Effects of Dissipation and Radiation on Heat Transfer Flow of a Convective Rotating Cuo-Water Nano-fluid in a Vertical Channel

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1 50, Issue 2 (208) 08-7 Journal o Advanced Research in Fluid Mechanics and Thermal Sciences Journal homepae: ISSN: Eects o Dissipation and Radiation on Heat Transer Flow o a Convective Rotatin Cuo-Water Nano-luid in a Vertical Channel Open Access Madduleti Naasasikala, Bommanna Lavanya 2, 2 Department o Mathematics, Govt. Deree Collee (Autonomous),Anantapuramu-5500, A.P, India Department o Mathematics, Manipal Academy o Hiher Education, Madhav Naar, Manipal-57604, Karnataka India ARTICLE INFO Article history: Received Received in revised orm Accepted Available online Keywords: Viscous dissipation, nanoluid, heat transer, vertical channel ABSTRACT In this paper, we systematically investiate the operative o radiation and dissipaton on steady convective heat transer low o a nanoluid in a vertical channel. Analytical closed orm solutions are obtained or both the enery and momentum equations. The impact o various parameters on nanoluid velocity, temperature and concentration ields are shown raphically and tables and analyzed in detail. We ound the siniicance o various parameters on the nanoluid velocity and temperature distributions. Copyriht 208 PENERBIT AKADEMIA BARU - All rihts reserved. Introduction The vertical channel is a most requently encountered coniuration in thermal enineerin equipment, or example, collectors o solar enery, coolin devices o electronic and micro-electronic equipment s etc. The inluence o electrically conductin the case o ully developed mixed convection between horizontal parallel plates with a linear axial temperature distribution was solved by Gill and Casal [2]. Lavanya [] discussed eect o radiation on ree convection heat and mass transer low throuh porous medium in a vertical channel with heat absorption/eneration and chemical reaction. Nanotechnoloy has been broadly used in several industrial applications. It aims at manipulatin the structure o the matter at the molecular level with the oal or innovation in virtually every industry and public endeavour includin bioloical sciences, physical sciences electronics coolin, transportation, the environment and national security. The study o heat transer in the presence o nanoluids is o reat practical importance to enineers and scientists because o there universal occurrence in many branches o science and enineerin. The onoin research ever since then has extended to utilization o nanoluids in Correspondin author. address: lavanyab205@mail.com (Bommanna Lavanya) 08

2 microelectronics, Deense and ships, and boiler lue as temperature reduction [3]. The nanoluids are more stable and have acceptable viscosity and better wettin, spreadin, and dispersion properties on a solid surace [4,5]. Despite vast amount o literature on the low o nanoluid usin a model proposed by Buoniorno [6] and ew others [7,8], we will consider a dierent model which proposed by Abu-Nada Das [9]. This model is bein applied by many rescent studies, like Noriiah et al., [0] on various low ields. The study o low heat transer and MHD Many authors have studied the low and heat transer in a rotatin system with various eometrical situations [-3]. Lavanya [4] studied unsteady MHD convective laminar low between two vertical porous plates with mass transer. Thermal radiation is plays a very important role overall surace heat transer in situations where convective heat transer coeicients are small. The Newtonian approach may be suicient to understand the low o classical luids throuh microchannel under various assumptions [8-9] Satyanarayana et al., have studied the eect o radiation on the convective heat transer low o a rotatin nanoluid past a porous vertical plate with oscillatory velocity. Rahman and sultana investiated the thermal radiation interaction o the boundary layer low o micro polar luid past a heated vertical porous plate embedded in a porous medium with variable suction as well as heat lux in the plate. Recently, Sunitha [6] has discussed the convective heat transer low o Cuo-water nanoluid in a vertical channel in the presence o heat sources. In this paper we carry the systematic enquiry o the eect o dissipation on steady convective heat transer low o rotatin Cuo-water nanoluid in a vertical channel. Analytical closed orm solutions are obtained or both the momentum and the enery equations. Graphs are used to illustrate the siniicance o key parameters on the nanoluid velocity and temperature distributions. 2. Methodoloy We have considered the steady, three dimensional low o a nanoluid consistin o a base luid and small nanoparticles in a vertical porous channel with dissipation and thermal radiation. Table shows the thermo properties o nanoparticles and water. A uniorm manetic ield o strenth Ho is applied normal to the plate. It is assumed that there is no applied voltae which implies the absence o an electric ield. The low is assumed to be in the x-direction which is taken alon the plane in an upward direction and z-axis is normal to the plate. The radiation heat lux in the x-direction is considered neliible in comparison with that in the z-direction. As the low is ully developed, the low variables are unctions o z and t only. Under the above mentioned assumptions, the overnin equations o momentum and thermal enery respectively, can be taken in dimensional orm or this investiation as =0 () 2 = ( +( )( ) ( ) (2)! +2 = (! ( )) (3) " =# " ($ % ) (& ' ) +2 ( + ) (4) 09

3 Where the appropriate boundary conditions are (±)) =0,(±))=0, ( ))=,(+))= The physical properties o the nanoluids are mentioned as ollows = /(.).0 = # (2 3 ) =(.) +. 4 (2 3 ) =(.)(2 5 ) +.(2 5 ) 4 () =(.)() +.() 4 # = # (# 4 +2# 2.(# # 4 ) (# 4 +2# +2.(# # 4 ) Table Thermo properties o nanoparticles and water [7] Properties o particles H20 Cu Al2O3 Cp (J/k K) ρ (k/m 3 ) K (W/m K) β X 0-5 (/K) Equations (2) to (4) in the ordinary non-dimensional orm are = 9 : 9 ; < 9 ; =>? 9 ; (5) 6! !? 9 : 9 ; 7 9 ; (6) 7 = 5 ' ( 9 9 A (+ BC D 7 +2E FG( + ) (7) where E =(.).0 E = # # + 4I 3,E D =.+.( 4 ) E B =.+.(( () 4 () ),E 0 =.+. (2 5) 4 (2 5 ) We have to ind the solution o Equation () as W = -w 0. In this paper, we introduce radiation heat term considerin the Rosseland approximation as ollow K L = BM " < DO P (8) B 4 D 3 B (9) RK S R RT = 6 3 S RT D 0

4 where E =(.).0 E = # # + 4I 3,E D =.+.( 4 ) E B =.+.(( () 4 () ),E 0 =.+. (2 5) 4 (2 5 ) The boundary conditions (5) reduce to (±) =0,(±) =0,>( )=0,>(+)=. 3. Method o Solution The coupled non-linear coupled Equations (5) to (7) have been solved by considerin Fourth order Rune-Kutta Shootin method. The physical quantities o interest are skin riction and Nusselt number which are, represented as 2 = V W X Y (0) Z = [& W \ (" W ]" ) () where τ w and q w are the wall heat lux and the wall shear rom the plate respectively, which are iven by ^ = ( R RT ) _`abck = # ( R RT ) _` In view o Equation () we obtained the ollowin Z = # # > (±)= E > (±) 4. Discussion o Numerical Results In the present paper, we discussed the combined inluence o dissipation and thermal radiation on convective heat and mass transer low o a Cuo-water nanoluid in a vertical channel. The coupled equation overnin the low and heat transer are analytically solved and exhibited in raphs (2-9) or dierent variations o the parameters G,M,R,S F, Ec, φ and Pr. Fiure a and b shows the primary and secondary velocity components with reerence to Grasho number (G). Fiure 2a and 2b represents the imae o velocity component with the chane in manetic parameter. From Fiure 3a and 3b the velocity o nanoluid proiles or dierent values o rotational parameter R. Fiure 4a and 4b depicts velocity with Suction parameter. we observed that velocity enhances with increase in Suction parameter. Fiure 5a and 5b shows the behaviour o the primary and secondary velocities with Eckert parameter (Ec). Fiure 6a and 6b exhibit the eect o thermal radiation. It can be noticed that an increase in thermal radiation results in a decrease in T. Fiure 7a and 7b shows When the volume o the nanoparticle o a luid enhances, the thermal conductivity and the thermal boundary layer thickness increase. Fiure 8b shows that the with φ. Fiure 8a, 8b depicts the variation with respect to Eckert number.

5 Table 2 exhibits the behavior o local skin riction component τ x and Nusselt number Nu at the plates η=±. It is ound that an increase in the Hartmann number M reduces τx at η=- and increases it at η==while an enhance in the rotation parameter R decreases τ x at both the walls. Also τ x reduces with increase in the suction parameter S and the radiation parameter F at η=±. The variation o the skin riction component τx with Ec shows that it decreases with Ec at let wall η=- and enhances at the riht wall η=+.an increase in the nanoparticle volume raction φ reduces τ x or Cu-water nanoluid Lesser the thermal diusivity smaller the skin riction component at η=±. The local Nusselt number (Nu) at η=+ is ound to reduce with enhance in S or Q or φ or F or Prandtl number Pr while at η=-,it enhances with enhance in F or Q >0 or S or φ or Pr and decreases with Q<0 in Cuo-water nanoluid G= 2, 4, 6, 0 Fi. a. Variation o Primary velocity with G M=2, R=, F=, Fi. b. Variation o Secondary velocity () with G M=2, R=, F=, Ec=0.0, Pr=6.2, s=0.2 M=2, M=6, M=2, 4, 6, 8 Fi. 2a. Variation o with M G=0, R=, F=, Fi. 2b. Variation o with G=0, R=, F=, 2

6 3 2 R=,.5, 2, R=,,.5,2, 2.5 Fi. 3a. Variation o with R M=2, G=0, F=, Fi. 3b. Variation o with R M=2, G=0, F=, S=,.5, 2, S=,.5, 2, 2.5 Fi. 4a. Variation o with S M=2, R=, F=, Ec=0.0, Pr=6.2, G=0 Fi. 4b. Variation o with M=2, R=, F=, Ec=0.0, Pr=6.2, G=0 Fi. 4c. Variation o Temperature (θ) with S M=2, R=, F=, Ec=0.0, Pr=6.2, G=0 3

7 Ec= 0.0, 0.03, 0.05, Fi. 5a. Variation o with Ec G=0, M=2, R=, s=0.2, F=, φ=0., Pr= Ec=0.0, 0.03, 0.05, 0.07 Fi. 5b. Variation o with Ec M=2, R=, F=, G=0, Pr=6.2, s=0.2 Fi. 5c. Variation o θ with Ec M=2, R=, F=, G=0, Pr=6.2, s= F=,.5,3,5, F=,.5,3,5,5.0 Fi. 6a. Variation o with F M=2, R=, G=0, Fi. 6b. Variation o with F M=2, R=, G=0, 4

8 F=,.5,3,5, Fi. 6c. Variation o θ with F M=2, R=, G=0, Ec=0.0, Pr=6.2, s=0.2 φ=0.,0.3,, φ=0.,0.3,,0.7 Fi. 7a. Variation o with φ M=2, R=, F=, Fi. 7b. Variation o with φ M=2, R=, F=, θ φ=0.,0.3,, η Fi. 7c. Variation o θ with φ M=2, R=, F=, 5

9 Pr=0.7,.7,3.7, Pr=0.7,.7,3.7, Fi. 8a. Chane o with Pr M=2, R=, F=, Fi. 8b. Variation o θ with Pr M=2, R=, F=, Table 2 Skin riction(τ), Nusselt Number(Nu at η=± M R S Ec F φ Pr τx(+) τx(-) Nu(+) Nu(-) Reerences [] Lavanya, B. "Unsteady MHD Convective laminar low between two Vertical Porous plates with mass transer." Journal o Mechanical Enineerin Research and Developments 47 (208): [2] Ghadimi, A., R. Saidur, and H. S. C. Metselaar. "A review o nanoluid stability properties and characterization in stationary conditions." International journal o heat and mass transer 54, no. 7-8 (20): [3] Mazumder, B. S. "An exact solution o oscillatory Couette low in a rotatin system." Journal o applied mechanics 58, no. 4 (99): [4] Akbarinia, A., Morteza Abdolzadeh, and R. Laur. "Critical investiation o heat transer enhancement usin nanoluids in microchannels with slip and non-slip low reimes." Applied Thermal Enineerin 3, no. 4 (20): [5] Rana, Puneet, and R. Bharava. "Flow and heat transer o a nanoluid over a nonlinearly stretchin sheet: a numerical study." Communications in Nonlinear Science and Numerical Simulation 7, no. (202): [6] Buoniorno, Jacopo. "Convective transport in nanoluids." Journal o heat transer 28, no. 3 (2006): [7] Alsaedi, A., M. Awais, and T. Hayat. "Eects o heat eneration/absorption on stanation point low o nanoluid over a surace with convective boundary conditions." Communications in Nonlinear Science and Numerical Simulation 7, no. (202): [8] Hajipour, Mastaneh, and Ashar Molaei Dehkordi. "Analysis o nanoluid heat transer in parallel-plate vertical channels partially illed with porous medium." International journal o thermal sciences 55 (202): [9] Kumar, B. Rushi, and R. Sivaraj. "Heat and mass transer in MHD viscoelastic luid low over a vertical cone and lat plate with variable viscosity." International Journal o Heat and Mass Transer 56, no. -2 (203):

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