MHD Flow and Heat Transfer of a Dusty Nanofluid over a Stretching Surface in a Porous Medium

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1 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 MHD Flow and Heat Transer o a Dusty Nanoluid over a Stretching Surace in a Porous Medium Sandee, N. 1) and Saleem, S. ) 1) Proessor, VIT University, India. sandee@vit.ac.in ) COMSATS Institute o Inormation Technology; Pakistan. salmansaleem_33@hotmail.com ABSTRACT With every assing day, heat transer enhancement in convectional base luids lays a major role in several industrial and engineering rocesses. During this rocess, nanoluids attained great imortance to enhance the heat transer rate in convectional lows. Keeing this into view, in this study, we analyzed the MHD low and heat transer characteristics o a dusty nanoluid over a stretching surace in the resence o a volume raction o dust and nano-articles. We have considered two tyes o nanoluids; namely, CuO-water and Al O 3 -water immersed with dust articles. The governing artial dierential equations are transormed into a set o nonlinear ordinary dierential equations by using similarity transormation, which are then solved numerically using Runge-Kutta based shooting technique. We ound an excellent agreement o the resent results with the existing literature. The eects o non-dimensional governing arameters; namely, magnetic ield, volume raction o dust articles, volume raction o nano-articles, orosity, mass concentration o dust articles and luid article interaction on velocity and temerature roiles or both luid and dust hases are discussed and resented through grahs. Also, skin riction coeicient and local Nusselt number are discussed and resented in tabular orm. KEYWORDS: MHD, Dusty luid, Nanoluid, Stretching sheet, Volume raction, Convection, Porous medium. INTRODUCTION The momentum and heat transer characteristics o an MHD low over a stretching surace have tremendous alications in engineering and alied sciences. Many researchers have investigated the momentum and heat transer characteristics o either dusty or nanoluids through dierent channels. In the resent study, we are taking initiation to analyze the momentum and heat transer characteristics o a dusty nanoluid (nanoluid embedded with dust articles) over a stretching surace, by considering volume raction o dust articles (in m) and volume raction Received on 11/9/015. Acceted or Publication on 9/11/016. o nano-articles (in m). During the ast decade, research on nanoluids was very much develoed due to its alications in engineering, such as transortation, micro-mechanics, otical devices, electronics and cooling devices. All these alications are due to the enhancement in heat transer erormance in nanoluids. Laminar low o dusty gases was irst discussed by Saman (196). Hamilton and Crosser (196) roosed a ormulation or the eective thermal conductivity or two-comonent systems. The behavior o dusty gases at dierent environments was irst analyzed by Marble (1970). Chakrabarti and Guta (1979) studied MHD low and heat transer characteristics over a stretching surace. Bujurke et al. (1987) illustrated heat transer characteristics o a JUST. All Rights Reserved.

2 MHD Flow and Heat Transer Sandee, N. and Saleem, S. second order luid over a stretching surace. Debnath and Ghosh (1988) discussed an unsteady MHD low o a dusty luid between two oscillating lates. Chen and Char (1998) analyzed the heat transer characteristics o a nanoluid over a continuous stretching surace by considering suction/injection eects. Sattar and Alam (1994) studied MHD heat and mass transer low over an accelerated vertical orous late. Choi (1995) was the irst erson who introduced the concet o nanoluid. He immersed nanometer-sized articles into a base luid and observed the increase in heat transer rate o nano-article mixed base luid. Sandee and Sulochana (015) analyzed the heat transer characteristics o a nanoluid by immersing the conducting dust articles. Chen (1998) studied the laminar mixed convection low over a continuously stretching surace. An unsteady MHD low over a nonisothermal stretching sheet in a orous medium was studied by Chamkha (1998). MHD dusty viscoelastic Maxwell luid low over a rectangular channel was discussed by Ghosh (000). Begewadi and Shantharajaa (000) have considered Frenet Frame and discussed dusty gas low over it. Stagnation-oint low and heat transer behavior o Cuwater nanoluid with two dierent channels were discussed by Sulochana and Sandee (015). A mathematical model or dusty gas low over a naturally occurred orous media was resented by Allan et al. (004). Elena and Dilee Singh (009) studied the inluence o article shae on alumina nanoluid lows. Saidu et al. (010) discussed the convective low and heat transer o dusty luid by considering volume raction o dust articles. Khan and Po (010) studied the boundary layer theories o a nanoluid over a stretching surace. Eect o radiation and viscous dissiation on stagnation-oint low o a microolar luid over a nonlinearly stretching surace with suction or injection eects was studied by Jayachandra Babu et al. (015). Abu-Nada and Chamka (010) analyzed the natural convection low o a nanoluid illed with CuO- EG-water with variable thermal roerties. Magneto hydrodynamic low and heat transer characteristics o a dusty luid over a stretching surace were resented by Gireesha et al. (01). Remeli et al. (01) considered a Marangoni-driven boundary layer model and discussed the low and heat transer characteristics o a nanoluid with suction and injection eects. Dusty viscous luid low in a orous medium over a moving hot vertical surace with diusion eect was analyzed by Anurag Dubey and Singh (01). Sandee et al. (013) analyzed the radiation eects on ethylene glycol-based nanoluids over an ininite vertical late. Mohan Krishna et al. (014) analyzed the radiation eect on an unsteady natural convective low o an MHD nanoluid over a vertical late by considering heat source eect. Recently, Ramana Reddy et al. (014) discussed the eects o an aligned magnetic ield and radiation on dusty viscous low by considering heat generation/absortion. Ferdows et al. (014) have studied the boundary layer low and heat transer o a nanoluid over a ermeable stretching surace. Dessie et al. (014) discussed the scaling grou analysis on MHD ree convective heat and mass transer over a stretching surace with suction/injection eects. All the above mentioned studies ocused on either dusty or nanoluid lows through dierent channels. To the authors knowledge, the resent study is a new initiative and no studies have so ar been reorted on the MHD low and heat transer characteristics o a dusty nanoluid over a stretching surace in the resence o a volume raction o dust and nanoarticles in a orous medium. Numerical results have been extracted or this study. The eects o nondimensional governing arameters on velocity and temerature roiles or both luid and dust hases are discussed and resented through grahs. Also, skin riction coeicient and Nusselt number are discussed and resented in tabular orm. FLOW ANALYSIS Consider a steady, two-dimensional, laminar, incomressible and electrically conducting boundary

3 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 layer low o a dusty nanoluid ast a stretching sheet. The sheet is along the lane y 0 and the low is being conined to y 0. The low is generated by the two equal and oosite orces acting along the x - axis and the y - axis is normal to it. The sheet is being u x along the x - axis. stretched with the velocity w() The low ield is exosed to the inluence o the B along the x -axis. external magnetic ield strength 0 The dust articles are assumed uniorm in size. Sherical shaed nano and dust articles are considered. Number density o dust articles along with volume raction o dust and nano-articles are taken into account. The boundary layer equations that govern the resent low as er the above assumtions are given as ollows: u v 0, (1) x y u u u n (1 d ) u v (1 d ) n KN( u ) u B0 u u, x y y k1 () u u K u v ( uu), x y m u v x y 0, with the boundary conditions: u u ( ), 0 w x v at y 0, u 0, u 0, v v as y, (5) (3) (4) where (,) uv and ( u, v ) are the velocity comonents o the nanoluid and dust hases in the x and y directions, resectively, d is the volume raction o dust articles (i. e., the volume occuied by the dust articles er unit volume o the mixture), n is the dynamic viscosity o the nanoluid, K is the Stokes resistance, m is the mass o the dust articles, N is the number density o dust articles, n is the density o the nanoluid,, B0 are the electrical conductivity and induced magnetic ield, resectively, k is the ermeability o the orous medium and 1 u (), 0 w x cx c is the stretching sheet velocity. The nanoluid constants are: ( c) n (1 )( c) ( c) s,, n.5 (1 ) kn ( ks k ) ( k ks ), k ( k k ) ( k k ) s s (1 ), (6) n s where is the volume raction o nano-articles. The subscrits and s reer to luid and solid roerties, resectively. For similarity solution, we introduced the ollowing similarity transormation: u cx '( ), u v c ( ), 1/ 1/ 1/ 1/ c y, 1/ 1/ cxf '( ), v c F( ), (7) Equation (7) identically satisies equations (1) and (4). Now, equations () and (3) become: 1 d F M K.5 (1 ) s (1 d ) 1 ( '') ( ' ') ( 1) 0, (8)

4 MHD Flow and Heat Transer Sandee, N. and Saleem, S. F ' FF '' ( F ' ') 0, (9) with the transormed boundary conditions: '( ) 1, ( ) 0 at 0, '( ) 0, F '( ) 0, F( ) ( ) as, (10) where Nm / is the mass concentration o dust articles, K / cm is the luid article interaction arameter or the velocity, M B / 0 c is the magnetic ield arameter and K1 / ck1 is the orosity arameter. HEAT TRANSFER ANALYSIS The governing boundary layer heat transort equations or dusty nanoluid are: T T T N1( c) N1 ( c) n u v kn ( T ) ( ), T u u x y y T (11) T T N1( c) Nc 1 mu v ( T T), x y T (1) where T and T are the temerature o nanoluid and dust articles, resectively, k n is the eective thermal conductivity o the nanoluid, ( c), c m are the seciic heat o the luid and dust articles, resectively, N1 Nm is the density o the article hase, T is the thermal equilibrium time and is the relaxation time o dust articles. We considered temerature boundary conditions in order to solve equations (11) and (1) as: / T T T A x l at y 0, w, T T T T as y, (13) where Tw, T are the temeratures near the wall and ar away rom the wall, resectively and 1/ 1/ l c 0 is a characteristic length. We now introduce the ollowing non-dimensional variables to get the similarity solutions o equations (11) and (1). T T T T ( ), ( ), T T T T where w T T A x l A ( / ) ( ), 0. w (14) Using Eqs. (13) and (14) in Eqs. (11) and (1), we get the ordinary dierential equations as: / / " / 0, (15) The transormed boundary conditions are: ( ) 1at 0, ( ) 0, ( ) 0 as, (17) ' F ' F T ( ) 0, (16) where Pr v / is the Prandtl number, T 1/ c T is the luid article interaction arameter or temerature, Ec cl /A( c ) is the Eckert number, ( c ) / c is the ratio o seciic heat m o the luid to that o the dust articles

5 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 For the engineering interest, the skin riction coeicient C and the local Nusselt number Nu x are deined as: C / u, Nu xq / k ( T T ), w n w x w n w (18) where the surace shear stress w and the surace heat lux qw are given by: u T w n, qw kn, (19) y y y0 y0 Using non-dimensional variables, we get: C 1/ 1/ Re x ''(0),Nu x Re x '(0), (0) where / is the local Reynolds number. RESULTS AND DISCUSSION The couled ordinary dierential equations (8), (9), (15) and (16) subject to the boundary conditions as in equations (10) and (17) are solved numerically using Runge-Kutta based shooting technique. The results obtained show the inluences o the non-dimensional governing arameters; namely: magnetic ield arameter M,volume raction o dust articles d, volume raction o nano-articles, orosity arameter K, mass concentration o the dust articles, luid article interaction arameter or velocity and luid article interaction arameter or temerature T on velocity and temerature roiles or luid and dust hases or CuO-water and Al O 3 -water dusty nanoluids. These inluences were discussed and resented in tabular orm. Also, skin riction coeicient and Nusselt number are discussed and resented through tables. For numerical results, we considered 0., 0.5, 3, 0.1, 1. These values were ket constant in the entire study as shown in the igures. The thermohysical roerties o water, coer oxide (CuO) and aluminum oxide (Al O 3 ) are given in Table 1. Table 1. Thermo-hysical roerties o base luid and dierent nano-articles ( Kg m ) c J Kg K kwm 1 K 1 ( ) ( ) HO CuO Al O Figs. 1 and deict the variation in velocity and temerature roiles or luid and dust hases or dierent values o the magnetic ield arameter (M). It is evident that an increase in the magnetic ield arameter dereciates the velocity roiles and enhances the temerature roiles o both luid and dust hases. Generally, an increase in the magnetic ield develos the oosite orce to the low, which is called Lorentz orce. This orce declines the velocity boundary layer and imroves the thermal boundary layer. We noticed an interesting result; namely that an increase in the magnetic ield arameter imroves the temerature roiles o CuO-water dusty nanoluid comared with those o Al O 3 -water dusty nanoluid. Figs. 3 and 4 illustrate the variation in velocity and temerature roiles or luid and dust hases o CuOwater and Al O 3 -water dusty nanoluids or dierent values o volume raction o nano-articles ( ). It is clear rom Figure 3 that an increase in the volume raction o nano-articles enhances the velocity roiles o the luid and dust hases. But rom Figure 4, we observe an arousing result; namely that an increase in the volume raction o nano-articles increases the temerature roiles o the luid hase, but declines the

6 MHD Flow and Heat Transer Sandee, N. and Saleem, S. temerature roiles o the dust hase. We may exlain this henomenon by that increased values o volume raction o the nano-articles enhance the thermal conductivity o the luid due to good interaction with the base luid. But, in dust hase, the mean interacting time between articles is longer than that between luid and articles. Figs. 5 and 6 show the variation in velocity and temerature roiles or luid and dust hases o CuOwater and Al O 3 -water dusty nanoluids or dierent values o volume raction o dust articles ( d ). It is clear that an enhancement in the volume raction o dust articles dereciates the velocity roiles and imroves the temerature roiles o both luid and dust hases. Generally, size o dust articles is in micro/millimeters. So, an increase in the volume raction o dust articles enhances the volume occuied by dust articles. These articles slow down the velocity roiles due to shear stress near the walls. We have noticed a slight enhancement in the temerature roiles o both luid and dust hases due to increased thermal conductivity. Here, it is worth mentioning that rom Figs. 4 and 6, it is ound that the increasing sense in the temerature roiles is due to an increase in the volume raction o nano-articles. But, we have seen a very small amount o increment in the temerature roiles with an increase in the volume raction o dust articles. This roves that nano-articles are eective thermal enhancement materials while comared with dust articles. Figs. 7 and 8 dislay the variation in velocity and temerature roiles or luid and dust hases or dierent values o orosity arameter ( K ). It is evident rom these igures that an increase in the orosity arameter decreases the velocity roiles and increases the temerature roiles o both luid and article hases. This is due to the act that increasing values o orosity arameter widen the orous layers, thereby leading to decline the velocity roiles. But, orosity arameter has a tendency to generate internal heat to the low, thereby imroving the temerature roiles o both luid and dust hases. Figs. 9 and 10 reveal the variation in velocity and temerature roiles or luid and dust hases or dierent values o mass concentration o dust articles ( ). It is observed that an increase in the mass concentration o dust articles dereciates the velocity roiles o the luid and dust hases and boosts the temerature roiles or both hases. Generally, an increase in mass concentration o dust articles means an increase in the number density o dust articles. It is exected that i the number density o dust articles increases, then this declines the velocity roiles and enhances the thermal boundary layer thickness. This agrees with the general act. Figs. 11 and 1 deict the variation in velocity and temerature roiles or luid and dust hases or dierent values o luid article interaction arameter or velocity ( ). It is noticed that an increase in the luid article interaction arameter increases the velocity and temerature roiles o the dust hase and decreases the velocity and temerature roiles o the luid hase or both luids. This is due to the act that the interaction between luid and articles is high, causing the article hase to slow down the luid velocity till article velocity reaches luid velocity. During this time interval, the article hase continuously dominates the luid hase till both are having equal velocities. The enhancement in temerature roiles is due to imrovement in thermal conductivity. Fig. 13 shows the variation in temerature roiles or luid and dust hases or dierent values o luid article interaction arameter or temerature ( T ). It is clear that an increase in the luid article interaction arameter or temerature dereciates the temerature roiles or both luid and dust hases. A uniorm dereciation in temerature roiles o both dusty nanoluids is noticed with an increment in. Physically, increasing the T values o T develos the oosite orce to the low and reduces the thermal boundary layer thickness. Tables and 3, resectively, reresent the eects o various non-dimensional governing arameters on skin riction coeicient and Nusselt number oral O 3 -water and CuO-water dusty nanoluids. It is observed rom the tables that enhancing the values o magnetic ield arameter, volume raction o nano-articles, volume

7 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 raction o dust articles, orosity arameter and mass concentration o dust articles dereciates riction actor along with heat transer rate in both dusty nanoluids. But, an increase in the volume raction o dust articles causes a artial decrement in heat transer rate. Increasing luid article interaction arameters or velocity and temerature causes an enhancement in heat transer rate in both dusty nanoluids. But, we have seen negligible dereciation in riction actor o Al O 3 -water dusty nanoluid by an increase in luid article interaction arameter or temerature. Increasing the value o luid article interaction arameter or velocity does not show any eect on riction actor o CuO-water dusty nanoluid. Table 4 shows the validation o the resent results with the existing results o Gireesha et al. (01) under some secial assumtions. We ound an excellent agreement o the resent results with the existing results. This roves the validity o the resent study along with the numerical technique used in this study. Table. Variation in ''(0) and '(0) or Al O 3 -water dusty nanoluid M d K T "(0) - '(0)

8 MHD Flow and Heat Transer Sandee, N. and Saleem, S. Table 3. Variation in "(0) and - '(0) or CuO-water dusty nanoluid M d K T "(0) - '(0) Table 4. Comarison o the resent results with existing studies in the resence o Prandtl number Pr Gireesha et al. (015) Present Study Figure (1): Velocity roiles o luid and dust hases or various values o M

9 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 Figure (): Temerature roiles o luid and dust hases or various values o M Figure (3): Velocity roiles o luid and dust hases or various values o

10 MHD Flow and Heat Transer Sandee, N. and Saleem, S. Figure (4): Temerature roiles o luid and dust hases or various values o Figure (5): Velocity roiles o luid and dust hases or various values o d

11 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 Figure (6): Temerature roiles o luid and dust hases or various values o d Figure (7): Velocity roiles o luid and dust hases or various values o K

12 MHD Flow and Heat Transer Sandee, N. and Saleem, S. Figure (8): Temerature roiles o luid and dust hases or various values o K Figure (9): Velocity roiles o luid and dust hases or various values o

13 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 Figure (10): Temerature roiles o luid and dust hases or various values o Figure (11): Velocity roiles o luid and dust hases or various values o

14 MHD Flow and Heat Transer Sandee, N. and Saleem, S. Figure (1): Temerature roiles o luid and dust hases or various values o Figure (13): Temerature roiles o luid and dust hases or various values o T

15 Jordan Journal o Civil Engineering, Volume 11, No. 1, 017 CONCLUSIONS In this study, we resented the numerical results or analyzing the momentum and heat transer characteristics o MHD low o a dusty nanoluid over a stretching surace in the resence o volume raction o dust and nano-articles in a orous medium. We considered CuO-water and Al O 3 -water nanoluids immersed with dust articles. The eects o nondimensional governing arameters on velocity and temerature roiles or both luid and dust hases are discussed and resented through grahs. Also, skin riction coeicient and Nusselt number are discussed and resented or two dusty nanoluids searately in tabular orm. The conclusions o the resent study are as ollows: An increase in luid article interaction enhances the heat transer rate. An increase in the volume raction o dust articles and volume raction o nano-articles imroves the temerature roiles o the low. This eect is higher on CuO-water dusty nanoluid comared with that on Al O 3 -water dusty nanoluid. Enhancement in mass concentration o dust articles declines the velocity boundary layer thickness and imroves the temerature boundary layer thickness. A rise in the value o luid article interaction arameter or velocity dereciates the velocity roiles o luid hase, but imroves the velocity o dust hase. REFERENCES Abu-Nada, E., and Chamkha, A.J. (010). Eect o nanoluid variable roerties on natural convection in enclosures illed with a CuO-EG-water nanoluid. Int.J. o Thermal Sci., 49, Allan, F.M., Qatanani, N., Barghouthi, I., and Takatka, M.K. (004). Dusty gas model o low through naturally occurring orous media. A. Math.Com., (148), Anurag Dubey, and Singh, U.R. (01). Eect o dusty viscous luid on unsteady laminar ree convective low through a orous medium along a moving orous hot vertical sheet with thermal diusion. Alied Mathematical Sciences, 6, Begewadi, C.S., and Shantharajaa, A.N. (000). A study o unsteady dusty gas low in Frenet Frame ield. Ind. J. Pure and A. Math., 31, Bujurke, N.M., Biradar, S.N., and Hiremath, P.S. (1987). Second-order luid low ast a stretching sheet with heat transer. Z. Angew Math.Phys., 38, Chamkha, A. J. (1998). Unsteady hydro-magnetic low and heat transer rom a non-isothermal stretching sheet immersed in a orous medium. Int.Comm. in Heat and Mass Transer, 5, Charkrabarti, A., and Guta, A.S. (1979). Hydro-magnetic low and heat transer over a stretching sheet. Quart.Al.Math., 37, Chen, C.H. (1998). Laminar mixed convection adjacent to vertical, continuously stretching sheets. Heat Mass Transer, 33, Chen, C.K., and Char, M.I. (1998). Heat transer o a continuous stretching surace with suction or blowing. J. Math. Anal. Al., 135, Choi, S.U.S. (1995). Enhanced thermal conductivity o nanoluids with nano-articles, develoment and alications o Newtonian lows. FED, 66, Debnath, L., and Ghosh, A.K. (1988). On unsteady hydromagnetic lows o a dusty luid between two oscillating lates. Al. Sci. Res., 45,

16 MHD Flow and Heat Transer Sandee, N. and Saleem, S. Dessie, H., and Kishan, N. (014). Scaling grou analysis on MHD ree convective heat and mass transer over a stretching surace with suction/injection, heat source/sink considering viscous dissiation and chemical reaction eects. Alications and Alied Mathematics: An International Journal, 9 (), Elena, V.T., and Dilee Singh, J. L. R. (009). Particle shae eect on thermo-hysical roerties o alumina nanoluids. Journal o Alied Physics, 106, DOI: / Ferdows, M.S., Chaal, M., and Aiy, A.A. (014). Boundary layer low and heat transer o a nanoluid over a ermeable unsteady stretching sheet with viscous dissiation. J. Eng. Thermo-hysics, 3, Ghosh, B.C. (000). Hydromagnetic low o a dusty viscoelastic Maxwell luid through a rectangular channel. Int. J. Al. Mech. Eng., 7, Gireesha, B.J., Rooa, G.S., Lokesh, H.J., and Bagewadi, C.S. (01). MHD low and heat transer o a dusty luid over a stretching sheet. Int. J. Phys. and Math. Sci., 3, Hamilton, R.L., and Crosser, O.K. (196). Thermal conductivity o heterogeneous two-comonent systems". J. o Industrial and Eng. Chemistry Fundamentals, 1 (3), Jayachandra Babu, M., Radha Guta, and Sandee, N. (015). Eect o radiation and viscous dissiation on stagnation-oint low o a microolar luid over a nonlinearly stretching surace with suction/injection". J. o Basic and Alied Research Int., 7, 73-8 Khan, W.A., and Po, I. (010). Boundary-layer low o a nanoluid ast a stretching sheet. Int. J. Heat Mass Trans., 53, Marble, F.E. (1970). Dynamics o dusty gases. Annual Review o Fluid Mechanics,, DOI: /annurev. l Mohankrishna, P., Sugunamma, V., and Sandee, N. (014). Radiation and magnetic ield eects on unsteady natural convection low o a nanoluid ast an ininite vertical late with heat source. Chemical and Process Engineering Research, 5, Ramana Reddy, J.V., Sugunamma, V., Mohan Krishna, P., and Sandee, N. (014). Aligned magnetic ield, radiation and chemical reaction eects on unsteady dusty viscous low with heat generation/absortion. Chemical and Process Eng. Research, 7, Remeli, A., Ariin, N.M., Ismail, F., and Po, I. (01). Marangoni driven boundary layer low in a nanoluid with suction/injection. World Alied Sciences Journal, 17, 1-6. Saman, P.G. (196). "On the stability o laminar low o a dusty gas". J. Fluid Dynamics, 13, Saidu, I., Waziri, M.M., Abubakar Roko, and Hamisu, M. (010). MHD eects on convective low o dusty viscous luid with volume raction o dust articles. ARPN J. o Eng. and Alied Sciences, 5, Sandee, N., Sugunamma, V., and Mohan Krishna, P. (013). Eects o radiation on an unsteady natural convective low o an EG-nimonic 80 nanoluid ast an ininite vertical late. Int. Journal o Advances in Physics Theories and Alications, 3, Sandee, N., and Sulochana, C. (015). MHD low o a dusty nanoluid over a stretching surace with volume raction o dust articles. Ain Shams Engineering Journal (In Press). Sattar, M.A., and Alam, M.M. (1994). Thermal diusion as well as transiration eects on MHD ree convection and mass transer low ast an accelerated vertical orous late. Indian J. Pure A. Math., 5, Sulochana, C., and Sandee, N. (015). Stagnation-oint low and heat transer behavior o Cu-water nanoluid towards horizontal and exonentially stretching/shrinking cylinders. Alied Nanoscience, 5,