# Conjugate heat transfer of a nanofluid in a vertical channel adjacent to a heat generating solid domain

## Abstract

The effect of thermal dispersion in the conjugate 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, aspect ratio parameter and thermal diffusivity constant increasing has been found.

## Author

Flavius Patrulescu
(Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy)

Teodor Groşan
(Babeş-Bolyai University Faculty of Mathematics and Computer Sciences)

## Keywords

nanofluid; vertical channel; free convection; conjugate heat transfer; heat generation

## PDF

##### Cite this paper as:

F. Pătrulescu, T. Groşan, Conjugate heat transfer of a nanofluid in a vertical channel adjacent to a heat generating solid domain, Rev. Anal. Numer. Theor. Approx., vol. 39, no. 2 (2010), pp. 141-149

1222-9024

2457-8126

## References

[1] Aung,  Fully developed laminar free convection between vertical plates heated\linebreak asymmetrically, Int. J. Heat Mass Transfer 15 (1972), 1577-1580.
[2] Aung, L.S. Fletcher, V. Sernas, Developing laminar free convection between vertical flat plates with asymmetric heating, Int. J. Heat Mass Transfer 15 (1972), 2293-2308.
[3] Barletta, Analysis of combined forced and free flow in a vertical channel with viscous dissipation and isothermal-isoflux boundary conditions, J. Heat Transfer 121 (1999),349-356.
[4] C. Brinkman, The viscosity of concentrated suspensions and solutions, J. Chem. Phys. 20 (1952), 571-581.
[5] Daungthongsuk, S. Wongwises, A critical review of convective heat transfer of nanofluids, Renewable and Sustainable Energy Reviews 11 (2007), 797-817.
[6] R.A. Khaled, K. Vafai, Heat transfer enhancement through control of thermal dispersion effects, Int. J. Heat Mass Transfer 48 (2005), 2172-2185.
[7] Khanafer, K. Vafai, M. Lightstone, Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids, Int. J. Heat Mass Transfer 46 (2003), 3639-3663.
[8] P. Kumar, J.C. Umavathi, A.J. Chamkha, I. Pop, Fully-developed free-convective flow of micropolar and viscous fluids in a vertical channel, Appl. Math. Modell.  34 (2010), 1175-1186.
[9] Kumar, S.K. Prasad, J. Banerjee, Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model, Appl. Math. Modell. 34 (2010),573-592.
[10] Mokmeli, M. Saffar-Avval, Prediction of nanofluid convective heat transfer using the dispersion model, Int. J. Thermal Sci. 49 (2010), 471-478.
[11] F. Oztop, E. Abu-Nada,  Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, Int. J. Heat Fluid Flow,  29 (2008),1326-1336.
[12] Vajravelu, K. Sastri, Fully developed laminar free convection flow between two parallel vertical walls-I, Int. J. Heat Mass Transfer, 20 (1997), 655-660.
[13] Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer  43 (2000), 3701–3707.
[14] Q. Wang, A. S. Mujumdar,  A review on nanofluids-part I: Theoretical and numerical investigations}, Brazilian Journal of Chemical Engineering,25 (2008), 613-630.