Influence of thermal Radiation on Natural Convection Boundary Layer Flow of a Nanofluid Past a Vertical Plate with Uniform Heat Flux

Influence of thermal Radiation on Natural Convection Boundary Layer Flow of a Nanofluid Past a Vertical Plate with Uniform Heat Flux

Machireddy Gnaneswara Reddy

Department of Mathematics, Acharya Nagarjuna University Campus, Ongole, A.P. (India) -523001

Corresponding Author Email: 
mgrmaths@ gmail.com
Page: 
1-7
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DOI: 
https://doi.org/10.18280/ijht.320101
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Published: 
31 December 2014
| Citation

OPEN ACCESS

Abstract: 

In this analysis, the boundary layer flow and heat and mass transfer over a vertical plate due to a nanofluid with the effects of thermal radiation and uniform heat flux have been investigated. The transport equations used in the analysis took into account the effect of Brownian motion and thermophoresis parameters. Similarity transformation is used to convert the governing non-linear boundary-layer equations into coupled higher order non-linear ordinary differential equations. These equations are numerically solved using fourth order Runge-Kutta method along with shooting technique. An analysis has been carried out to elucidate the effects of governing parameters corresponding to various physical conditions. The dimensionless skin friction increases as the Prandtl number, but decreases as the buoyancy ratio parameter and radiation parameter increases. The reduced Nusselt number increases as the Prandtl number and radiation parameter increase. Comparison with published results is presented.

Keywords: 

thermal radiation, brownian motion, thermophoresis, nanofluid, vertical plate

1. Introduction
2. Formulation of the Problem
3. Numerical Solution
4. Results and Discussion
5. Conclusions
Acknowledgement
  References

[1] Choi, S.U.S. Enhancing Thermal Conductivity of Fluids with Nanoparticles (1995), Developments and Applications of Non-Newtonian Flows, FED-231/ MD-vol.66,  pp. 99-105.

[2] Masuda, H., Ebata, A., Teramea, K., Hishinuma, N., Altering the thermal conductivity and viscosity of liquid by dispersing ultra-fine particles, (1993) Netsu Bussei, 4(4), pp. 227-233.

[3] Das, S.K., Putra, N., Thiesen, P., Roetzel, W., Temperature dependence of thermal conductivity enhancement for nanofluids, (2003) Journal of Heat Transfer, 125 (4), pp. 567-574.

[4] Pak, B.C., Cho, Y.I., Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, (1998) Experimental Heat Transfer, 11 (2), pp. 151-170. 

[5] Xuan, Y., Li, Q., Investigation on convective heat transfer and flow features of nanofluids, (2003) Journal of Heat Transfer, 125 (1), pp. 151-155. 

[6] Eastman, J.A., Choi, S.U.S., Li, S., Yu, W., Thompson, L.J., Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles, (2001) Applied Physics Letters, 78 (6), pp. 718-720. 

[7] Mintsa, H.A., Roy, G., Nguyen, C.T., Doucet, D., New temperature dependent thermal conductivity data for water-based nanofluids, (2009) International Journal of Thermal Sciences, 48 (2), pp. 363-371.

[8] Buongiorno, J., Hu, L.-W., Nanofluid coolants for advanced nuclear power plants, (2005) Proceedings of the American Nuclear Society - International Congress on Advances in Nuclear Power Plants 2005, ICAPP'05, 6, pp. 3581-3585. 

[9] Shukla, K.N., Solomon, A.B., Pillai, B.C., Ibrahim, M., Thermal performance of cylindrical heat pipe using nanofluids, (2010) Journal of Thermophysics and Heat Transfer, 24 (4), pp. 796-802. 

[10] Trisaksri, V., Wongwises, S., Critical review of heat transfer characteristics of nanofluids, (2007) Renewable and Sustainable Energy Reviews, 11 (3), pp. 512-523. 

[11] Wang, X.-Q., Mujumdar, A.S., Heat transfer characteristics of nanofluids: a review, (2007) International Journal of Thermal Sciences, 46 (1), pp. 1-19. 

[12] Eastman, J.A., Phillpot, S.R., Choi, S.U.S., Keblinski, P., Thermal transport in nanofluids, (2004) Annual Review of Materials Research, 34, pp. 219-246. 

[13] Kakaç, S., Pramuanjaroenkij, A., Review of convective heat transfer enhancement with nanofluids, (2009) International Journal of Heat and Mass Transfer, 52 (13-14), pp. 3187-3196. 

[14] Buongiorno, J., Venerus, D.C., Prabhat, N., McKrell, T., Townsend, J., Christianson, R., Tolmachev, Y.V., (...), Zhou, S.-Q., A benchmark study on the thermal conductivity of nanofluids, (2009) Journal of Applied Physics, 106 (9), art. no. 094312. 

[15] Khanafer, K., Vafai, K., Lightstone, M., Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, (2003) International Journal of Heat and Mass Transfer, 46 (19), pp. 3639-3653. 

[16] Kim, J., Kang, Y.T., Choi, C.-K., Analysis of convective instability and heat transfer characteristics of nanofluids, (2004) Physics of Fluids, 16 (7), pp. 2395-2401. 

[17] Tzou, D.Y., Thermal instability of nanofluids in natural convection, (2008) International Journal of Heat and Mass Transfer, 51 (11-12), pp. 2967-2979. 

[18] Putra, N., Roetzel, W., Das, S.K., Natural convection of nano-fluids, (2003) Heat and Mass Transfer/Waerme- und Stoffuebertragung, 39 (8-9), pp. 775-784. 

[19] Wen, D., Ding, Y., Formulation of nanofluids for natural convective heat transfer applications, (2005) International Journal of Heat and Fluid Flow, 26 (6), pp. 855-864. 

[20] Abu-Nada, E., Masoud, Z., Oztop, H.F., Campo, A., Effect of nanofluid variable properties on natural convection in enclosures, (2010) International Journal of Thermal Sciences, 49 (3), pp. 479-491. 

[21] Khan, W.A., Aziz, A., Natural convection flow of a nanofluid over a vertical plate with uniform surface heat flux, (2011) International Journal of Thermal Sciences, 50 (7), pp. 1207-1214. 

[22] Reddy, M.G., Mass transfer effects on the unsteady mhd radiative- convective flow of a micropolar fluid past a vertical porous plate with variable heat and mass fluxes, (2013) Journal of Engineering Physics and Thermophysics, 86 (2), pp. 431-441.

[23] Reddy, M.G., Thermophoresis effects on MHD combined heat and mass transfer in two-dimensional flow over an inclined radiative isothermal permeable surface, (2013) Acta Technica CSAV (Ceskoslovensk Akademie Ved), 58 (1), pp. 41-58. 

[24] Gnaneswara Reddy, M., Influence of magnetohydrodynamic and thermal radiation boundary layer flow of a nanofluid past a stretching sheet, (2014) J. Sci. Res., 6 (2), pp. 257-272. 

[25] Reddy, M.G., Effects of thermophoresis, viscous dissipation and joule heating on steady mhd heat and mass transfer flow over an inclined radiative isothermal permeable surface with variable thermal conductivity, (2012) International Journal of Heat and Technology, 30 (1), pp. 99-107. 

[26] Rahman, M.M., Ariz, A., Heat transfer in water based nanofluids (TiO2-H2O, Al2O3-H2O and Cu-H2O) over a stretching cylinder, (2012) International Journal of Heat and Technology, 30 (2), pp. 31-42. 

[27] Kuznetsov, A.V., Nield, D.A., Natural convective boundary-layer flow of a nanofluid past a vertical plate, (2010) International Journal of Thermal Sciences, 49 (2), pp. 243-247. 

[28] Brewster, M.Q., (1992) Thermal Radiative Transfer and Properties, John Wiley & Sons, New York.

[29] De Wrachien, D., Lorenzini, G., Medici, M., Water droplet and aerial path in irrigation systems: Classical and quantum termofluidynamical approaches and numerical approximation methods, (2013) Int.J. of HEAT &tECH, 31, pp. 81-86.