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Sunday, January 26, 2020

Effect of Magnetic Field on Hydrodynamic Behavior

Effect of Magnetic Field on Hydrodynamic Behavior Effect of Magnetic Field on hydrodynamic behavior in a Microchannel Heat Sink Mohammad Nasiri 1*, Mohammad Mehdi Rashidi 2, 1 Department Mechanical Engineering, Faculty of Mechanical Engineering, University of Tabriz, Tabriz 5166616471, Iran 2 Department of Civil Engineering, School of Engineering, University of Birmingham, Birmingham, UK. ABSTRACT In this study, hydrodynamic behavior nanofluid (Fe3O4-water) in a MicroChannel Heat Sink (MCHS) with Offset Fan Shaped under magnetic field was numerically investigated. The two phase mixture model was used to simulate the nanofluid flow. Flow was assumed laminar, steady and incompressible. The effects of changing Reynolds number, power magnetic field, and nanoparticle diameter on fluid behavior are considered. The results show that the friction factor decreases and Nusselt number enhances whit rising Reynolds number. Whit increases intensity magnetic field the pressure drop, friction factor and Nusselt number increasing. The results indicate that non-uniform magnetic field has more effect on nanofluid behavior compare uniform magnetic field. Keywords Nanofluid; Microchannel heat sink; Magnetic field; Friction factor; Nusselt number Nomenclature ,z Cartesian coordinate axes Velocity component in x and y and z direction, respectively (m/s) (a,b) Center of magnetic wire (m) Velocity vector (m/s) 0 Velocity inlet (m/s) Acceleration vector (m/s2) Thermal conductivity (W/m K) Specific heat capacity at constant pressure Boltzmann constant (1.3806503ÃÆ'-10-23 J/K) Temperature (K) I Electric intensity (A) H Magnetic field intensity vector (A/m) Heat flux (1 MW/m2) Channel width (300ÃÆ'-10-6m) Hydraulic diameter (0.00001333 m) Channel length (2.70ÃÆ'-10-3m) Drag coefficient Mean velocity (m/s) Drift velocity (m/s) Slip velocity (m/s) d Mean diameter (nm) Nu= Nuselt number friction factor = Reynolds number Prandtlnumber Magnetic field (T) Greek symbols magnetic permeability in vacuum (4à Ã¢â€š ¬ÃƒÆ'-10-7 Tm/A) Dynamic viscosity (kg/m s) Thermal expansion coefficient(thermal expansion coefficient (K-1) Density (kg/m3) Mean free path (17ÃÆ'-10-9 m) Magnetic susceptibility Particle volume fraction Electrical conductivity (s/m) Subscripts Particle Base fluid bw Bottom wall Effective Average Introduction Nanofluids has higher thermal conductivities compared to them base fluids [1-5]. Currently the use of nanofluids in thermal engineering systems such as heat exchangers [6-7], microchannels [8-10] , chillers, medical applications [11,12], and solar collectors [13]. Tsai and Chein[14] investigated analytically nanofluid (water-copper and nanotube)   flow in microchannel heat sink. They was found that optimum values of aspect ratio and nanofluid did not make conversion in MCHS thermal resistance. Kalteh et al. [15] investigated the laminar nanofluid flow in rectangular microchannel heat sink both numerically and experimentally. Compared the experimental and numerical results presented that two-phase Eulerian-Eulerian method results are in better accordance with experimental results than the single-phase modeling. The reasons experimentally   study by Azizi et al.[16] reported that Nusselt numbers decreases whit rising Reynolds number and enhancement heat transfer by using nanoparticles camper to that of pure water for similar Reynolds number. Sheikholeslami et al. [17] studied effect nanoparticle on heat transfer in a cavity square containing a rectangular heated body numerically. They indicated that using nanoparticle increasing he at transfer and dimensionless entropy generation. Micro channel heat sink (MCHS) using in many applications, such as microelectronics and high energy laser. MCHS cooling is very important because heat flux in this channel higher than regular channel. Many studies analyzed the convective heat transfer characteristics of nanofluids in micro channel heat sink in recently many years ago[18-24]. Sakanova et al. [25] investigated effects of wavy channel structure on hydrodynamic behavior in microchannel heat sink. They found that increasing nanoparticles in pure water the effect of wavy wall unnoticeable. Radwan et al. [26] using nanofluid on heat transfer microchannel heat sink in low concentrated photovoltaic systems investigated numerically. They show that nanofluids is effective technique for enhance heat transfer. Tabrizi and Seyf [27] investigated laminar Al2O3-water nanofluid flow in a microchannel heat sink. They showed that increasing volume fraction of Al2O3 and nanoparticle size reducing the entropy generation. Chai et al. [28-30] studied hydrothermal characteristics of laminar flow microchannel heat sink with fan-shaped ribs. Their results presented that used the fan-shaped ribs the average friction factor 1.1-8.28 times larger than the regular microchannel, while used the offset fan-shaped ribs was 1.22-6.27 times increases. Also the microchannel with large ribs height and small ribs spacing, the frictional entropy generation rate increases and thermal entropy generation rate decreases comparing than the smooth microchannel. Magnetic fluid (ferrofluid) is a stable colloidal suspension consisting of a base liquid and magnetic nanoparticles that are coated with a surfactant layer and it can be controlled by external magnetic fields [31]. Sundar et al. [32-33] experimentally studied the heat transfer characteristic of Fe3O4 ferrofluid in a circular tube whit applied magnetic field. They detected that the heat transfer increases compared to water flow at same operating condition. Aminfar et al. [34-36] studied effect different magnetic field on ferrofluid for different channels. They showed that using the uniform and non-uniform transverse magnetic increasing heat transfer coefficient and friction factor. Also shown that non-uniform transverse magnetic enhanced heat transfer more than axial non-uniform magnetic field. In this study, the uniform and non-uniform transverse magnetic effect on heat transfer of ferrofluids flow in a microchannel heat sink with offset fan shaped by using mixture model. The effects of uniform and non-uniform transverse power magnetic fields, Reynolds number and nanoparticle diameter variation are studied in details. Governing Equations Researchers presented different models for numerical analysis in multi-phase flows [37-40]. The mixture model is one of methods for nanofluid analyses [38-41]. In this study, flow is assumed steady state, incompressible and laminar with constant thermo-physical properties. The effects of body forces and dissipation are negligible. Also, for calculate the density variations due to buoyancy force was used the Boussinesq approximation. Considering these assumptions, the dimensional equations define as: Continuity equations: (1) Momentum equations: (2) The term refers to Kelvin force; it results from the electric current flowing through the wire. In this equation, H is Magnetic field intensity vector that determined as [42]: (3) where (4) (5) I is electric intensity. The wire direction is parallel to the longitudinal channel and in the center of cross section at the (a, b). Also, M is the magnetization in Equation (2) and determined as [36]: (6) where is magnetic susceptibility of ferrofluid at 4% volume fraction for different mean diameter is present in Table 1. Table 1. magnetic susceptibility of ferrofluid for different mean diameter mean diameter magnetic susceptibility 10 0.34858668 20 2.7886935 30 9.4118388 In Equation (2), is called Lorentz force that determined as: (7) Where and are respectively effective electrical conductivity and nanofluid velocity vector, also is the induced uniform magnetic field that can be calculated by intensity of magnetic field: (8) Energy equation: (9) Volume fraction equations: (10) In Equation (10), Vm, and Vdr are the mean velocity and the drift velocity, respectively, that be defined as: (11) (12) where à Ã¢â‚¬   is the volume fraction of nanoparticles. The drift velocity depends on the slip velocity. The slip velocity defined as the velocity of base fluid (bf) with respect to velocity of nanoparticles (p) and determined as: (13) (14) The slip velocity is presented by Manninen et al. [31e]: (15) In Equation (15) f drag and r are drag coefficient and acceleration respectively, which can be calculated by: (16) (17) In Equation (16), Rep = Vmdp/veff is the Reynolds number of particles. Nanofluids Properties The physical properties of water and Fe3O4 nano-particles are shown in Table 2. The water-Fe3O4 nanofluidis assumed is homogenous that the thermos-physical mixture properties calculated for 4% volume fraction of nanoparticles. Table 2. Properties of base fluid and nanoparticles [35,40]. Properties Water Fe3O4 Density (kg/m3) 997.1 5200 Specific heat capacity (J/kgà ¢Ã‹â€ Ã¢â€ž ¢K) 4180 670 Thermal conductivity (W/mà ¢Ã‹â€ Ã¢â€ž ¢K) 0.613 6 Electrical conductivity (s/m) 5.3 25,000 Dynamic viscosity (kg/mà ¢Ã‹â€ Ã¢â€ž ¢s) 0.0009963 The physical mixture properties are calculated by means of the following equations: Density of nanofluid: (18) Specific heat capacity of the nanofluid: (19) Dynamic viscosity of nanofluid [43]: (20) Thermal expansion coefficient of nanofluid [35]: (21) Electrical conductivity [36]: . (22) Based on the Brownian motion velocity is Thermal conductivity of nanofluid [44]: (23) dp and dbf are particle diameter(nm) and molecular base fluid (0.2 nm). In Equation (23) Pr and Re are Prandtl and Reynolds number, respectively defined as: (24) (25) Also, in Equation (25) is water mean free path (17 nm) and kB is Boltzmann constant (1.3807 ÃÆ'- 10à ¢Ã‹â€ Ã¢â‚¬â„¢23 J/K). Deà ¯Ã‚ ¬Ã‚ nition of Physical Domain and numerical method Fig.1 shown the geometry of the microchannel heat sink with offset fan-shaped reentrant cavities in sidewall. The channel width and space between a pair cavity is 300 ÃŽÂ ¼m.The channel length is 2.70 mm with a thickness of 350 ÃŽÂ ¼m and the pitch distance of two longitudinal microchannels is 150 ÃŽÂ ¼m. The channel cross section heat sink has a constant width of 100 ÃŽÂ ¼m and constant depth of 200 ÃŽÂ ¼m and   radius of the fan-shaped reentrant cavity is 100 ÃŽÂ ¼m. a) b) c) Fig. 1. a) Geometry of microchannel in the present study b) Cross-sectional plane of transverse non-uniform magnetic field c) Transverse uniform magnetic field In this study, used the finite volume (FV) method to numerically solved non-linear partial differential equations. The velocity pressure coupling by SIMPLEC algorithm. The discretization of momentum and energy equations used the second order upwind scheme and the solid phase equations became discretization by first order scheme. In this study for evaluate of effect the mesh points on the precision of the results, several grid sizes have been tested for the constant heat flux at Re = 300 are given in Table 3. The 1188000 grids is adequately suitable. Table 3. Grid independent test (Re = 200,T0 = 300, 4% vol.). V/V0 T/T0 Grid 1.038 1.027 672914 1.029 1.019 889440 1.023 1.013 1188000 1.02 1.011 1591128 In order to validate this, the amount of mean temperature at the bottom of the microchannel compared by numerical result of Chai et al.[45](Fig.2). Also for comparison effect the magnetic field, the dimensionless velocity under the magnetic field compared by analytical results of Shercliff [46] that shown in Fig. 3 and can be seen a good agreement between results. Figure 2. Comparison of the results for average temperature bottom heat sink Fig.3 Comparison between numerical and analytical results for flow under magnetic field Boundary conditions The set of non-linear elliptical governing equations are solved by using the boundary conditions in the entrance of microchannel (Z = 0), u = 0; v = 0; w = v0 ; T = T0 (26) at the microchannel outlet (Z = 2.7 mm): ; u = 0; v = 0 ;P = Patm (27) In the left and right sides of microchannel outer adiabatic walls (X = 0 w): (28) In the microchannel inner walls: (29) (30) Finally, a constant heat flux condition is imposed at micro heat sink bottom wall (y = 0). Results and discussion The variations of pressure drop and Reynolds number for various transverse magnetic fields are shown in Fig. 3a. It can be seen that for a given fluid, the pressure drop increases by increasing the Reynolds number because rising the velocity inlet. As shown in Fig. 3b whit increases intensity uniform and non-uniform magnetic field in the same Reynolds number (Re=300), the pressure drop increases for non-uniform magnetic because the secondary flow near wall became larger and powerful. Also scale up particle diameter of 10nm to 30nm decreasing pressure drop (Fig. 3c). a) b) c) Fig. 3. Effects of various a) Reynolds number [H=6ÃÆ'-106, dp=30nm] b) power magnetic field gradients [Re=300, dp=30nm] c) particle diameter [H=8ÃÆ'-106, Re=300] on the pressure drop Fig. 4 presented streamlines for various magnetic fields at 0.0015à ¢Ã¢â‚¬ °Ã‚ ¤ Z à ¢Ã¢â‚¬ °Ã‚ ¤0.002. As shown in Fig.4, when magnetic field is weak the streamlines same together because the magnetic field had not enough powerful for veer stream. By increases intensity magnetic field the nanofluid flow shift to near wall and thereupon the vortex in reentrant cavities became powerful Fig.5. Fig. 4. Stream lines in same Reynolds number (Re=300) and particle diameter [dp= 30nm] for a) non-magnetic field b) non-uniform magnetic field (H=6ÃÆ'-106 A/m) c) uniform magnetic field (H=6ÃÆ'-106 A/m) Fig. 5. Stream lines in same Reynolds number (Re=300) and particle diameter [dp= 30nm] for non-uniform magnetic field a) H= 6ÃÆ'-106 A/m c) H=8ÃÆ'-106 A/m The friction factor decreases as Reynolds number increases (Fig. 6a). The magnetic field cannot overcome viscous force and affect mean velocity when intensity magnetic field is low, therefor the friction factor is almost fixed for using magnetic and non-magnetic field. Whit increases intensity magnetic field the mean velocity decreases and while the pressure drop increases (Fig. 3.b); therefore, the friction factor increases at maximum intensity field (Fig. 6b). Also scale up particle diameter the main velocity and pressure drop decreases. The uniform transverse magnetic field is depended to velocity that whit decreasing velocity the uniform transverse effect decreases on flow, so friction factor rising (Fig. 6c). a) b) c) Fig. 6. Effects of various a) Reynolds number [H=6ÃÆ'-106, dp=30nm] b) power magnetic field gradients [Re=300, dp=30nm] c) particle diameter [H=8ÃÆ'-106, Re=300] on the friction factor Figure 7 shows the variations of average temperature bottom heat sink for different condition. Whit increasing Reynolds numbers the velocity increasing too and the vortex in reentrant cavities became bigger and powerful, thus average temperature bottom heat sink decreases (Fig. 7a). Effects of various power magnetic field gradients [Re=300, dp=30nm] on average temperature bottom heat sink presented in Fig. 7b. When the intensity magnetic field is weak cannot affect average velocity because cannot overcome viscous force. By strengthening the non-uniform transverse magnetic field the average velocity became larger and growth vortex in channel, therefore average temperature bottom heat sink reduces. Particle diameter rising, the non-uniform transverse magnetic had more effect than uniform transverse magnetic and non-magnetic on average temperature bottom heat sink (Fig. 7c). Whit scale up particle diameter decreasing thermal conductivity and heat transfer for when applied uniform transv erse magnetic because it independent of particle diameter. Figure 8 presented the variations of average Nusselt number for different condition. Nusselt number enhances with Reynolds number in

Saturday, January 18, 2020

Reitman’s Financial Analysis Essay

Reitmans – Financial Analysis From an analysis of the Company’s ratios over the last three years since 2009, as found in the Appendix: Exhibit _, the quantitative data reveals an unfavourable trend in performance. Liquidity Reitmans has the strongest current ratio when compared to its competitors—The Gap and Le Chateau—at almost double their value. However, the Company’s ratio has been in decline since 2009; at that time, it was at 4. , then fell to 4. 3, and finally, to 4. 1 in 2011. This trend reveals a slight decline in Reitmans’ short-term liquidity; however, even with the decline, the Company has more than enough liquidity to meet their short-term cash requirements. It could even be argued that they are not utilizing their assets to their full potential, as the usual acceptable current ratio is 2:1. Even when inventory is not considered, as with the quick ratio and cash ratio, Reitmans’ ratios are unusually high when compared to their competitors—which adds strength to the argument that they are not utilizing their assets as effectively as they could be if they were to invest their funds instead of leaving them sitting idle within an account. Asset Management As revealed by their inventory turnover of 1. 2, Reitmans sells its inventory more slowly than its competitor, the Gap, does with their ratio of 5. 7 in 2011. However, the Gap may have a higher than normal turnover, as Reitmans is favourable when compared to their other competitor, Le Chateau. The Company’s accounts receivable turnover has remained relatively stable over the past three years, fluctuating slightly but still taking just one day on average to collect from customers. In contrast, Reitmans’ accounts payable turnover has been experiencing an unfavourable decline since 2009; it used to take just 106 days to make payments to suppliers, but now it takes 257 days, over twice the time. Long-term Debt Paying Ability Reitmans’ debt ratio measures the extent of creditor financing and leverage. Their percentage of debt, 22%, is much smaller than their competitors at 63% and 39% and a result, Reitmans’ is much more solvent and more able to maintain their long-run financial viability. Further, when looking at the Company’s times interest earned, we see that Reitmans is considered to be less-risky for lenders as they are able to earn their fixed interest charges ver 3 times per year; this exceeds the general guideline that says creditors are reasonably safe if the company has a times interest earned ratio of two or more times. Profitability Most merchandising companies need sufficient gross profit in order to cover their operating expenses or else they will likely fail. Reitmans, as similar to their competitors, maintains a higher profit ratio of 64% in 2011 and 67% in 2010. Even though the Company’s other measures of profitability are still fa vourable compared with their competitors, Reitmans’ profitability ratios have declined by almost half from 2010 to 2011.

Friday, January 10, 2020

Brandy Norwood

To develop a healthier eating habit for dent that work out in the gym instead of eating junk food while exercising eating healthier will help control weight, improve health conditions and diseases, and also boosts energy levels to perform better while exercising. Give some background information about why you are proposing your suggestion so that the reader has a better understanding of the problem. The gym should be a positive place to work out at, when you go to a vending machine to get a snack what would you eat? Snickers or a granola bar?Students don't have the option to make that decision. Time and time again I e students having to make the wrong choice by eating unhealthy. Making vital decisions to choose to eat unhealthy because they don t have healthier items to offer students. This effects the students in many ways this makes the student unfit after having a full work out, this puts more calories into the students body that they just burned while working out, and lastly it d oesn't stimulate the body as would a healthier choice item Having them ready to go to class to be ready to participate in class.State a solution to the problem; this is where you give specifics about your suggestion. A solution to this problem would be to take an evaluation from the student body, where they are able to voice their opinion on if they fill that they want a healthier vending machine in the recreational center. If so move forward and by getting the student body to get the Southern University to provide a better vending machine by asking if Southern University A&M college could add a 1. 00 charge to tuition to make a possible attraction for students in their health.The dollar will exceed beyond its limits there are a little over 5,000 students that attend Southern University at the moment which is the cost of a vending machine from BBS. Com. The money that we assets from the student body every semester will go towards healthier vending machine primarily in the gym. This also will be for maintenance of the machine and also to cut cost. By working with this company they would be able to give the university a discount. Continue with any costs that will be involved. It was added in the previous paragraph Conclude by restating the problem and proposed solution.To develop a healthier eating habit for student that work out in the gym instead of eating junk food while exercising eating healthier will help control weight, improve class participation , and also boosts energy levels to perform better while exercising. The conception of having a better quality and healthier environment for people that uses Southern university a&m college recreational center. Is the ideal good or bad to use a survey of 25 stimulating questions to get to the bottom of it once and for all? How do students really feel about having Auditor or yogurt ? Would they rather drink a coke or a bottle of water?What do students want? Student survey (6-7 ) questions ). How will healthy vendi ng machines in the recreational center help improve students' performance? 2). If a healthier snack machine was put into the recreational center would you purchase snacks? 3). What snacks would you like to see put into the machine? And why? 4). Do you think students will perform better if eating heather snacks while working out? 5). What snacks would you not support being a part of the snack machine? 6). Has this ever been a concern for you to see heather snacks in the vending machine? People that uses Southern University a college recreational center.

Thursday, January 2, 2020

The Increased Use of Steroids in Athletics Essay - 867 Words

The Increased Use of Steroids in Athletics In the past three decades, steroids have become a serious problem in the athletic field. The demand for it has increased within recent years and the prices shot up since the mid-1980s. The smuggling of steroids into the United States increases every year. The methods have become easy. Simple methods such as stashing it inside a teddy bear, sneaking it across the Mexican border inside shampoo bottles have worked. These type of steroids are anabolic drugs that build growth hormones that include testosterone, which are the male sex hormones that improve performance. Testosterone in the male is produced mainly in the testes and a small amount is†¦show more content†¦Steroids can be injected or taken orally. Androgenic steroids have a fairly limited use in medicine. They are effective in males with testicular failure and are occationally used in osteoporosis and as an appetite stimulant. Many athletes take anabolic steroids at higher dosages. Unfortunately most athletes will not restrict their dosages to theraputic dosages. Many people are fascinated about steroids because of their ability to build up the body. Steroids help muscular tissue after a workout by speeding up the muscle healing process which add more fiber and increasing their bulk, but for these results, dosages need to be pretty high, causing greater side effects. These benefits of steroids help athletes obtain the competitive edge over their opponents. Everybody wants better biceps and triceps. There is a large price to pay when using steroids to achieve these goals. Numerous side effects can result while on steroids depending on the type of steroid taken, gender and body chemistry. Injectable steroids are longer lasting in the body, but the trade off being that it can be detected in your body for a longer period of time and the result take a while to kick in. Some athletes prefer to take it orall y because they obtain faster results. You swallow the pill and results will come faster because it goes through the digestive tract. The problem with orals is they put a lot of strain on the liver. Most of the side effects of steroid use result from theShow MoreRelatedAnabolic Steroids Should Be Banned1348 Words   |  6 PagesSteroids, more specifically anabolic steroids, are drugs that can be legally prescribed or taken illegally, to boost strength and increase athletic performance. They are based off of the hormone testosterone. On the street where the drug is sold illegally, the common slang names are â€Å"arnolds†, â€Å"gym candy†, â€Å"pumpers†, â€Å"roids†, â€Å"stackers†, â€Å"weight trainers†, and â€Å"juice†. Steroids have a long, long history, especially in regards to sporting events. Anabolic steroids were not really used worldwide untilRead MoreSteroids : A Lifestyle Of Cheating1639 Words   |  7 Pagesclear, beans and hype (Steroids and their). 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