MHD effects for a rotating nanofluid layer for LTNE model

Jyoti Ahuja¹,Urvashi Gupta²*

¹Energy Research Centre, Panjab University, Chandigarh-160014, INDIA

²Dr. S.S. Bhatnagar University Institute of Chemical Engineering and Technology, Panjab University, Chandigarh-160014, INDIA

*Corresponding Author Email:dr_urvashi_gupta@yahoo.com

ABSTRACT:

Rayleigh-Bénard convection of a rotating nanofluid layer under local thermal non-equilibrium model in the presence of magnetic field is investigated. The impact of external applied forces rotation and magnetic field are exhibited by introducing Coriolis force term and Lorentz force term in the momentum equations along with the Maxwell’s equations. For considering the impact of local thermal non-equilibrium between the fluid and particle phases; a two-temperature model has been considered. The problem is analysed by making use of the normal mode technique and one term approximation of Galerkin type weighted residual method. Due to thermal non-equilibrium three additional parameters Nield number, modified thermal capacity ratio, modified thermal diffusivity ratio and due to the presence of rotation and magnetic field Taylor number and Chandrasekhar number are introduced. The impact of these parameters on thermal Rayleigh number has been found analytically as well as numerically and presented graphically.

1. INTRODUCTION:

With the invention of nanofluids by Choi (1995), a lot of research work on the thermal instability of nanofluids has been done by Nield and Kuznetsov (2010), Gupta et al. (2013, 2015) and many others with the assumption that temperature difference at any location between the fluid phase and particle phase is negligible. But Vadasz (2006) had proposed that there is thermal lagging between the particle and fluid phase and therefore there is need to take account the local thermal non-equilibrium (LTNE). LTNE model for convective heat transfer has been dealt by Ingham and Pop (1998); Baytas and Pop (2002) and a few among several others. They found that system with LTNE model is found to exhibit less stability than LTE model. Due to applications of nanofluids in everyday technology like microwave heating, freezing of foods, rapid heat transfer through computer chips; study of LTNE model on nanofluids becomes important. In the present paper we investigated the combined impact of rotation and magnetic field on the thermal instability of a nanofluid layer under LTNE model. With the introduction of LTNE some additional parameters Nield number, modified thermal capacity ratio and modified thermal diffusivity ratio get introduced. The impact of all these parameters on the thermal instability of a nanofluid layer is found numerically & presented graphically. It is found that Taylor number, Chandrasekhar number, modified thermal diffusivity and modified thermal capacity ratio enhance the stability of the system while concentration Rayleigh number, Nield number, modified diffusivity ratio and Lewis number hasten the onset of thermal convection.

Figure 2: Comparison of LTNE and LTE

Figure 2 gives a comparative analysis of the stability curves of LTNE and LTE by keeping the values of other parameters fixed. Here the curve of LTNE lies below the curve of LTE which means that LTNE model is less stable as compared to LTE model in the presence of rotation and magnetic field. In LTNE model there is a temperature difference between the fluid phase and particle phase which hastens the onset of convection i.e. convection starts earlier in LTNE model.

2. CONCLUSIONS:

Thermal instability of a rotating nanofluid layer under local thermal non-equilibrium model in the presence of magnetic field is investigated. The problem is investigated by making use of the normal mode technique and one term approximation of Galerkin type weighted residual method. Due to thermal non-equilibrium model, three additional parameters Nield number, modified thermal capacity ratio, modified thermal diffusivity ratio and due to the presence of rotation and magnetic field, Taylor number and Chandrasekhar number are introduced. It is found that rotation and magnetic field while acting simultaneously, inhibit the onset of convection in LTNE model as well. System with LTNE model is found to exhibit less stability than LTE model in the presence of magnetic field and rotation. Further, Taylor number, Chandrasekhar number, modified thermal diffusivity ratio and modified thermal capacity ratio enhance the stability of the system while concentration Rayleigh number, Nield number, modified diffusivity ratio and Lewis number hasten the onset of thermal convection for top heavy distribution of nanoparticles in LTNE.

REFERENCES:

1. Agarwal, S. and Bhadauria, B.S. (2015), Thermal instability of a nanofluid layer under local thermal non-equilibrium, Nano Convergence, DOI:10.1186/s40580-014-0037-z, 1-16.

2. Baytas, A.C., Pop, I. (2002), Free convection in a square porous cavity using a thermal non-equilibrium model, Int. J. thermal Science, 41, 861-870.

3. Buongiorno, J. (2006), Convective transport in nanofluids, ASME Journal of Heat Transfer, 128 (3), 240-250.

4. Chandrasekhar, S. (1981), Hydrodynamic and hydromagnetic stability, Dover Publication, New York.

5. Choi, S. (1995), Enhancing thermal conductivity of fluids with nanoparticles: In D.A. Siginer, H.P. Wang (Eds.), Development and Applications of Non-Newtonian flows, ASME FED- 231/MD-Vol. 66, 99-105.

6. Gupta, U., Ahuja, J., Wanchoo, R.K. (2013), Magneto convection in a nanofluid layer. Int. J. Heat and Mass Transfer, 64, 1163–1171.

7. Gupta, U., Ahuja, J., Wanchoo, R.K. (2015), Rayleigh-Bénard Convection of Nanofluids with Magnetic Field and Permeability Effects, Procedia Engineering, 127C, 325-332.

8. Ingham, D.B. and Pop, I. (1998), Transport Phenomenon in Porous Media, Pergamon, Oxford.

9. Nield, D.A. and Kuznetsov, A.V. (2010), The onset of convection in a horizontal nanofluid layer of finite depth. European J. Mech, B/Fluids, 29, 217–223.

10. Vadasz, P. (2006), Heat conduction in nanofluid suspensions, ASME J. HeatTransf., 128, 465-477.

11. Yadav, D., Bhargava, R., Agrawal, G.S., Hwang, G. S., Lee, J. and Kim, M.C. (2014), Magneto-convection in a rotating layer of nanofluid, Asia-Pacific Journal of Chemical Engineering, 9(5), 663-677.

Received on 26.08.2016 Accepted on 11.09.2016

Int. J. Tech. 2016; 6(2): 209-214.

DOI: 10.5958/2231-3915.2016.00032.8