Sains Malaysiana 40(12)(2011): 1429–1435

Thermal Dispersion Effect on Fully Developed Free Convection of Nanofluids in a Vertical Channel

(Kesan Serakan Terma Nanobendalir Olakan Bebas Terbentuk Sepenuhnya dalam Saluran Mengufuk)

Teodor Grosan*

Faculty of Mathematics and Computer Science, Babes-Bolyai University of Cluj, 3400 Cluj, Romania

Received: 24 November 2010 / Accepted: 21 May 2011

ABSTRACT

The effect of thermal dispersion on the steady free convection flow of a nanofluid in a vertical channel is investigated numerically using a single phase model. Considering the laminar and fully developed flow regime a simplified mathematical model is obtained. In the particular cases when solid phase and thermal dispersion effects are neglected the problem was solved analytically. The numerical solution is shown to be in excellent agreement with the close form analytical solution. Nusselt number enhancement with the Grashof number, volume fraction and thermal diffusivity constant increasing has been found.

Keywords: Free convection; fully developed; nanofluid; thermal dispersion

ABSTRAK

Kesan serakan terma pada aliran olakan bebas mantap dalam saluran mengufuk dikaji secara bernombor menggunakan model fasa tunggal. Dengan mengandaikan satu laminar dan regim aliran terbentuk bebas, satu model matematik ringkas telah diperoleh. Dalam kes-kes apabila fasa pepejal dan kesan serakan terma diabaikan, masalah ini dapat diselesaikan secara analitik. Penyelesaian bernombor dan penyelesian analitik didapati bersetuju dengan baik. Peningkatan nombor Nusselt dengan nombor Grashof, pecahan isipadu dan peningkatan pemalar keresapan terma telah diperoleh.

Kata kunci: Nanobendalir; olakan bebas; serakan terma; terbentuk sepenuhnya

REFEREMCES

Abu-Nada, E. 2008. Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. International Journal of Heat and Fluid Flow 29: 242-249.

Aung, W. 1972. Fully developed laminar free convection between vertical plates heated asymmetrically. International Journal of Heat and Mass Transfer 15: 1577-1580.

Aung, W., Fletcher, L.S. & Sernas, V. 1972. Developing laminar free convection between vertical flat plates with asymmetric heating. International Journal of Heat and Mass Transfer 15: 2293-2308.

Bachok N., Ishak, A. & Pop, I. 2010. Boundary-layer flow of nanofluids over a moving surface in a flowing fluid. International Journal of Thermal Sciences 49: 1663-1668.

Bachok, N., Ishak, A., Nazar R. & Pop I. 2010. Flow and heat transfer at a general three-dimensional stagnation point in a nanofluid. Physica B 405: 4914-4918.

Barletta, A. 1999. Analysis of combined forced and free flow in a vertical channel with viscous dissipation and isothermal-isoflux boundary conditions. Journal of Heat Transfer 121: 349-356.

Brinkman, H.C.1952. The viscosity of concentrated suspensions and solutions. Journal of Chemical Physics 20: 571-581.

Daungthongsuk, W. & Wongwises, S. 2007. A critical review of convective heat ransfer of nanofluids. Renewable and Sustainable Energy Reviews 11: 797-817.

Jou, R.-Y. & Tzeng, S.-C. 2006. Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures. International Communications in Heat and Mass Transfer 33: 727-736.

Khaled, A.-R.A. & Vafai, K. 2005. Heat transfer enhancement through control of thermal dispersion effects. International Journal of Heat and Mass Transfer 48: 2172-2185.

Khanafer, K., Vafai, K. & Lightstone, M. 2003. Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids. International Journal of Heat and Mass Transfer 46: 3639-3653.

Kumar, J.P., Umavathi, J.C., Chamkha, A.J. & Pop, I. 2010. Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel. Applied Mathematical Modelling 34: 1175-1186.

Kumar, S., Prasad, S.K. & Banerjee, J. 2010. Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model. Applied Mathematical Modelling 34: 573-592.

Maïga, S.E.B., Nguyen, C.T., Galanis, N. & Roy, G. 2004. Heat transfer behaviour of nanofluids in a uniformly heated tube. Superlattices and Microstructures 35: 543-557.

Mokmeli, A. & Saffar-Avval, M. 2010. Prediction of nanofluid convective heat transfer using the dispersion model. Int. J. Thermal Sci. 49: 471-478.

Oztop, H.F. & Abu-Nada, E. 2008. Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids. International Journal of Heat and Fluid Flow 29: 1326-1336.

Tiwari, R.K. & Das, M.K. 2007. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids. International Journal of Heat and Mass Transfer 50: 2002-2018.

Vajravelu, K. & Sastri, K.S. 1977. Fully developed laminar free convection flow between two parallel vertical walls-I. International Journal of Heat and Mass Transfer 20: 655-660.

Wang, X.-Q. & Mujumdar, A.S. 2008. A review on nanofluids-part I: Theoretical and numerical investigations. Brazilian Journal of Chemical Engineering 25: 613-630.

Xuan, Y. & Roetzel, W. 2000. Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer 43: 3701-3707.

Yacob, N.A., Ishak, A. & Pop, I. 2011. Falkner-Skan problem for a static or moving wedge in nanofluids. International Journal of Thermal Sciences 50: 133-139.

Yacob, N.A., Ishak, A., Nazar R. & Pop, I. 2011. Falkner-Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid. International Communications in Heat and Mass Transfer doi: 10.1016/j.icheatmasstransfer.2010.12.03.

*Corresponding author; email: tgrosan@math.ubbcluj.ro