Free convection of nanoliquids in an enclosure with sinusoidal heating

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1 IOP Conerence Series: Materials Science and Engineering PAPER OPEN ACCESS Free convection o nanoliquids in an enclosure with sinusoidal heating To cite this article: S. Sivasanaran et al 018 IOP Con. Ser.: Mater. Sci. Eng View the article online or udates and enhancements. This content was downloaded rom IP address on 17/10/018 at 01:15

2 The 3rd International Conerence on Materials and Manuacturing Engineering 018 IOP Con. Series: Materials Science and Engineering (018) doi:1088/ x/390/1/01086 Free convection o nanoliquids in an enclosure with sinusoidal heating S. Sivasanaran 1, T. Aasaithambi, M. Bhuvaneswari 1, S. jan 3 1 Deartment o Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia Deartment o Mathematics, Sri Shanmugha College o Engineering and Technology, Pullialayam, Sanari, Tamilnadu, India 3 Deartment o Mathematics, Erode Arts and Science College, Erode, Tamilnadu, India Corresonding author sd.siva@yahoo.com; sdsiva@gmail.com. Abstract. The goal o the current numerical research is to exlore the convection o dierent nanoliquids in a square cavity. The temerature at let wall varies sinusoidally whereas the temerature at right wall is et as constant. The horizontal walls are taen as adiabatic. The inite volume method is utilized to discretize the governing equations and the solutions are ound iteratively or diverse combinations o relevant arameters involved in the study. It is established that the energy transer enhances with raising the nanoliquid volume raction. The growth in the averaged energy transort strongly deends on the nanoarticle chosen. 1. Introduction Convective cooling augmentation method has been a ey roblem in many industrial and technological alications because o thermal controlling o devices. In recent years, nanoliquids are considered in heat transer research to analyze the number o actors in dierent ways. Ho et al. [1] numerically examined the roerties o nanoliquids on convection in the enclosure. Sivasanaran et al. [] numerically examined the ree convection o nanoliquids in an enclosed sace with linearly heated wall. Ho et al. [3] exerimentally investigated the ree convection o nanoliquid in a vertical enclosure. The thermohoresis, sedimentation, and Brownian motion eects on yleigh Bénard ree convection o nanoliquids in an enclosed sace were examined by Ho et al. []. The maximum number o the reorts on convection o nanoliquids in cavities have been considered either isolux and/or isothermal thermal conditions in boundaries. But, these temerature conditions at boundary are not aroriate in numerous alications. Thereore, we want the awareness o the outcome o non-isothermal wall temerature to analyze several alications. The non-uniorm heating eect on both walls in a cavity was examined by Sivasanaran et al. [5]. The MHD convection in cavities with non-uniorm boundary heating was examined by several authors [6-7]. Convection in a orous enclosed sace with sinusoidal boundary heating on side walls was reorted in Re. [8-9]. The asect ratio and inclination eects on ree convection with sinusoidal surace condition was exlored by Cheong et al. [10]. Sivasanaran and Pan [11] numerically examined the ree convection o nanoliquids with sinusoidal heating walls. The non-uniorm temerature on sidewall(s) in a cavity under dierent situations is examined by several authors in dierent studies [1-16]. No wor has been executed on convection low o nanoliquids or non-uniorm boundary conditions with dierent nanoliquids. Hence, the resent reort aims to exlore the eects o ree convection characteristics with sinusoidally varying wall temerature utilizing dierent nanoliquids.. Mathematical Modelling A two-dimensional enclosed sace o height L illed with water-based nanoliquids containing various nano-articles (Al O 3, Cu, Ag and TiO ) is taen or examination as dislayed in the Figure 1. The vertical let wall is sinusoidally heated and the vertical right wall is cooled at a uniorm temerature. The bottom & to boundaries are adiabatic. The nanoliquid is a liquid-solid blend with uniorm shae, size, and volume raction o nano-articles distributed within base liquid water. The low is resumed to be incomressible and laminar. It is resumed that both water and nano-articles are in thermally equilibrium. The buoyancy term based on Boussinesq aroximation is added and other thermohysical roerties are exected to be constant. It is resumed that no chemical reaction between the nanoarticles and water. The mathematical model or the above said geometrical and hysical conditions can be written as ollows. Content rom this wor may be used under the terms o the Creative Commons Attribution 3.0 licence. Any urther distribution o this wor must maintain attribution to the author(s) and the title o the wor, journal citation and DOI. Published under licence by Ltd 1

3 The 3rd International Conerence on Materials and Manuacturing Engineering 018 IOP Con. Series: Materials Science and Engineering (018) doi:1088/ x/390/1/01086 Fig. 1. Physical coniguration u x v y 0 (1) ut uux vux ( 1/ n ) x n / n u () vt uvx vvx (1/ n ) y n / n v g( ) n / n ( c ) (3) u v () t x y n The no-sli velocity conditions are taen on all walls. The temerature on let and right walls are taen as = sin(y/l) and 0. The thermo-hysical roerties o the nanoliquid calculated using several ormulae are as ollows. n ( 1) ( ) n ( ) (1 )( ) ( c ) n ( c ) (1 )( c ) 1 n with / 1. 5 n 1 The roerties o the water and various nano-articles are ound in (Ho et al., 008). The dimensionless variables are derived as ollows. t c ( U, V) ( u, v) L / n, ( X, Y) ( x, y) / L, T n L, F0, and P ( h c ) L n. n Using this non-dimensional variables, the equations are non-dimensionalized and they are given as ollows: U V 0 (5) X Y U U U P C, n n U U U V Pr (6) FO X Y X n X Y V V V P C, n n V V nc, n U V Pr Pr n T FO X Y Y n X Y (7) n

4 The 3rd International Conerence on Materials and Manuacturing Engineering 018 IOP Con. Series: Materials Science and Engineering (018) doi:1088/ x/390/1/01086 T F O T U X T V Y X n T X Y n T Y (8) The surace conditions in the non-dimensional orm are as ollows. No sli condition or velocity on side walls. The let and right walls temerature are taen as T = sin(y) and T=0. The hysical roerties ratios aear in equations (-) are as ollows. n n, n n, Cn Cn C, n n, and n n, where the subscrits n and denote the nanoliquid and water. The non-dimensional numbers erormed in the above equations 3 g ( h c) L are,, yleigh number, and Pr, Prandtl number (Pr=6.7). The stream unction is deined by U and V. Y X The energy transer rate at the heated surace is obtained by the Nusselt number, which is hn L T estimated as Nuh n The averaged Nusselt number along the heated surace is Y X 0. 1 acquired as Nu Nu dy. Moreover, it is also signiicant to enumerate the energy transort eicacy 0 h o using the nanoliquid to that o the water. The averaged energy transer coeicient ratio o nanoliquid to that o the water, h, is comuted as h hn h. The solution o the dimensionless governing systems are done by inite volume method. The detailed solution methodology is ound in Re. Sivasanaran et al. (010). 3. Results and Discussion (a) =10 3 (b) =10 (c) =10 5 (d) =10 6 Fig.. Streamlines (u) and isotherms (down) o Al O 3-nanoluid with =% or various. 3

5 The 3rd International Conerence on Materials and Manuacturing Engineering 018 IOP Con. Series: Materials Science and Engineering (018) doi:1088/ x/390/1/01086 The calculations are done or the yleigh numbers rom 10 3 to 10 6, and the volume raction o nano-articles rom 0% to %. Figure dislays liquid stream and temerature characteristics o Al O 3-nanoluid or dierent yleigh numbers. The stream attern is involves a cell occuying the comlete enclosure. The core area o the cell is at central art o the cavity or the wea buoyancy orce (=10 3 ). The isotherms are sread equally inside the cavity. Here energy transort is by means o conduction dominated mode. When increasing, the core area o the cell elongated horizontally ( 10 5 ). The minor cell exists in the high values o yleigh number at the let-to corner due to nonuniorm heating. The isotherms illustrate the vertical stratiication o temerature in the cavity. The isotherms are crowded beside the thermal walls and orming the thermal boundary layers. It clearly indicates that convection mode o heat transer is dominated here. V = % =10 6 hot wall 1,,3, cold wall 1,,3, Al o 3 -nanoluid - Tio -nanoluid Cu-nanoluid - Ag-nanoluid X Fig. 3. Local Nusselt number or various nanoluids with =10 6 and =%. The eect o local energy transer rate among the dierent nanoluid is dislayed in Figure 3. It is witnessed that the higher energy transer is gained when using Ag-nanoliquid. A urther insection o the roiles exoses that the highest value o local energy transer rate is achieved at Y=0.35 or =10 6, that is ¼ rom the bottom o the warmer wall. It is witnessed that the highest local energy transort rate is achieved at the middle art o let wall or sinusoidally varying wall temerature and at the to o the wall or isothermal surace temerature. The wavy shae o local Nusselt number roile indicates the direct eect o non-uniorm heating o sidewall on energy transer. Nu Al o 3 -nanoluid - Tio -nanoluid Cu-nanoluid - Ag-nanoluid =10 3 =10 1,,3, 1,,3, Nu Al o 3 -nanoluid - Tio -nanoluid 3 - Cu-nanoluid - Ag-nanoluid =10 6 =10 5 1,,3, 1,,3, (a) (b) Fig.. Averaged Nusselt number or various volume ractions and nanoluids.

6 The 3rd International Conerence on Materials and Manuacturing Engineering 018 IOP Con. Series: Materials Science and Engineering (018) doi:1088/ x/390/1/01086 Figure rovides the eect o total energy transort rate through the enclosure among the various nanoliquids. The avorable eects o the nano-article raction on the averaged Nusselt number trend can be erceived clearly with raising the article raction. Averaged Nusselt number enhances on raising the values o. It is established that the maximum energy transer rate is witnessed or using Ag-nanoarticle comaring among other nanoarticles, lie Cu, Al O 3 and TiO. When raising the nanoliquid volume raction, the variation in the energy transort rate amongst the various nanoliquids is increased. The change amongst several nano-articles lays a ey actor on the convective energy transort rate, which is evidently shown in the Figure Al O 3 -nanoluid = Cu-nanoluid 1.05 h = = = 1 = 0 h = = 1 = (a) (b) = Ag-nanoluid TiO -nanoluid 1.10 h = = 1 = h = = = 1 = (c) (d) Fig. 5. Heat transer ratio or dierent nanoluids. Figure 5 demonstrated the energy transer eicacy o the nanoliquid or various volume raction o the nanoarticle versus. The heat transer ratio o oxide-nanoliquids (Al O 3 & TiO ) gets minimum when =10. However, the reverse tendency is detected or using metal nano-articles (Cu and Ag), that is, maximum energy transort rate is achieved at =10. It is also acquired that energy transort coeicient ratio is higher than one always. It is concluded rom these igures that nanoliquids with Al O 3 and TiO -article are having similar behaviour while Cu and Ag-nanoliquids are so. The maximum value o the heat transort ratio or the nanoliquids with the oxide article is attained or =10 3 whereas highest value o the heat transer coeicient ratio or Ag- and Cu-nanoliquids is obtained or =10. Table 1 shows a signiicant variance on the averaged Nusselt number or various nano-articles.. Final Remars The study numerically insects the heat transer augmentation o nanoliquids o our dierent 5

7 The 3rd International Conerence on Materials and Manuacturing Engineering 018 IOP Con. Series: Materials Science and Engineering (018) doi:1088/ x/390/1/01086 nanoarticles (Al O 3, Cu, Ag and TiO ) in a rectangular cavity with sinusoidally changing wall temerature. The energy transer ability o base liquid can be imroved when immersing the nanoarticles in base luid and the eect is noticeable as the article volume raction increases. However, the growth in averaged Nusselt number is owerully deending on the nano-article selected. The heat transer ratio o Al O 3- and TiO -nanoliquids is minimum when =10 while it is high or Cu- and Agnanoluid. The nanoliquids with oxide-articles having the similar behaviour on the low and heat transer while the nanoliquids with metal articles are having similar trend. A signiicant variance on the averaged Nusselt number is detected or various nano-articles. The outcomes evidently demonstrate that the tye o nanoarticle considered is vital actor on the convective cooling alications. Table 1. Heat transer enhancement or dierent values o (%) and dierent nanoluids Enhancement (%) (A-B)/B 100 (%) Al O 3 TiO Cu Ag Reerences [1]. Ho C.J., Chen M.W., and Li, Z.W Int. J. Heat Mass Transer, 51, []. Sivasanaran, S., Aasaithambi, T., and jan, S Maejo Int. J. Sci. Tech. (3), [3]. Ho, C.J., Liu, W.K., Chang, Y.S., Lin, C.C Int. J. Thermal Sciences, 9, []. Ho C.J., Chen D., Yan W.M., Mahian O. 01. Int. Commun. Heat Mass Transer 57, -6. [5]. Sivasanaran S., Sivaumar V., Praash P Int. J. Heat Mass Transer, 53, [6]. Bhuvaneswari M, Sivasanaran S, Kim YJ, 011, Numerical Heat Transer A, 59, [7]. Sivasanaran S., Malleswaran A., Lee J., Sundar P Int. J. Heat Mass Transer, 5, [8]. Sivasanaran S., Bhuvaneswari M Numerical Heat Transer A, 63(1), [9]. Sivasanaran S., Pan K.L. 01. Numerical Heat Transer A, 61(), [10]. Cheong H.T., Zailan Siri, Sivasanaran S. 013, Int. Commun. Heat Mass Transer, 5, [11]. Sivasanaran S., Pan K.L. 01. Numerical Heat Transer A, 65, [1]. Janagi, K., Sivasanaran, S., Bhuvaneswari, M., Eswaramurthi, M Int. J. Numerical Methods Heat Fluid Flow, 7(), [13]. Sivaumar, V., Sivasanaran, S. 01. J. Alied Mech. Tech. Physics, 55(), [1]. Cheong H.T., Sivasanaran S., Bhuvaneswari M, 017. Int. J. Numerical Methods Heat Fluid Flow, 7 (), [15]. Sivasanaran, S., Ananthan, S.S., Abdul Haeem, A.K Scientia Iranica -B Mech Engg, 3(3), [16]. Sivasanaran S., Cheong H.T., Bhuvaneswari M., Ganesan, P Numerical Heat Transer A, 69(6),