Derivation of turbulent energy of fiber suspensions

[1] Lundell, L. Soderberg and P. Alfredsson, “Fluid mechanics of papermaking”, Annual Review of Fluid Mechanics, Vol. 43, pp. 195-217, (2011).

[2] Zhen-Jiang, L. Jian-Zhong, S. Xueming and Z. Wei-Feng, “Stability and drag reduction in transient channel flow of fiber suspension”, Chinese Journal of Chemical Engineering, Vol. 12, No. 3, pp. 319-323, (2004).

[3] Z. Lin and Z. J. You, “Stability in channel flow with fiber suspensions”, Progress in Natural Science, Vol. 13, No. 2, pp. 95-99, (2003).

[4] Bracco, P. H. Chavanis and A. Provenzale, “Particle aggregation in a turbulent Keplerian flow”, Physics of Fluids, Vol. 11, No. 8, pp. 2280-2287, (1999).

[5] A. Luketina and J. Imberger, “Determining turbulent kinetic energy dissipation from batchelor curve fitting”, Journal of Atmospheric and Oceanic Technology, Vol. 18, No. 1, pp. 100-113, (2001).

[6] R. Osborn, “Estimates of the local rate of vertical diffusion from dissipation measurements”, Journal of Physical Oceanography, Vol. 10, No. 1, pp. 83-89, (1980).

[7] T. Crowe, T. R. Troutt and J. N. Chung, “Numerical models for two-phase turbulent flows”, Annual Review of Fluid Mechanics, Vol. 28, pp. 11-43, (1996).

[8] S. Oakey, “Determination of the rate of dissipation of turbulent energy from simultaneous temperature and velocity shear microstructure measurements”, Journal of Physical Oceanography, Vol. 12, No. 3, pp. 256-271, (1982).

[9] B. Saito and M. J. S. de Lemos, “A macroscopic two-energy equation model for   turbulent flow and heat transfer in highly porous media”, International Journal of Heat and Mass Transfer,  Vol. 35, No. 11-12, pp. 2424-2433, (2010).

[10] Jian-Zhong, Z. Wei-Feng and W. Ye-Long, “Research on the orientation distribution of fibers immersed in a pipe flow”, Journal of Zhejiang University Scence , Vol. 3, No. 5, pp. 501-506, (2002).

[11] Jian-Zhong,  L. Jun and Z. Wei-Feng, “Orientation distribution of fibers in a channel flow of fiber suspension”, Chinese Physics, Vol. 14, No. 12, pp. 2529-2538, (2005).

[12] F. Zhang and J. Z. Lin, “Research on the motion of particles in the turbulent pipe flow of fiber suspensions”, Applied Mathematics and Mechanics, Vol. 25, No. 7, pp. 741-750, (2004).

[13] Jian-Zhong, L. Jun,  Z. LI, and J. A. Olson, “New equation of turbulent fiber suspensions and its solution and application to the pipe flow”, Chinese Physics, Vol. 14, No. 6, pp. 1185-1192, (2005).

[14] Andersson, “Some observation of fiber suspensions in turbulent motion”, Svensk papperstidn, Vol. 69, No. 2, pp. 23-31, (1966).

[15] O. Hinze, Turbulence, 2^nd ed., McGraw-Hill Co., New York, pp. 27-135, (1975).

[16] Chandrasekhar, “Hydro magnetic Turbulence. II. An Elementary Theory”, Proceedings of the Royal Society, Vol. 233, No. 1194, pp. 330-350, (1955).

[17] F. Ahmed and M. S. A. Sarker, “Fiber suspensions in Turbulent Flow with Two-Point Correlation”, Bangladesh Journal of Scientific and Industrial Research, Vol. 46, No. 2, pp. 265-270, (2011).

[18] S. A. Sarker and S. F. Ahmed, “Motion of fibers in turbulent flow in a rotating system”, Rajshahi University Journal of Science, Vol. 37, No. 1, pp. 107-117, (2009).

[19] F. Ahmed, “Turbulent energy for dusty fluid in a rotating system”, International Journal of Applied Mathematics and Mechanics, Vol. 9, No. 1, pp. 50-61, (2013).

[20] F. Ahmed, “Derivation of turbulent energy in a rotating system”, Journal of Computational and Applied Research in Mechanical Engineering, Vol. 3, No. 1, pp. 75-83, (2013).

[21] S. Alam Sarker and S. F. Ahmed, “Fiber Motion in Dusty Fluid Turbulent Flow with Two-point Correlation”, Journal  of  Scientific  Research,  Vol.  3, No. 2, pp. 283-290, (2011).

[22] Mathematics, Vol. 1, No. 4, pp. 71-77 (2013).

[23] F. Ahmed and M. S. A. Sarker, “Fiber Motion in Dusty Fluid Turbulent Flow in a Rotating System”, International Journal of Applied Mathematics and Mechanics, Vol.10, No. 12, pp 92-109, (2014).