Effect of using RT-44 as phase-change material in the porous microchannel

In this paper, the influence of the utilizing RT-44 which, knows as a phase-change material (PCM) has used in an overall porous layer channel or optional additive nano particle of water/ZnO with three injecting fluid from its lower wall is investigated. The boundary condition slip-walls for the lower and higher walls of the micro-channel as insulation and constant temperature is considered. respectively, for assessment of PCM and nanoparticles consequences, the volume fraction of 0,2% and 5% determined for both of nanofluid and PCM. The result show that the Nusselt number increased with adding PCM to the porous media and decreasing with adding nanoparticles. When volume fraction of nano fluid is 5% the relative Nusselt number was calculated for PCM volume fraction of 1%,2% and 5% with amount of .respectively, for more supplementary the microchannel has levelized in two stage and three stage. The bulk temperature calculated for three stages for each level, at first stage was 299.90 K, at second stage was 302.38 K and 302.72 K at third stage. For considering the geometric parameters effect an optimization with monte Carlo(MC) method has been simulated in terms of maximizing Nusselt number ,it approved the relative Nusselt number Nusselt 1.026 and it increasing 0.26 K at the end of micro channel. Finally, the Additive PCM to porous material purposed for heating and additive nanofluid to the porous media purposed for cooling as well, the multistage channel purposed for heating at the latest stage.

. . Microchannel heat sinks integrated with heaters and temperature microsensors fabricated using a unique technique of mask-less and self-aligned silicon etching between bonded wafers where the heat sink performance under forced convection conditions ,where with CHF condition developed . [ 7 ] numerically investigated enhancing the heat transfer through a porous MCHS by enlarging the width or height of the channel where overall thermal resistance of a porous MCHS was not necessarily smaller than that without porous media [8] . an investigation reported the preparation of porous PDMS layers fabricated inside the microchannel of a microfluidic structure where ,expected that the porous layers and blocks of PDMS can be used to immobilize different reagents, e.g. enzymes, or to prepare filtering membranes inside microfluidic structures. [ 9 ] The first investigation of the heat transfer of nanofluids were reported by Masuda et al [ 10 ] . Seetharamu et al. investigated the energy transport by applying the Darcy-Brinkman flow in a local thermal non-equilibrium (LTNE) case with the thermal behavior of the porous-fluid system [ 11 ] . Finding the best nanoparticle from nanofluid in MCHS by least square and numerical methods based on saturated porous medium found [12]. A 3D space purposed microchannel at laminar flow with working fluid water nanofluid/GNP-SDBS (graphene nanoplatelet-sodium dodecylbenzene sulfonate) with solid nanoparticles mass fraction in range of 0-0.1% and for possibility of increasing average Nusselt number for each Reynolds number in range of 50-1000 via finite volume method was investigated. [13] the effects of solid phase heat generation on the entropy generation of water-Al2O3 nanofluid flow in asymmetrically heated porous microchannel developed an analytical model according to first law and second law of thermodynamics shows that the minimization of entropy generation.
The intensification of solid-phase heat generation further reduces the discrepancy between the two models to less than 1% [14]. represented nanofluid flow through a horizontal porous microchannel was scrutinized for effects of MHD field and heat generation in the solid on the generated entropy by the heat transfer processes with a wide variety of Re and Bejan number variations [15].
Accordingly, exploring of the previous literature with delicacy, many researches has been studied on the practical of the microchannel with different material on the heat transfer of the microchannels. In this study, the effect of diverting the phase-change material with porous medium with optional using of nanofluid microchannel. For more investigation, geometric optimization has done by Monte Carlo method for maximization the Nusselt number in concept bounded, also the microchannel levelized in one stage, two stage and three stage for discovering the best way of enhancing the heat transfer. All of the hypothesis channels have three jets and covered by porous-medium layer.

Materials and Methods.
In this case, several two-dimensional micro-channel by mixing aluminum porous foam as a porous media and phase-change material (PCM) and injective inlet velocity in three jets with velocity of The basically governing equation such as Momentum, Continuity and energy equations can be reviewed as, The dimensionless parameters habitually utilized such as dimensionless geometric parameters, dimensionless slip coefficient, dimensionless velocities, dimensionless drop pressure, temperature profile, Reynolds number, Prandtl number, Nusselt number and Darcey number. Orderly defined as, Where h D ,h, k and  are the hydraulic diameter, heat transfer convection coefficient, thermal conductivity. The boundary condition for each stage determined in following equations. (13) Presentively, adding porous material to the micro-channel has discussed the dimensionless momentum equation when the porous medium has used in the microchannel should be calculated by Brinkman ,Darcey frochimeters momentum equation such as, [20] The conservation energy in the porous medium is: Where, eff  is the effective dynamic viscosity of the porous medium.
The effective Nusselt can be determined with as a function of gradient temperature profile and a factor of bf eff k k in uppers walls. (16) formerly, the slip velocity U s has been calculated with the Brownian motion [21].
In each stage, the boundary condition should be defined same as first stage where can be find in the following formula. the boundary conditions of the injection jets bounded by, According to the mixture modeling, the effective thermophysical properties can be obtained by using equations in table 1.
The thermophysical properties of nanofluid such as , , , , c K nf p nf nf nf   gotten in table1, also, the thermophysical properties of porous material which has been used can be find in table2, lastly, the thermophysical properties of PCM materials has been given in table 2.     Finite Element method (FEM) is a influential numerical technique where multifaceted geometries and material heterogeneities.outstanding of numerous restrictions in FEM technique such as large computational competences habitually is desirable for such actions, the usage of FEM within optimized models is so far a inspiring command. The technique coding of COMSOL commericial software is a FEM scheme as numerical analysis with various physics and applicant engineering modules which could be coupled as with an integrated user interface,as weel as multiphysics arrangement.which permits users to contribution the different modules,which coupled the partial differential equations (PDE) directly. Besides, the COMSOL code application producer can be utilized to concept dedicated applications founded on the physics model. The adaptive mesh refinement choice could be applied the intensification of correctness of the solution by increasing the number of elements in the areas of largest numerical error, thus reducing the spatial discretization errors of the results.
implementation of COMSOL models within Monte Carlo (MC) optimization procedures. MC optimazed tecnique operated as a random number generator to generate the input distributions where used in this sutdy. [24][25][26] For more empathetic of methodology the flowchart delivered in fig 4.   Figure 2. flowchart of methodology.

Results
In this case, the usage effect of PCM in porous medium a two-dimensional micro-channel on dimensionless heat transfer number which named Nusselt number is investigated. To verify of this numeric correlation has validated with the same literature, which has done in 2020 by Alibeigi and Farahani [3] this analogy reproved of the numerical analyses in this scope, the consequences for the case where the Reynolds number is 100 and illustrated in Fig.5. At this point is a moral match between the results of the present study and the reference and there is less than 10% difference. It can be realized that with increasing volume fraction, Nusselt number has been reduced 2.017% cause of the increasing k in the equation (24). The slip velocity has any changing with alternative of volume fraction. Volume fraction changes do not have a substantial effect on slip velocity.       .the effects of adding PCM and nanofluid showed PCM can be decreased the Nusselt number by increasing the volume fraction of nanofluid in order to use with total covered porous layer and nanofluid .also by increasing the volume fraction of PCM, the Nusselt number was increased.   Another novel microchannel with total porous layer covered adding the new stage to the top of micro channel with relevancy of jet injection. The three microchannel with One-stage, Two-stage and three-stage considered. The temperature counter of each stage showed in fig. at

0.02L
Where, H0 is the primary amount of microchannel height and n L is the distance between two jets.

.Conclusions
In this study, the usefulness of using PCM and nanofluid of ZnO in the porous material within multi stage microchannels on heat transfer appearances was studied. A number of several volume fraction for both of PCM and ZnO at the porous layer were tested. The functional software was the Comsol software base on Darcy equation for porous media and Monte carlo method in order to optimize the geometry of microchannel with finite element method. The demonstration consequences with increasing the amount of , relative Nusselt number decreased. Also, effects of growing the amount of  on relative Nusselt number was increasing the relative Nusselt number. correspondingly, it can be purposed by adding PCM to the porous media. It can be more suitable for heating and by adding nano fluid the channel should be more suitable for cooling. finally, the multistage channel purposed for heating at the latest stage.