NUMERICAL STUDY ON THE EFFECT OF INCLINATION ANGLE ON HEAT TRANSFER PERFORMANCE IN BACK-WARD FACING STEP UTILIZING NANOFLUID

Transcription

1 NUMERICAL STUDY ON THE EFFECT OF INCLINATION ANGLE ON HEAT TRANSFER PERFORMANCE IN BACK-WARD FACING STEP UTILIZING NANOFLUID Saleh Etaig*, Reaz Hasan, Noel Perera, ABSTRACT This paper reports a numerical investigation the eect o inclination angle o the vertical ace o a backward-acing step on the heat transer perormance utilizing Nanoluid or laminar low. AlO3 is the nanoparticle used in this investigation, and water is the base luid. The inite volume technique is used to solve the momentum and energy equation in D backward acing step geometry with an expansion ration o 1.5. The eect o Re on Nu is investigated or the Reynolds numbers 40, 100 and 150 and or dierent volume ractions o the nanoparticles o %, 4% and 6% or all simulations. Nusselt number distribution at the bottom wall is computed. Pressure losses also reported or dierent Reynolds numbers and entropy is studied or a range o Reynolds numbers and or dierent volume ractions o Nanoluid. The results are validated with available literature. Four angles o inclination o the vertical step is investigated 90 o,97.5 o,105 o and 115 o. The eect o the inclination angle on the heat transer showed that the heat transer was enhanced with a decrease in the inclination angle.

2 INTRODUCTION Separations in lows due to the adverse pressure gradient can be encountered in many industrial applications such as electronic cooling, passage o turbine blades, combustors, and many heat exchangers. Backward acing step is one o the basic conigurations where low separation takes place. The separation and reattachment o the low play a vital role in determining the low structure and aect the heat transer perormance. A signiicant amount o high luid energy occurs in the reattachment region o these devices. There are several ways to enhance heat transer, one o which is to employ nanoluids. Nanoluids are ormed by dispersing nanoparticle in a base luid; the base luid could be water, ethylene glycol or oil. The application o nanoluids in many industrial application are investigated by many researchers since the irst research by (Choi and Eastman, 1995). There were many studies ocused on the low separation and reattachment in the past decades, and the BFS geometry received much attention. (Armaly et al., 1983) conducted an experimental work on backward acing step to investigate the reattachment length. (Biswas et al., 004) investigated Laminar backward-acing step low or a wide range o Reynolds numbers and expansion ratios in two and three-dimensional simulations. The inding was that this primary recirculation length increases non linearly with increasing expansion ratio. (Abu- Nada, 006) presented a numerical study o entropy generation over a D backward acing step with various expansion ratios and the results showed that total entropy generation increases with the increase in Reynolds number.. (Mohammed et al., 011) studied the eect o Nanoluids on heat transer perormance in Backward acing step and ound that there is a primary recirculation region or all nanoluids behind the step and the skin riction coeicient is sensitive to the recirculation lows. (Pour and Nassab, 01) has numerically studied the convective low o nanoluids with dierent volume ractions over a BFS under bleeding condition. They ound that the recirculation zones and the reattachment length increase as bleed coeicient increases. (Togun et al., 014) investigated numerically the eect o volume raction on the heat transer rate using nanoluid, the results showed that the recirculation low as created by the backward-acing step enhanced heat transer. (Erturk, 008) presented a comprehensive numerical work o the -D steady incompressible backward-acing step low, the results showed that, or the backward-acing step low an inlet channel that is at least ive step heights long is required or accuracy, he also ound that the size o the recirculating regions grows almost linearly as the Reynolds number increases. (Lan et al., 009) reported the eect o aspect ratio and the Re number on the low and the heat transer perormance and showed that the eect o Re on the low reattachment is minimal in the range o the parameters. (Mohammed et al., 015) carried out Numerical simulation o laminar and turbulent mixed convection heat transers o nanoluid low over backward acing step placed in a horizontal duct having bale. They reported that Nusselt number and velocity distribution increased gradually by increasing the Reynolds number o laminar and turbulent lows. (Kherbeet et al., 014a) and (Kherbeet et al., 014b) studied numerically and experimentally the heat transer characteristic o nanoluid laminar low over the microscale backward acing step. They also carried out a simulation o three dimensional laminar mixed convection to study the eect o step height on the low and heat transer characteristics. They ound that the Nusselt number increase with increases volume raction. Water SiO nanoluid showed a higher enhancement o the average Nusselt number in comparing to the pure water and water AlO3 nanoluid. The inding was also revealed that the increasing o the step height increases the reattachment length and thus Nusselt number, the size o the sidewall reverse low region. (Chen et al., 006) presented simulations o three-dimensional laminar orced convection adjacent to inclined backward-acing step in rectangular duct, the inding was that the riction coeicient inside the primary recirculation region increases with the increase o the step inclination angle. The aim o the present work is to investigate the eect o the inclination o the acing step on the heat transer perormance in the backward acing step geometry using AlO3/water as a working luid and investigate the entropy generation.

3 DESCRIPTION OF PROBLEM The problem geometry considered in this work is shown in Figure 1. A channel with a backward acing step with length L1 is considered illed with AlO3 /water nanoluid. The luid is assumed to be Newtonian, incompressible and there is no slip velocity between the particle and the base luid. The thermal properties o the nanoparticle and base luid are presented in Table 1. The step size o backward acing step is h and channel height H and expansion ration (H/h) equal to 1.5 and the bottom length is L. At the inlet o the channel, a velocity U and a uniorm temperature (T = 300 K) are imposed. The downstream length starting rom the edge o the step to the exit o the channel is 0H to ensure that the low is ully developed low. The downstream bottom surace o the backward acing step is maintained at T=74 K, while the other walls o the channel are assumed to be adiabatic, the outlet is assumed to be outlet boundary condition. These boundary conditions have been previously used by other authors and the present work is an extension in line with those works. L1=1300 mm, L=800 mm and h=0 mm L1 Adiabatic Inlet Tinlet U Y-Axis h Adiabatic T α T L H Outlet X-Axis Figure 1 Problem Geometry Figure Mesh Figure 3 Detailed low eature o the backward acing low(kostas et al.)

4 Table 1 Thermophysical properties o the base luid and nanoparticle Physical property Base luid ( water) AlO3 Heat Capacity(J/Kg K) Density (Kg/m 3 ) Thermal conductivity (W/m K) Thermal diusivity α x 10 7 (m /s) GOVERNING EQUATIONS AND THERMOPHYSICAL PROPERTIES OF NANOFLUID The governing equations are continuity, momentum equation and energy equation and can be written as ollows Continuity equation ρ +. = t ( ρν ) 0 (1) Momentum equation ( ρν ) +. t ( ρν ) ν = p +. ( t ) + ρg + F () Energy equation ( ρe) τ ( ) +. (3) ( ν ( ρe + P) ) =. k T h J + ( τν ) e j j The thermophysical properties o the nanoluid are expressed as The Nanoluid density ρ = 1 ) ρ + ρ n ( (4) s The speciic heat o the nanoluid C pn ( )( ρc ) + ( ρc ) p p s = 1 (5) ρ n The eective thermal conductivity was modelled as (Corcione, 011) K static T K s 0.66 (6) K φ = Re Pr φ T φr K φ Where k and k are the thermal conductivity o base luid and particle respectively s

5 Re n ρk T = pµ b d p (7) 3 k = J/K is the Boltzmann s constant; b base luid and expressed as: d is the particle diameter; Pr is the Prandtl number or p Pr µ c = k p (8) T is the reezing temperature or the base luid. r The viscosity was modelled by (Corcione, 011) as µ nφststic µ φ = 0.3 d p φ d φ ) Where dp is the nanoparticle diameter, d is the equivalent diameter o the base luid and given by: d M = Nπρ (10) Where M is the molecular mass weight o the base luid, N is the Avogadro number, ρ 0 is the mass density o the base luid calculated at T=93 K q is the heat lux h is the heat transer coeicient q h = (11) ( T H T C ) h. L Nu = (1) k ρud Re = (13) µ Where D is the hydraulic diameter and H is chosen as the hydraulic diameter in this calculations

6 The entropy is modelled as (Mahian et al., 013). S /// gen K = T T T µ n n y n n x x y (14) x y T x y y x NUMERICAL PROCEDURE In the present work the conservation equation ( 1 to 3 ) are solved numerically using inite volume scheme, the Ansys Work bench 15 package was sued. A source code written in C language was developed to introduce the thermophysical properties o the nanoluids as a user deined unction. The geometry was created using ANSYS Workbench design modeler, the mesh created using ANSYS Mesh. Explicit relaxation actor 0.75 or momentum and pressure, standard or pressure spatial discretization. A convergence criterion o 1X10-6 is chosen or continuity, x-velocity and y-velocity, reined mesh is adopted in the near wall region as shown in Figure. A grid independence test was carried out and 4x100 grid, 36 x 1385 grid and 48x 160 were tested. The average Nu or these cases was 4.89, 4.9 and Hence the inal calculations were obtained with 36X SIMULATION VALIDATION This simulation is validated by comparing the present results with experimental results rom Armaly or Re=800 and other numerical published results as shown in Table 1. The present results have good agreement with the other numerical results. However, most o the numerical published works, including the present work, underestimate the reattachment length. According to Armaly et al the low at Re = 800 has three dimensional eatures, this eatures arises when using Reynolds number equal to or greater than 400. The reason or the underestimation o x 1 (as shown in Fig. 3) and x which are the reattachment lengths or irst and second circulation zones respectively is the assumption o the two-dimensional assumption by all numerical published data. Table Simulation Validation Authors Work Type x 1 x Armaly Experimental Vradis Numerical Pepper Numerical Abu-Nada Numerical Present simulation Numerical

7 RESULTS AND DISCUSSION The eect o inclination angle α o the ace step using nanoluid is investigated numerically and the results o this eect is shown in Figure 4, our angles o acing step is investigated 90 o, 97.5 o, 105 o and 115 o. The increase in angle o the ace step was ound to decrease Nu number and hence the heat transer rate, the angle 90 was ound 4% higher, it is clearly seen that on the bottom wall Nu number has the peak value at the reattachment o Nu is in the separation region where the generated recirculation low. The low in the separating region is impinged on the stepped wall and it is responsible or developing the peak values in Nusselt number. As a result o adding the nanoparticle to the base luid the thermal conductivity is increased and this is the reason or the reduction in temperature gradient at the bottom wall, developing in thermal conductivity is accompanied by developing in thermal diusivity. The surace Nu number on the bottom wall increases linearly rom zero (just beore the bottom wall) up to a peak value which lies in the circulation zone( coincide with the point o reattachment), ater this point the value o Nu decreases due to the temperature gradient decreases. It is clearly seen that the our angles 90, 97.5, 105 and 115 have identical variation o Nu umber in the bottom wall except in the circulation zone, where 90 o angle o ace step has the higher Nu number. The reason or this is the change o the shear stress in this area as well as the thermal diusivity is pronounced in the circulation zone. Figure 4 eect o inclination angle on the heat transer rate

8 The entropy is also investigated or Re number 40, 100 and 150 or α=90 o and volume raction %. The results are presented in Fig 5. As shown in equation (13) entropy is a unction o thermal conductivity and viscosity, these two thermal properties are the most important properties among nanoluid thermal properties. Entropy generation determines the level o the gained irreversibilities during a thermal process. Thereore, entropy production can be employed as a measure to evaluate the perormance o engineering devices. For proper optimization o engineering systems in terms or operation and design, the entropy has to be minimized as well as maximizing the heat transer. It is clearly seen that the increase in Re number results in decrease in entropy, this change is in a good agreement with results in Figure 5 (will be discussed later) which implies that increasing Re number has an advantage o enhancing the heat transer rate. Re number 150 has minimum entropy compared with Re 40 and 100, the minimum value o the entropy is noted in the circulation zone, the entropy decreases with Re number up to circulation zone and has the minimum value at 0.35 m rom the corner o the geometry, i.e. coincides with the reattachment point. The same trend applies to 100 and 40 Re numbers, the only change is the point o the minimum entropy, the explanation or this is that decreasing Re number will result in decreasing the reattachment length which was one o the indings rom (Armaly et al., 1983) experimental work. Figure 5 eect Re on the entropy on the bottom wall

9 The eects o the Re number on the surace Nusselt number in the bottom surace or the laminar ranges are depicted in Fig 6. The increase in Re number increases Nu number along the bottom surace, three Re numbers are investigated 40, 100 and 150, where the substantial compression o thermal boundary layer exist (Kumar et al 014) the Nu number has a maximum value. Increasing Re number results in increasing in inertia orce and increase in thermal conductivity and subsequently an enhancement in Nu number, Re number is also increased by minimizing the viscous orces, using nanoluid may result in increasing the viscosity o the luid, the increase is very small compared to the develop in the thermal conductivity and hence the inertia orce ampliying is the pronounce. The increase in the Re number has a peak value o Nu umber in the reattachment point and then decreases linearly, along the bottom wall, as the reattachment length increases with the increase in Re ( as discussed previously) so the Peak value o Nu number or Re= 100 lies at a point beore the location o the peak o Nu or Re=150 Figure 6 Variation o Nu number or dierent Re number The eect o volume raction on the pressure coeicient is shown in Figure 7. The results show that increasing the volume raction leads to a slight penalty in the pressure coeicient, the pressure coeicient decreases linearly to the point in which the circulation zone exist, ater which the curve increases until the low passes the circulation zone and drops linearly ater that the circulation, the negative sign arises due to the outlow boundary condition at the outlet. In order to ensure the low is ully developed and to prevent ill-posed. This boundary condition is assumed ar rom the reattachment point where the diusion lux or all low variables in the outlet direction are zero. It is also noted that the three volume ractions %, 4% and 6% are almost identical trend beore the reattachment point in which the shear stress changes, and ar rom the circulation zone the more evident the change o these volume ractions.

10 Figure 7 Variation o Pressure coeicent vs vlume raction The eective thermal conductivity increase o the nanoluid due to the nanoparticle dispersing is presented in Fig. 8. A comparison o the indings with those o the base luid (water) is also presented, the results shows that the increase in the volume raction o the nanoparticle will increase the thermal conductivity o the nanoluid. This increase is due to the high thermal conductivity o the nanoparticle compared to the base luid as stated in Table1. This increase in thermal conductivity is the main cause o the increase in the heat transer rate in the system, it is evident that the nanoluid has a higher thermal conductivity than the base luid which is water, i.e. decreasing the volume raction results in decreasing in thermal conductivity which is expressed in equation (6) Figure 8 Thermal conductivity enhancement or dierent volume ractions

11 NOMENCLATURE AA Area [m ] kk Theraml conductivity [W/m K] NNNN Nusselt number qq" Heat lux [W/m K] C p Speciic heat at constant pressure [Kj kg -1 K -1 ] P r Prandtl number µ Viscosity [kg m -1 s -1 ] α Inclination angle o acing step H Downstream channel height [m] ρ Density [Kg m -3 ] ɸ /// S QQ RRRR Volume raction Entropy [L K -1 ] Heat transer rate [W] Reynolds number TT Temperature [ o K] h L Heat Transer Coeicient length [m] α Thermal diusivity[k/(ρc p )] Subscripts eeeeee P NNn H C eictivt luid particle nanoluid Hot cold

12 CONCLUSION The eect o inclination angle on the heat transer o laminar AlO3/water nanoluid low over a backwardacing step was numerically studied. Three nanoluid volume ractions %, 4% and 6% were considered at an expansion ratio 1.5 and Reynolds numbers 40,100 and 150 or the laminar regime at a uniorm temperature on the wall. Four inclination angles were tested 90 o, 97.5 o, 105 o and 115 o.. The results showed that the increase in the angle decreases the heat transer rate, 4% enhancement in angle 90 o was ound. REFERENCES: ABU-NADA, E Entropy generation due to heat and luid low in backward acing step low with various expansion ratios. International Journal o Exergy, 3, ARMALY, B. F., DURST, F., PEREIRA, J. C. F. & SCHÖNUNG, B Experimental and theoretical investigation o backward-acing step low. Journal o Fluid Mechanics, 17, 473. BISWAS, G., BREUER, M. & DURST, F Backward-Facing Step Flows or Various Expansion Ratios at Low and Moderate Reynolds Numbers. Journal o Fluids Engineering, 16, 36. CHEN, Y. T., NIE, J. H., HSIEH, H. T. & SUN, L. J Three-dimensional convection low adjacent to inclined backward-acing step. International Journal o Heat and Mass Transer, 49, CHOI, S. U. S. & EASTMAN, J. A Enhancing thermal conductivity o luids with nanoparticles. CORCIONE, M Rayleigh-Bénard convection heat transer in nanoparticle suspensions. International Journal o Heat and Fluid Flow, 3, ERTURK, E Numerical solutions o -D steady incompressible low over a backward-acing step, Part I: High Reynolds number solutions. Computers & Fluids, 37, KHERBEET, A. S., MOHAMMED, H. A., MUNISAMY, K. M., SAIDUR, R., SALMAN, B. H. & MAHBUBUL, I. M. 014a. Experimental and numerical study o nanoluid low and heat transer over microscale orward-acing step. International Communications in Heat and Mass Transer, 57, KHERBEET, A. S., MOHAMMED, H. A., MUNISAMY, K. M. & SALMAN, B. H. 014b. The eect o step height o microscale backward-acing step on mixed convection nanoluid low and heat transer characteristics. International Journal o Heat and Mass Transer, 68, KOSTAS, D., SORIA, J. & CHONG, M. A study o a backward acing step low at two Reynolds numbers. Kumar, Ankit, Dhiman, Amit Forced Convection Heat Transer o Newtonian Fluids rom a Backward- Facing Step: Eects o Expansion Ratio, Reynolds, and Prandtl Numbers. Heat Transer -Asian Reasearch LAN, H., ARMALY, B. F. & DRALLMEIER, J. A Three-dimensional simulation o turbulent orced convection in a duct with backward-acing step. International Journal o Heat and Mass Transer, 5, MAHIAN, O., KIANIFAR, A., KLEINSTREUER, C., AL-NIMR, M. D. A., POP, I., SAHIN, A. Z. & WONGWISES, S A review o entropy generation in nanoluid low. International Journal o Heat and Mass Transer, 65, MOHAMMED, H. A., AL-ASWADI, A. A., ABU-MULAWEH, H. I. & SHUAIB, N. H Inluence o nanoluids on mixed convective heat transer over a horizontal backward-acing step. Heat Transer- Asian Research, 40, MOHAMMED, H. A., ALAWI, O. A. & WAHID, M. A Mixed convective nanoluid low in a channel having backward-acing step with a bale. Powder Technology, 75, POUR, M. S. & NASSAB, S. A. G. 01. Numerical Investigation o Forced Laminar Convection Flow o Nanoluids Over a Backward Facing Step Under Bleeding Condition. Journal o Mechanics, 8, N7- N1. TOGUN, H., SAFAEI, M. R., SADRI, R., KAZI, S. N., BADARUDIN, A., HOOMAN, K. & SADEGHINEZHAD, E Numerical simulation o laminar to turbulent nanoluid low and heat transer over a backward-acing step. Applied Mathematics and Computation, 39,