2
Comment on the paper “MHD pseudo-plastic nanofluid unsteady flow and heat transfer in a finite thin film over stretching surface with internal heat generation, Yanhai Lin, Liancun Zheng, Xinxin Zhang, Lianxi Ma, Goong Chen, International Journal of Heat and Mass Transfer 84 (2015) 903–911"
Asterios Pantokratoras
School of Engineering, Democritus University of Thrace,
67100 Xanthi – Greece
e-mail:
In the above paper the energy equation is written as
(1)
where T is the fluid temperature, t is the time, u and v are the velocity components in x and y directions, is the fluid thermal diffusivity, Q(t) is the heat source and n is the power-law index of the non-Newtonian fluid. The fluid is characterized as shear-thinning for, shear-thickening for , and Newtonian for. The above energy equation is an artificial equation and is not correct. The correct form is
(2)
One of the first works of heat transfer in non-Newtonian power-law fluids is that by Acrivos (1960). The investigation continues up to date. See for example the recent work by Guha and Pradnan (2014). In all these works (see also the references) the energy equation (2) is used and not the form of equation (1).
References
1. Acrivos, A. A Theoretical Analysis of Laminar Natural Convection Heat Transfer to Non-Newtonian Fluids, AIChE Journal, 1960, Vol. 16, pp. 584-590.
2. Capobianchi, M. and Aziz, A. Laminar Natural Convection From an Isothermal Vertical Surface to Pseudoplastic and Dilatant Fluids, ASME Journal of Heat Transfer, 2012; 134: 122502-1.
3. Guha, A. and Pradnan, K. Natural convection of non-Newtonian power-law fluids on a horizontal plate International Journal of Heat and Mass Transfer 70 (2014) 930–938
4. Huang, M-J., Huang, J-S, Chou, Y-L and Chen, C-K, Effects of Prandtl Number on Free Convection Heat Transfer From a Vertical Plate to a non-Newtonian fluid, ASME Journal of Heat Transfer, Vol. 111 (1989), 189-191.