193 Downloads 1117 Views
Author(s)
Md. Mamun Molla, Department of Mathematics & Physics, North South University, Dhaka, Bangladesh.
S. Ghosh Moulic, Department of Mechanical Engineering, Indian Institute of Technology, Kharagpur, Kharagpur 721302, India
LunShin Yao, School for Engineering of Matter, Transport and Energy, Arizona State University, Arizona, 85287, USA.
Abstract
Fullydeveloped forced convection heat transfer of a pseudoplastic fluid in a uniformly heated circular tube has been studied. The model used is a modification of the twoparameter Ostwaldde Waele power law, which correctly represents the upper and lower regions of Newtonian behavior shown by pseudoplastic or shearthinning polymer melts and solutions. Results for a shearthinning polymer solution, for which experimental data for the apparent viscosity is available over a large range of shearrate magnitudes, predicted using the modified powerlaw viscosity model, have been presented. A new nondimensional shearrate parameter governing the flow has been identified. The nonNewtonian fluid mechanics community has been unaware of the existence of this parameter. The paradox in the prediction of boundary layer flows caused by lack of knowledge of this parameter has been well documented by our previous studies. In this paper, we discuss it for nonboundarylayer flows. The momentum and energy equations have been solved numerically, for fully developed pipe flow, by the trapezoidal rule and finite volume method respectively. The results indicate that there are three regimes of flow. When the shearrate parameter is small, the fluid behaves like a Newtonian fluid and the Nusselt number is identical to that for a Newtonian fluid. At intermediate values of the shearrate parameter, there are two regions of flow: a central region where the fluid behaves like a Newtonian fluid and an outer region where the fluid behaves like a powerlaw fluid. The Nusselt numbers predicted by the modified power law and power law models agree in this intermediate range of shear rates. When the shearrate parameter is large, there are two Newtonian regions, one near the axis and one near the wall, with a middle powerlaw zone.
Keywords
NonNewtonian fluid, modified powerlaw, forced convection heat transfer, Boger’s experimental data
Cite this paper
Md. Mamun Molla,
S. Ghosh Moulic,
LunShin Yao,
Prediction of Heat Transfer to Fully Developed Pipe Flows with a Modified Power Law Viscosity Model, SCIREA Journal of Mechanics. Vol.
1
, No.
1
,
2016
, pp.
1

47
.
References
[ 1 ]  Yao, L.S., and Molla, M.M., “NonNewtonian Fluid Flow on a Flat Plate，Part I: Boundary Layer,” Journal of Thermophysics and Heat Transfer, Vol. 22, 2008, pp. 758761. 
[ 2 ]  Molla, M.M., and Yao, L.S, “NonNewtonian Fluid Flow on a Flat Plate，Part II: Heat Transfer,” Journal of Thermophysics and Heat Transfer, Vol. 22, 2008, pp. 762765. 
[ 3 ]  Yao, L.S., and Molla, M.M., “Forced Convection of NonNewtonian Fluids on a Heated Flat Plate,” International Journal of Heat and Mass Transfer, Vol. 51, 2008, pp. 51545159. 
[ 4 ]  Molla, M.M., and Yao, L.S., “The Flow of NonNewtonian Fluid on a Flat Plate with a Uniform Heat Flux,” Journal of Heat Transfer, Vol. 131, 2009, pp. 0117021~6. 
[ 5 ]  Molla, M.M., and Yao, L.S., “NonNewtonian Natural Convection Along a Vertical Heated Wavy Surface using a Modified Powerlaw Viscosity Model,” Journal of Heat Transfer, Vol. 131, 2009, pp. 0125011~6. 
[ 6 ]  Molla, M.M., and Yao, L.S., “NonNewtonian Natural Convection Along a Vertical Plate Heated with Uniform Surface Heat Fluxes,” Journal of Thermophysics and Heat Transfer, Vol. 23, 2009, pp. 176185. 
[ 7 ]  Molla, M.M., and Yao, L.S., “Mixed Convection of NonNewtonian Fluids Along a Heated Vertical Flat Plate,” International Journal of Heat and Mass Transfer, Vol. 52, 2009, pp. 32663271. 
[ 8 ]  Ghosh Moulic, S., and Yao, L.S., “NonNewtonian Natural Convection Along a Vertical Flat Plate with Uniform Surface Temperature,” Journal of Heat Transfer, Vol. 131, 2009, pp. 0625011~8. 
[ 9 ]  Bhowmick, S., Molla, M.M. and Yao, L.S., “NonNewtonian Mixed Convection Flow along a Horizontal Circular Cylinder,” Numerical Heat Transfer, Part A: Applications: An International Journal of Computation and Methodology, Vol. 66(5), 2014, pp. 509529. 
[ 10 ]  Hinch, J., “NonNewtonian Geophysical Fluid Dynamics,” Conceptual Models of the Climate:2003 Program in Geophysical Fluid Dynamics, Woods Hole Oceanographic Institution, Woods Hole, MA, 2003. 
[ 11 ]  Bird, R.B., Armstrong, R.C., and Hassager, O., Dynamics of Polymeric Liquids, Vol. 1, Fluid Mechanics, 2nd ed., Wiley, New York, 1987. 
[ 12 ]  Chhabra, R.P., and Richardson, J.F., NonNewtonian Flow in the Process Industries, Fundamentals and Engineering Applications, Butterworth Heinemann, Oxford, 1999. 
[ 13 ]  Chhabra, R.P., and Richardson, J.F., NonNewtonian Flow and Applied Rheology: Engineering Applications, 2nd ed., Butterworth Heinemann, Oxford, 2008. 
[ 14 ]  Bird, R.B., Stewart, W.E., and Lightfoot, E.N., Transport Phenomena, 2nd ed., Wiley, New York, 2002. 
[ 15 ]  Boger, D.V., “Demonstration of Upper and Lower Newtonian Fluid Behaviour in a Pseudoplastic Fluid,” Nature, Vol. 265, 1977, pp. 126128. 
[ 16 ]  Bejan, A., Entropy Generation Minimization: The Method of Thermodynamic Optimization of FiniteSize Systems and FiniteTime Processes, CRC Press, Boca Raton, 1996. 
[ 17 ]  Naterer, G.F. and Camberos, J.A., EntropyBased Design and Analysis of Fluids Engineering Systems, CRC Press, Boca Raton 2008. 
[ 18 ]  Bejan, A., Convection Heat Transfer, 3rd ed., Wiley, New Jersey, 2004. 
[ 19 ]  Morton, B.R., “Laminar convection in uniformly heated horizontal pipes at low Rayleigh numbers,” The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 12, 1959, pp. 410420. 
[ 20 ]  Yao, L.S. and Berger, S.A., “Flow in heated curved pipes,” Journal of Fluid Mechanics, Vol. 88, 1978, pp. 339354. 
[ 21 ]  Prusa, J. and Yao, L.S., “Numerical solution for fully developed flow in heated curved tubes,” Journal of Fluid Mechanics, Vol. 123, 1983,pp. 503522. 
[ 22 ]  Yao, L.S. and Ghosh Moulic, S., “Uncertainty of convection,” International Journal of Heat and Mass Transfer, Vol. 37, 1994, pp. 17131721. 
[ 23 ]  Yao, L.S. and Ghosh Moulic, S., “Nonlinear instability of travelling waves with a continuous spectrum,” International Journal of Heat and Mass Transfer, Vol. 38, 1995, pp. 17511772. 
[ 24 ]  Yao, L.S., “Is a fully developed and nonisothermal flow possible in a vertical pipe?,” International Journal of Heat and Mass Transfer, Vol. 30, 1987, pp. 707716. 
[ 25 ]  Yao, L.S., “Linear stability analysis for opposing mixed convection in a vertical pipe,” International Journal of Heat and Mass Transfer, Vol. 30, 1987, pp. 810811. 
[ 26 ]  Rogers, B.B. and Yao, L.S., “Finite amplitude instability of mixed convection in a heated vertical pipe,” International Journal of Heat and Mass Transfer, Vol. 36, 1993, pp. 23052315. 
[ 27 ]  Rogers, B.B. and Yao, L.S., “The effect of mixed convection instability on heat transfer in a vertical annulus,” International Journal of Heat and Mass Transfer, 1990, Vol. 33, 1990, pp. 7990. 
[ 28 ]  Rogers, B.B. and Yao, L.S., “Finite amplitude instability of mixed convection in a heated vertical annulus,” Proceedings of the Royal Society of London Series A, Vol. 437, 1992, pp. 267290. 
[ 29 ]  Yao, L.S., Molla, M.M. and, Ghosh Moulic, S., “FullyDeveloped CircularPipe Flow of a NonNewtonian Pseudoplastic Fluid,” Universal Journal of Mechanical Engineering, Vol. 1(2), 2013, pp. 2331. 
[ 30 ]  Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing Corporation, Washington, 1980. 
[ 31 ]  Neofytou, P., A third order upwind finite volume method for generalized Newtonian fluid flows, Adv. Eng. Softw. Vol.36 (2005) pp.664680 
[ 32 ]  Bell, B. C. and Surana, K. S., P verersion least squares finite elements formulation for twodimensional, incompressible, nonNewtonian and isothermal flow, Int. J. Numer. Methods Fluids, Vol.18 (1994) pp 127162. 