Abstract
Rayleigh–Bénard convection in nanoliquids is studied in the presence of volumetric heat source. The present analytical work concerns twenty nanoliquids. Carrier liquids considered are water, ethylene glycol, engine oil and glycerine and with them five different nanoparticles considered are copper, copper oxide, silver, alumina and titania. Expression for the thermophysical properties of the nanoliquids is chosen from phenomenological laws or mixture theory. Heat source is characterized by an internal nanoliquid Rayleigh number \(R_{I_{nl}}\). Heat source adds to the energy of the system and hence an advanced onset is observed in this case compared to the problem with no heat source. In the case of heat sink, however, heat is drawn from the system leading to delay in onset. The individual effect of all the nanoparticles is to advance convection. Enhanced heat transport situation is observed in each of the nanoliquids with engine-oil-silver transporting maximum heat and water-titania the least. Additional Fourier modes are found not to have any profound effect on the results predicted by minimal modes. The connection between the Lorenz model and the Ginzburg–Landau model is clearly shown in the paper.
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Acknowledgements
One of us (MN) is grateful to the Department of Science and Technology, Government of India, for awarding a junior research fellowship to carry out her research under the “Promotion for University Research and Scientific Excellence (PURSE)” programme. She is also grateful to the Bangalore University for supporting her research. The authors are grateful to the four anonymous referees for their most useful comments that helped them refine the paper to the present form.
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Meenakshi, N., Siddheshwar, P.G. A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source. J. Appl. Math. Comput. 57, 703–728 (2018). https://doi.org/10.1007/s12190-017-1129-9
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DOI: https://doi.org/10.1007/s12190-017-1129-9
Keywords
- Rayleigh–Bénard convection
- Heat transport
- Nanoliquids
- Heat source
- Lorenz model
- Coupled Ginzburg–Landau equation