# zbMATH — the first resource for mathematics

Meshless analysis of heat transfer due to viscous dissipation in polymer flow. (English) Zbl 1244.76099
Summary: This paper illustrates the results of meshless/meshfree solutions of a heat transfer to molten polymer flow in a tube with constant ambient temperature. Here, the rheological behaviors of the melt are based on a power law temperature-dependent model and heat produced by viscous dissipation, which satisfies an Arrhenius temperature-dependence law, is considered. Temperatures are obtained for different tube lengths, different inlet temperatures and different models. It shows that the temperature-dependent viscous disputation has significant impact on the heat transfer, and the limiting bulk temperature for both without viscosity dissipation model and with viscosity dissipation model is influenced by the wall boundary, but not by the inlet conditions of the melt. Meanwhile, the local Nusselt number is also presented for a variety of flow entry temperatures. Moreover, the element-free Galerkin solutions of steady state for different nodal distribution are validated by comparing with the analytical solution, which indicates that numerical solutions are excellent agreement with analytical solutions.

##### MSC:
 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76A05 Non-Newtonian fluids 80A20 Heat and mass transfer, heat flow (MSC2010)
Mfree2D
Full Text:
##### References:
 [1] Wei, D.M.; Luo, H.B., Finite element solutions of heat transfer in molten polymer flow in tubes with viscous dissipation, Int J heat mass transfer, 46, 3097-3108, (2003) · Zbl 1043.76040 [2] Wei, D.M.; Zhang, Z., Decay estimates of heat transfer to molten polymer flow in pipes with viscous dissipation, Electron J differential equations, 1-14, (2001) [3] Agur, E.E.; Vlachopoulos, J., Heat transfer to molten polymer folw in tubes, J appl polym sci, 26, 5, 765-773, (1981) [4] Prusa, J.; Manglik, R.M., Asymptotic and numerical solutions for thermally developing flows of newtonian and non-Newtonian fluids in circular tubes with uniform wall temperature, Numer heat transfer part A, 26, 119-217, (1994) [5] Monaghan, J.J., An introduction to SPH, Comput phys comm, 48, 1, 89-96, (1988) · Zbl 0673.76089 [6] Randles, P.W.; Libersky, L.D., Smoothed particle hydrodynamics: some recent improvements and applications, Comput methods appl mech eng, 139, 1-4, 375-408, (1996) · Zbl 0896.73075 [7] Jeong, J.H.; Jhon, M.S., Smoothed particle hydrodynamics applications to heat conduction, Comput phys comm, 153, 71-84, (2003) · Zbl 1196.82015 [8] Nayroles, B.; Touzot, G.; Villon, P., Generalizing the finite element method: diffuse approximation and diffuse elements, Comput mech, 10, 5, 307-318, (1992) · Zbl 0764.65068 [9] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods, Int J numer methods eng, 37, 2, 229-256, (1994) · Zbl 0796.73077 [10] Belytschko, T.; Krongauz, Y.; Organ, D., Meshless method: an overview and recent developments, Comput methods appl mech eng, 139, 1-4, 3-47, (1996) · Zbl 0891.73075 [11] Lu, Y.Y.; Belytschko, T.; Gu, L., A new implementation of the element free Galerkin method, Comput methods appl mech eng, 113, 3-4, 397-414, (1994) · Zbl 0847.73064 [12] Do, C.J., An element-free Galerkin method for simulation of stationary two-dimensional shallow water flows in rivers, Comput methods appl mech eng, 182, 1-2, 89-107, (2000) · Zbl 0966.76067 [13] Liu, G.R., Mesh free methods: moving beyond the finite element method, (2003), CRC Press Boca Raton, FL · Zbl 1031.74001 [14] Liu, G.R.; Gu, Y.T., An introduction to meshfree methods and their programming, (2005), Springer Berlin, New York [15] Liu, G.; Liu, T.X., Meshfree methods and their applications, (2005), Northwestern Polytechnical University Press Xi’An [16] Liu, W.K.; Chen, Y.; Jun, S., Reproducing kernel particle methods, Int J numer methods fluids, 20, 8-9, 1081-1106, (1995) · Zbl 0881.76072 [17] Günther, F.; Liu, M.K.; Diachin, D., Multi-scale meshfree parallel computations for viscous compressible flows, Comput methods appl mech eng, 190, 3-4, 279-303, (2000) · Zbl 0973.76045 [18] Zhao ML, Nie YF, Zuo CW. A new coupled MLPG-FE method for electromagnetic field computations. In: The third international conference on computational electromagnetics and its applications, ICCEA’04, Beijing, China, November 1-4, 2004 [19] Dolbow, J.; Belytschko, T., Volumetric locking in the element free Galerkin method, Int J numer methods eng, 46, 925-942, (1999) · Zbl 0967.74079 [20] Quarteroni, A.; Sacco, R.; Saleri, F., Numerical mathematics, (2000), Springer Berlin · Zbl 0943.65001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.