 Thank you. Thank you very much again for your presence. The second study I will present here is numerical investigation of turbulent flow through calling channels of a PEM fuel cell with metal foam as flow distributor. I'm Masood Zairad and here I will say some introduction and then literature review. We will see the governing equations, then the results and discussion and finally some concluding remarks. Actually a fuel cell is a device, maybe I can say these are the future devices which generate power from hydrogen, generate power for us from hydrogen. Here is a schematic of a fuel cell stack but it consists of many stacks together parallel and that's hydrogen comes from one side we called anode and oxygen from the air maybe from cathode hydrogen is provided from a hydrogen tank. And then the hydrogen ions cross or the catalysts and the electron goes through a cycle and generates power electricity and these ions that cross the catalysts goes and composes with the oxygen of the air and produced water. But this process also gives heat, some heat and it's not okay for us. So we want to cool up this system using some cooling channel to remove the heat, eject the heat from the stacks of the fuel cell. Here maybe you can see better the performance of the fuel cell system. The hydrogen comes, the ions, positive protons goes through the catalyst membrane, proton exchange membrane we denote it by PEM and then the electron comes from an electrical circuit and produce electricity. Then the ions compose with oxygen and produce water. So the advantages of fuel cell system is it's high efficiency or a low pollution, it's silent without moving parts but there are also some disadvantages about its performance, utilization and reliability, its price, maybe a little still high, size of the system should be maybe large and it also needs hydrogen. So we need hydrogen from some other sources. It can be used in many applications such as transportation systems or portable and non-portable devices. Okay here also you can see the fuel cell system stack that also a cooling system is explained here. The fuel cell stack is in the circuit. Here is the pump, the cooling tank radiator, the system is for the cooling of the fuel cell stack. So the cooling system Dionized need Dionized heat exchanger, cooling channels and pump for the process of cooling of the fuel cell stack. What we need, what we need from an optimal cooling system, here are the specifications of an optimal cooling system. It should provide consistent and uniform temperature for us along the fuel cell stack. It should provide minimum pressure drop. So it's good for pumping if we have lower pressure drop. We need lower power for pumping and also it should maintain the required system moisture because the protons of hydrogen should cross over the PEM and the domain, the space, the area for them should be moisture. Okay, if what happened if the temperature be high? For high temperature it will damage the cell materials, unsafe performance, increased catalyst particle size, membrane drying, increased membrane resistance and reduce the performance. These are the disadvantages of being high temperature and low temperature also reduce the performance and make some water accumulation inside the fuel cell stack that it will also prevent the hydrogen ions to cross the membrane. If the water accumulates and fill the spaces in the membrane the hydrogen protons cannot cross the membrane. So the temperature should be uniform. Here is a schematic of cooling channels of fuel cell. They carry reactant gases and water. They also conduct the electrons and help the cooling process. The characteristics of a cooling system is gas impermeability, thermal and electrical conductivity, low weight and corrosion resistance. Here we can see a figure from a metal foam system for the membrane, for the cooling system. Sorry. The idea is to use pulse medium to improve the performance of a cooling system in fuel cells. So there are many literatures down previously using pulse media for the cooling system in different geometries, not in fuel cells, but I'm not going to explain them. Just I can see you here that there is also an experimental work on using metal foam heat exchangers for thermal membrane fuel cell systems, but it was a laminar flow case. We have also a paper in Journal of Hydrogen Energy with my colleagues and that we also studied using metal foam as equivalent for a distributor in the polymer electrolyte membrane fuel cell, but that work was also laminar flow case. So previous studies showed us that using pulse media in different geometries leads to a uniform temperature distribution which we need for a fuel cell with an acceptor pressure drop. So as the flow Reynolds number increases to a pulse medium, the flow regime can be changed to turbulent. In turbulent flows the dominant parameters at moment one energy equations are the turbulent ones. With the dominance of turbulent terms momentum and heat transfer are intensified and more heat and momentum transfer results in greater uniformity of temperature and also increase the pressure drop. So by increasing the flow velocity through the pulse medium means to make the flow turbulent. The temperature distribution can be more uniform in the cooling system of PM fuel cell. Here is also some previous works on using pulse media in turbulent flows but not in fuel cells. Okay the problem profile is using turbulent flow in pulse media with different porosity, different pore sizes and to study the effects of PM fuel cell cooling. Some assumptions we made here we assumed that the flow is fully turbulent, the flow is neotonian, the flow is incompressible, it's in a steady state and we use uniform heat flux. The numerical scheme is to discretize the governing equation based on finite volume method using well-known simple algorithm to solve velocity and pressure field coupling using k-epsilon approach for turbulent viscosity and for k-epsilon approach the macroscopic k-epsilon turbulence model in pulse media is obtained by applying the volume averaging operator to the microscopic k-epsilon equations inside representative elementary volume noted by our EE. Here are the governing equations, we can see also the porosity, phi in this equation for the pulse media, continuity, momentum, k-epsilon equations and energy equation. So with the results we have first-year validation with theoretical results, also the data are available here in this table we can see various small differences between our work numerical study and the theory so it is acceptable in different Reynolds numbers. I should say that the Reynolds number in pulse media is defined according to the porosity, according to the pore size so it's not same as internal or external flows, the values are different so the flow is turbulent but because it's defined according to the pore sizes. Here is the effect of Reynolds number on pressure drop at different porosities, we can see that as the Reynolds increases the pressure drop is also increases but in this case with this porosity with lower porosity the increase is very high and it's acceptable because when you reduce the porosity so the pressure drop the flow is passing through the channels and the channels is fulfilled with the pulse medium which is metal foam. Okay here is the effect of Reynolds number on maximum temperature at different porosities. Here also we can see that as the Reynolds number increase in each porosities the maximum temperature decrease. Here is the effect of Reynolds number on temperature uniformity factor it's a very important factor for us in fuel cells because we can check the uniformity of temperature which is very important for us in fuel cells and we can see that it decreases with the Reynolds number but at different porosities with higher porosity it will be high temperature uniformity factor will be higher and with lower porosity it's lower. Here is the effect of porosity on pressure drop at different pore sizes we can see that as the porosity increases the pressure drop decreases rapidly at both pore sizes and here is the effect of porosity and maximum temperature also at different pore sizes also a little increase we see in maximum temperature as the porosity increases. Here is the effect of porosity on temperature uniformity factor at different pore sizes again and as the porosity increases the temperature uniformity factor increase in both pore sizes we studied here. Here is the pressure contour we can see easily the uniformity of the pressure contour through the cooling channels of the fuel cell and also the temperature contours here are become here becomes very uniform through the system of the fuel cell. So some concluding remarks as the Reynolds number increases we showed that the pressure drop increases and the temperature distribution becomes more uniform as the porosity increases the pressure drop is increased and the temperature distribution becomes even more uniform as the pore size decreases the pressure drop is increased and the temperature distribution becomes even more uniform. But here we can see that the pressure drop increases but the uniformity is also increased. One of them is good but one is not good for us. And finally after changing the flow regime to turbulent flow, we showed that the trend of improving the temperature uniformity is slowed down. Thank you for your attention. For our case, because we used, we studied the problem numerically, we assumed that we have a homogenous positive distribution in the metal form. But normally it's not uniform, yeah. So the kind of C, why you are not teaching me is very small, are you going to do the Darcy loans? Yeah, yeah, yeah, yeah, yeah, yeah, yeah, using using what? There's also a term of Darcy that can be located in the Navier-Stokes equation. Yeah, but what's your suggestion? Yeah, but there's a term in the Navier-Stokes equation that the Darcy law is also included in it. The term in the Navier-Stokes has also the Darcy law, yeah. But if you only use the Darcy law, you cannot study turbulent flow, I think. Let's say that it's turbulent, yeah, because if your regular number is basically you set off your porosity size, it's only if the porosity is well structured, if it's everywhere, I cannot understand that the rule became turbulent. Yeah, but it may happen in some parts, it may be laminar and in some parts it may be turbulent, yeah. It's an assumption, but in the literature also the flow in post-media, in some of them are turbulent, are assumed to be turbulent according to the size of the pores, yeah. Yeah, but then with the porous, is it always a random porosity or is it a very small channel where the flow is in? Do you understand? Yeah, but you talk about a real case, yeah. When a metal foam is used in a cooling channel, we cannot say that the distribution of the pores are uniform along the metal foam. But in a numerical study, we can assume that they are uniform. So according to the size of the pores and the value of the Reynolds example from the literature, we can say that the flow is turbulent or laminar. For example, when it exceeds the value of 150, we can say it's turbulent. What is called a particle flow? Yeah. Okay, so you have this flow that is going like that and then there is the porosity because your atom or ion, they go through and then they are going to interact. So they... No, no, you are talking about the membrane. This is the membrane. What you say is the membrane, yeah? Yeah. But we are not talking about the membrane. We are talking about the cooling channels. We use metal foam through the cooling channels, not in the membrane. They should be porous. I don't understand. Why the channel should be porous? Yeah, we use porous to increase the rate of heat transfer in the cooling channels. Also, together simultaneously with the turbulent flow, both can increase the rate of heat transfer in cooling channels because we have not a very long distance to transfer the heat between the fluid, coolant fluid and also the stack. We used several techniques to increase the rate of heat transfer. One of them is to use porous media inside the cooling channels. Another one is to make the flow turbulent, also to increase the rate of heat transfer. But here is... Yeah, these are the cooling channels I showed here. Yeah. The flow is going through these channels. Yeah. But this is the membrane. This is the membrane. Okay. Why is the heat coming from? The heat is generated by the field cell stacks inside the membrane layer. When the hydrogen is divided to proton and electrons, it generates heat. Yeah. Yeah. And warm up the membrane. Here, here. Yeah, inside here. And these cooling channels are used, these channels. One, two, three, four, five... Yeah, okay. Two cool... Yeah, yeah. Yeah, sure. Yeah, exactly. The size of these channels? The size? The size of channels. They are less than five centimeters maybe. Five? Maybe less. So the Reynolds number is around, you said, the one thousand? But we don't talk about Reynolds number through the channels because we have metal foam inside them. We cannot see here. Yeah. Here, here, inside them, we use metal foams. And the flow goes through the metal foams inside these channels. So the size of pores are important to determine the value of Reynolds number to say that the flow is laminar or tool. Yeah. You can put a rock wall on the side of this square channel. Yeah. Only in the... Because it said that you are going to have a very big pressure drop. No. Yeah. Excuse me, colleague. Yeah. Now I have to close because the next visitation will be shortly. Thank you very much, but I think it's some kind of discussion. We have a next discussion. Thank you very much.