop, a data acquisition system, and the fabricated heat loop. Eight Omega flexible heaters (four on each side of the cold plate) are clamped by two aluminum plates onto the cold plate with insulation layers sandwiched between the heaters and clamping plates. Each heater has a dimension of 2 cm by 12 cm and could provide a heat input up to 200 W [6]. Twelve thermocouples were placed at different locations of the heat loop. Nine of them (numbered as No. 1 through No. 9) are placed on the top surface of the cold plate at different locations for the study of temperature uniformity on the cold plate. Figure 2b shows detailed locations of these thermocouples. One thermocouple is placed near the condenser and another two thermocouples are placed on two ends of the bellows pump to monitor the heat loop temperature distribution in addition to those on the cold plate. These three thermocouples are numbered, respectively, as T10, T11, and T12, as shown in Fig. 2b. During the experimentation, the heat loss from the clamping plate to the ambient was amounted to be less than 1%. Therefore, the sources of the experimental uncertainty were primarily due to the instruments themselves. The scanning thermocouple thermometer has an accuracy of ±0.1% of reading ±0.4oC. The power meter has an accuracy of ± (1% reading + 5 digits). So the maximum uncertainty for the temperature and heat power measurements would be 1.0% and 2%, respectively. IV. # Numerical Analysis It should be mentioned that the RMDHL can work either a single-phase cooling loop or two-phase cooling loop. In this study a single-phase application. A Computational Fluid Dynamic (CFD) code was employed to numerically simulate both the Dynamic Pump Driven Heal Loop (DPDHL) and the reciprocating loop. The first step of the model development was the generation of a 3D CAD model of the process by Solid Works. The condenser and evaporator loops are enclosed with solid wall. The two loops are separated from each other by the wall off the part body. The solid walls are aluminum and thermo physical properties for them are obtained from the fluent database. The working liquid in the both loops is water. The heat fluxes are applied on both side of the evaporator and the boundary conditions are presented in the Table 1. The schematic for the RMDHL is presented in Figure 3. The configuration for the geometry for the numerical model of the RMDH loop and the mesh grid distribution for numerical simulations of the RMDH loop is shown in Fig. 3c. The displacement of the piston xp(t) with time is [21]: The pressure gradient takes the form: Reynolds number for the reciprocating flow in the main pipe is given by: ? ? ½ ½ () p x t S S cos t ? ? ? ? ? ? sin ? max u u t ? / ) 2 ( n ?? ? 1 it p ae x ? ? ? ?? ? D Re v ? ? ?(1) ( ( V. # Governing Equations As stated earlier, an open loop configuration of the heat loop is modeled. A C++ numerical code was used to determine the interfacial conditions between the end of the condenser and the pump. In this case, only a constant average temperature is initiated for the computation process and the final working fluid temperature at the interface had been determined through the iteration of the computational procedure. Even if physically the loop is open, the function has actually closed the loop from the computational point of view. The open loop is used to reduce the computational cost of solving the whole domain and to avoid the simulation of the bellows part which requires an FSI modeling. The constant heat flux condition is applied at the outer surface of the cold plate while the rest of the exterior surface of the loop was insulated. A constant temperature is applied at the inlet of the condenser cooling water. The geometry and thermal boundary conditions for the RMDHL is a bit more complex than the DPDHL. DPDHL will have permanent inflow and outflow regions, where one can easily define the inlet velocity and temperature boundary conditions. RMDHL flows require interchange between the inflow and outflow boundaries during a cycle. For most applications, it is difficult to determine the inflow/outflow boundary conditions, since fluid particles exiting the flow domain during a part of the cycle are fed back into the domain, later in the cycle. The DPDHL which represents the case of forced convection heat transfer in channels and tubes is well understood. Based on above assumptions, the governing equations for fluid and energy transport are: Fluid flow: (6) (7) Energy in fluid flow (8) Energy in heat sink solid part (9) The boundary conditions for these equations are specified in the previous table. Based on the operating conditions described above, the boundary conditions for the governing equations are given as: Inlet: Outlet: Fluid-solid interface: At the top wall: In Eq. ( 9), and are the fluid inlet pressure and temperature, respectively; is the pressure at the outlet, n is the direction normal to the wall or the outlet plane, and is the heat flux applied at the top wall of the heat sink. # VI. # Results and Discussion Details of the numerical solution scheme are presented in Table 2. The CFD numerical algorithm utilizes Pressure Implicit with Splitting of Operators (PISO) formulation for the solution of the Navier-Stokes and heat transport equations. Gradient discretization was Green-Gauss Node based, pressure discretization was Second order while the momentum and energy discretization were Second order upwind. Transient formulation was second order Implicit. Appropriate under relaxations were used to improve the numerical stability for all governing equations. The solver conditions for the DPDHL are similar to those for conventional unidirectional flow. The criteria for convergence was set at 10 -4 for the continuity and x, y and z momentum. While a convergence criterion of 10 -8 was set for the DPDHL and 10 -6 for the RMDHL. The resulting computational mesh is presented in Fig. 3c. In order to establish computational accuracy, grid independence studies are always necessary and were equally performed in this work. The mesh independence studies were conducted for two more grids with coarse and fine meshes settings. The variation of the results between the coarsest and finest meshes was 5% (the largest variation). However, for the mesh used for the numerical simulation the results showed less than 1.5% variation for the last two grid size. Fig 4 show the comparism of the results for the experimental data and the Numerical results for the RMDHL loop. This comparism shows that the values of the numerical model are significantly higher than those of the experimental data. However, statistical comparism using the best-fit regression, the Nash-Sutcliffe efficiency (NSE), the percentage bias (PBIAS) and RMSE-observations standard deviation ratio (RSR) table 3 show that the results of the computational study were compared with the experimental work and in general, good agreement with experimental data within acceptable limits. Details in Fig 4 and Table 4. As is widely adopted, NSE determines the relative magnitude of the residual variance ("noise") compared to the measured data variance ("information"). NSE ranges accurate the prediction. PBIAS measures the average tendency of the simulated data to be larger or smaller than the experimental data, the lower the magnitude the more accurate the model simulation, and the optimal value would therefore be zero. RSR measures the error index and like the PBIAS, its optimal value is zero. Hence the numerical solution was used as the basis for the comparism. For the RMDHL, the temperature profile is more uniform than the temperature profile for the DPDHL. Table 4 and Table 5 show that not only is the mean temperature for the RMDHL lower than the mean temperature for the DPDHL, the standard deviation around the mean is about 1.5 o C for the RMDHL and about 5 o C for the DPDHL. It will be observed that there is an average of about 7% difference when the average value of the numerical model is compared to the data collected. This is because the actual numerical modeling of the reciprocating flow would require a Fluid structure interaction (FSI) of the pump. To reduce computational costs associated with the FSI, This study adopted a 'virtual loop' analysis, a numerical code in C. The virtual loop assumed complete perfect mixing of the fluid in the pump and assigns the mean parameter formulation to inlets and outlets as flow direction changes. The details of the Virtual loop has been presented in details in [22] . The maximum temperature occurs at the midpoint of the walls while the maximum temperature for the DPDHL is at the exit side of the cold plate. In terms of performance; thus, the RHMDL is more effective in cooling the plate than the DPDHL by up to 5 o C. As shown in Table 5, for a heat transfer rate of 550 W, 500 W, 450 W, 400 W, the DPDHL produced an average hot plate temperature of 331.71, 327.77, 323.18, and 318.19 o C, respectively; while the RMDHL produced an average of 328.09, 327.31, 324.37 and 313.19 o C, respectively. The basis for determining the average hot plate temperature is provided in Equation ( 16). The reason for the better performance is that RMHDL is that rate of heat loss to the condenser is higher for the RMDHL than for the DPDHL. there are two temperature gradients. One gradient along the evaporator and another gradient across the evaporator. The gradient along the evaporator is common to both the DPDHL and the RMDHL and is as a result of pressure drop along the piping in the evaporator. The effect of this gradient will vary if a different piping configuration is adopted. 0 V ?? ? ? ? 2 V V p V ? ? ?? ? ?? ? ? ? ? 2 p c V T k T ? ?? ? ? ? ? 2 0 s s k T ? ? ? ? , in in out ave V V T T ? ? , 0 out T PP n ? ? ? ? 0, , s s s T T V T T k k n n ? ? ? ? ? ? ? s w s T q k n ? ?? ? in V in T out p w q (13) # Global The empirical variation of the temperature is investigated at 3 cross-sections. The cross sections are shown in Fig. 7, section A-A at one end, Section B-B at the center, and section C-C at the other end. Temperatures at the centerline was compared for both reciprocating and DPDHL flow at two heat transfer rate, 400 and 550 Wand compared statistically. Figure 8 and table 4 presents the details of the analysis. The plate temperature is minimum at the inlet of the evaporator and gradually increases toward the outlet of the outlet for the DPDHL flow loop. Another statistic indicator that may be used to gage the temperature uniformity over the cold plate is the standard deviation, defined [6] as: 1. Although the maximum temperature differences may vary with the power input, they are generally around 6 o C for the RMDHL and 20 o C for the DPDHL loop. The standard deviation for the RMDHL is less than half of the value for the DPDHL (Table 5). ? ? = ? 1 ??1 ? (? ? ? ? ? ) 2 ? ?=1 The standards deviation of the RMDHL changes only slightly with increasing rate of heat transfer but for the DPDHL it increases significantly with increasing rate of heat transfer. It should be pointed out that all of the data presented herein are based on a low driver reciprocating frequency of 0.14/s for a maximum stroke. The figures show that not only is the mean temperature for the RMDHL lower than the mean temperature for the DPDHL, the standard deviation around the mean is about 1.5 o C for the RMDHL and about 4 o C for the DPDHL. It should be pointed out that all of the data presented herein are based on a low driver reciprocating frequency of 0.14/s for a maximum stroke. The figures show that not only is the mean temperature for the RMDHL lower than the average temperature for the DPDHL cooling loop, the standard deviation around the mean is about 1.5 o C for the RMDHL and about 4 o C for the DPDHL Fig. 9 reveals that although the variation in hot plat temperature is different for the RHMDL and the DPDHL, the variation in the range of the temperature is the same. The range is highest at the entrance; it begins to drop towards as the cooling proceeds towards the entrance. The range is flattening towards the middle with a slight inflection and continues to fall at the outlet of the fluid. In a bid to determine the efficiency of both systems, this work also proposed a an expression for the Coefficient of Performance (COP) based on temperature. The requirement of adequate coefficient in predicting the system is that the coefficient must satisfies the second law of thermodynamics (Moran and Shapiro, 2004) and should be dependent on operating conditions, especially avearage plate temparature and relative temperature between sink and system. The coefficient is proposed in Equations 15 -17. The COP terms is similar to the term used for determination of the COP for carnot vapor refrigeration cycle. For the basis for selcting the cold reservoir and the hot reservoir is defined in Eq 18. The summary of the calculations is presented in Table 6. Table 6 shows the value of the COP and the resulting efficiency is similar irrespective of the changing heat flux, and the various temperature parameters (Fig 9) used in computing the terms on the hot plate. The trend follows variations in similar terms in the literature (Moran and Shapiro 2004;Mcquiston et al. 2006). Ultimately the efficiencies show that the value of the efficiency of the RMDHL is about 30% higher that those attained by the DPDHL flow system (Fig 9b). Thp = average temperature of hot plate (ATHP); Tcp = average temperature of cold plate (ATCP) Thf = average temperature of hot fluid (ATHF); ???? = efficiency # Conclusion A numerical model for the simulation of the RMDHL has been successfully built and validated by experimental data. The results indicate that the cooling efficiency of the RMDHL is meaningfully higher than that of the DPDHL with a reduced maximum temperature under the same heat input and cooling conditions. The results show that that the temperature increases with increase of heat flux on the walls or decrease of the flow rate. It was also shown that the temperature profiles are more uniform for an RMDHL loop compared to a DPDHL loop both in terms of temperature uniformity and efficiency. 1![Fig 1: (a) assembly diagram of RMDHL (a) Geometry of the RMDH loop](image-2.png "Fig 1 :") 2![Fig. 2: Experimental setup: (a) Overall arrangement and (b) Thermocouple locations on the cold plate (size in mm).](image-3.png "Fig. 2 :") 3![(c) Geometry of the RMDH loop used for numerical model (b) Geometry of the RMDH loop used for numerical model (c) Grid distribution for the RMDH loop Selection of the velocity for the DPHL was based on the average velocity was applied to the DPDHL system but increased by a factor of 22/14. In the present study for the DPDHL loop the following assumptions are made: (i) Both fluid flow and heat transfer are in steady-state and two dimensional. (ii) Fluid is in single phase and flow and turbulent. (iii) Properties of both fluid and heat sink materials are temperature independent. (iv) All the surfaces of heat sink exposed to the surroundings are assumed to be insulated except the walls of evaporator where constant heat flux simulating the heat generation from different components.](image-4.png "Fig. 3 :") ![and 1.0, the closer NSE is to 1, the more](image-5.png "") ![Fig 5 and Fig 6 shows the temperature distribution across the evaporator plate for RHMDL at 550 W and 450 W and also the DPDHL for 550 W and 450 W. The colder sections represent the portion of the evaporator in contact with the condenser. The reciprocating loop maintains a higher on the condenser side than the continuous loop and this represents a higher heat removal rate from evaporator by the reciprocatory loop.](image-6.png "") 24![Fig. 4: Comparison of numerical and experimental Temperature distributions over the cold plate at different heat inputs for a coolant inlet temperature of 10 o C (a) 550 W (b) 400 W (b)](image-7.png "Table 2 :Fig. 4 :") 56![Fig. 5: Contour of varying temperature across evaporator for varying heat transfer rate](image-8.png "Fig. 5 :GlobalFig. 6 :A") 7![Fig. 7: Volume rendering of cross section of hot plate showing cross section for temperature](image-9.png "Fig. 7 :") 148![Fig. 8: Temperature variation across various cross sectional areas of the hot plate](image-10.png "( 14 )Fig. 8 :") 9![Fig. 9: Plot of Heat transfer rate and (a) average temperature (b) efficiency of cooling systems (c) standard deviation](image-11.png "Fig. 9 :") 1Boundary conditionsValues and their ranges.Inlet velocity of the evaporatorvarying stroke (cm)7.62, 8.62, 9.62, 10.62frequency (n)0.14, 0.28, 0.42, 1Inlet velocity of the condenser1.223 m/sInlet temperature of the condenser283 KSolid wall thickness0.0001 mHeat (W)Heat Flux (W/m 2 )5517983Heat (Q)500 4557244 65924005795 3Year 2017Temperature (K)550W Experimental Numerical400W1305.9312.1301.8307.82302.0311.1297.7307.03304.4312.7299.9308.0Thermocouple No4306.8311.9302.0307.05306.9311.9303.0308.2A6 7306.1 308.2310.9 313.3302.1 302.9306.9 308.28303.3311.1299.0307.19307.2312.2303.1308.1R20.10.00.10.0RegressionSlope0.3311.860.3311.9Intercept (K)304.32311.86304.3311.9NSE-7.87-7.9PBIAS-2.04-2.1RSR2.983.0 4DPDHLRMDHLQ(W)400550400 RMDHL550 RMDHLx (m) TminTmaxÎ?"T TminTmaxÎ?"TTminTmaxÎ?"TTminTmaxÎ?"T0.01305.90 321.80 15.93 314.70 336.80 22.05 304.90 313.50 8.58 317.10 330.00 12.840.03305.90 321.20 15.33 314.80 336.00 21.22 306.10 313.00 6.88 320.30 329.20 8.970.04306.00 320.60 14.64 314.90 335.10 20.24 307.10 312.80 5.70 321.40 328.50 7.110.06306.00 320.40 14.36 314.90 334.70 19.83 307.50 313.40 5.85 322.80 328.50 5.710.08306.10 320 50.000.020.040.060.080.100.120.140.1625.0020.00y = -513368x 4 + 129219x 3 -10010x 2 + 227.05x + 20.494Temperature (K)10.00 15.00y = -362484x 4 + 91519x 3 -7112.6x 2 + 162.11x + 14.811 y = -80529x 4 + 9838.4x 3 + 1692.3x 2 -274.36x + 15.0875.00y = -9381.8x 3 + 2313x 2 -178.84x + 10.044-0.010.030.040.060.080.100.120.14Increasing X(m)400 W DPDHL550 W DPDHL400WRMDHL550W RMDHL400W550W400W550WRMDHLRMDHLSection A-A 2.964.091.671.38Section B-B2.863.960.860.86Section B-B3.494.741.991.51For this purpose, the steady-state minimumtemperature,maximumtemperature,andthetemperature difference, at different power input for watercoolant inlet temperatures of 10o C is shown in Table 6? ? =??? ??? ??? ???(17)??? ??? =?? ? ?ð??" ?? ??(15)? ? =? ? ??1 ?? ?(18)??? ??? =? ?ð??" ? ?? ?? ?ð??"(16)Year 2017Cooling system DPDHL RMDHLParameter ATHP (K) ATCP (K) COPhpT ATHF (K) COPcpT ? ?T (K) ATHP (K) ATCP (K) COPhpT ATHF (K) COPcpT ?551.00 331.71 290.29 22.40 317.54 10.65 0.49 3.88 328.09 295.03 21.53 313.53 15.95 0.74Heat transfer rate Q[W] 500.00 455.00 327.77 323.18 289.67 288.88 23.01 24.97 314.12 310.74 11.85 13.21 0.51 0.53 3.54 3.17 327.31 324.37 294.84 294.91 21.51 24.49 312.76 311.64 16.45 17.62 0.76 0.72400.00 318.19 288.41 30.01 307.93 14.77 0.49 2.83 313.19 289.99 30.04 303.10 22.12 0.74( ) Volume XVII Issue IV Version I AVII.?T (K)1.511.341.511.62Global Journal of Researches in Engineering © 2017 Global Journals Inc. (US) * Compact thermal modeling for packaged microprocessor design with practical power maps ZLiu STan HWang YHua AGupta Integr. VLSI J 47 1 Jan. 2014 * Nonuniform temperature distribution in electronic devices cooled by flow in parallel microchannels GHetsroni AMosyak ZSegal IEEE Trans. Components Packag. Technol 24 1 2001 * DARPA -Microsystems Technology Office DARPA-BAA-11- 09 Near Junction Thermal Transport (NJTT) 2010 * Reciprocating-Mechanism Driven Heat Loops and Their Applications YCao MGao ASME 2003 Heat Transfer Summer Conference Heat Transfer 2003 1 * Experimental and Analytical Studies of Reciprocating-Mechanism Driven Heat Loops (RMDHLs) YCao MGao J. Heat Transfer 2008 * Experimental study of a bellows-type reciprocating-mechanism driven heat loop YCao DXu MGao Int. J. Energy Res 37 6 May 2013 * Thermal Management of a High Packing Density Array of Power Amplifiers Using Liquid Cooling ZAWilliams JARoux J. Electron. Packag 129 488 December 2007. 2007 * TLBergman ASLavine FPIncropera Fundamentals of Heat and Mass Transfer Hoboken, NJ John Wiley 2012 7th ed. * M ÖzdinçÇarpinlio?lu M. Ya?arGündo?du A critical review on pulsatile pipe flow studies directing towards future research topics Jun. 2001 12 * MGundogdu MCarpinlioglu Present State of Art on Pulsatile Flow Theory : Part 1: Laminar and Transitional Flow Regimes 1999 42 * Turbulent flow regime MYGündo?du MÖÇarp?nl?o?lu Present state of art on pulsatile flow theory 1999 42 * Oscillating Flow in Channels with a Sudden Change in Cross Section MIbrahim WHashim Comput. Fluids 23 1 1994 * Numerical investigation of fluid flow and heat transfer of oscillating pipe flows YSu JHDavidson FAKulacki Int. J. Therm. Sci 54 Apr. 2012 * Analysis of heat transfer in oscillating flow through a channel filled with metal foam using computational fluid dynamics MGhafarian DMohebbi-Kalhori JSadegi Int. J. Therm. Sci 66 Apr. 2013 * An investigation of turbulent oscillatory heat transfer in channel flows by large eddy simulation LWang X.-Y.Lu Int. J. Heat Mass Transf 47 10 May 2004 * A 2-D axisymmetric CFD model of oscillatory flow with separation MBIbrahim ZZhang SKembhavi Energy Conversion Engineering Conference 2002. 2002 37th Intersociety, 2002 37 * MMMolla MCPaul GRoditi LES of additive and non-additive pulsatile flows in a model arterial stenosis * Biomed. Engin 13 July 2014. 2010 * LES and RANS Studies of Oscillating Flows over Flat Plate CHsu XLu MKwan J. Eng. Mech 126 2 Feb. 2000 * Three-dimensional numerical simulation of flow around a circular cylinder under combined steady and oscillatory flow MZhao LCheng HAn J. Hydrodyn. Ser. B 22 5 Oct. 2010 * A Numerical Study of Laminar Reciprocating Flow in a Pipe of Finite Length TSZhao PCheng Appl. Sci. Res 59 1998 * Pump Design. Veldhoven: Arrakis JDe-Jongh RRijs 2004 * Numerical Modelling of Reciprocating flow Using a Virtual Loop OTPopoola ABamgbade YCao 2nd Thermal and Fluids Engineering Conference (TFEC 2017 p. Unpublished * MJMoran HNShapiro Fundamentals of Engineering Thermodyna-mics 2004 * Heating, ventilating, and air conditioning: Analysis and design FCMcquiston JDParker JSpitler 2006