Topology optimization of convective heat transfer problems for non-Newtonian fluids
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We conduct topology optimization of convective heat transfer problems based on the power law type non-Newtonian fluid. A heat transfer maximization problem is studied by using a material distribution based optimization method to optimize configurations of non-Newtonian cooling devices. The key idea of the method is to discern the fluid and the solid domains by a design variable, namely the “material density.” It is updated according to the gradient information obtained from an adjoint-based sensitivity analysis process. The non-Newtonian effects on optimal configurations of thermal devices are numerically investigated. Our results show that more branched flow channels appear in the optimal designs as the pressure difference or heat generation grows. Meanwhile, the dependence of the optimal layout on the power law index is demonstrated and higher power law index can result in more complex configurations and lower flow rate. Compared with the low power law index one, the optimal design of the high power law index problem has much better heat transfer performance on the same condition.
KeywordsTopology optimization Non-Newtonian fluid Thermal-fluid Convective heat transfer Power law model Sensitivity analysis
The authors are grateful to Professor X.-P Chen for helpful discussions and language editing.
B.Z. is supported by the Fundamental Research Funds for the Central Universities (No. G2018KY0306). L.G. is supported by the National Natural Science Foundation of China (No. 51790512).
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
- Bendsoe MP, Sigmund O (2003) Topology optimization: theory, methods, and applications. (Second Edition). Springer - Verlag Berlin Heidelberg GmbHGoogle Scholar
- Chhabra RP, Richardson JF (2008) Non-Newtonian flow and applied rheology (second edition). Elsevier Ltd. https://doi.org/10.1016/B978-0-7506-8532-0.X0001-7
- Dede E (2009) Multiphysics topology optimization of heat transfer and fluid flow systems. Proceedings of the COMSOL Conference, BostonGoogle Scholar
- Esmaeilnejad A, Aminfar H, Neistanak MS (2014) Numerical investigation of forced convection heat transfer through microchannels with non-Newtonian nanofluids. Int J Therm Sci 75:76–86. https://doi.org/10.1016/j.ijthermalsci.2013.07.020 CrossRefGoogle Scholar
- Haertel JHK, Nellis GF (2017) A fully developed flow thermofluid model for topology optimization of 3D-printed air-cooled heat exchangers. Appl Therm Eng 119:10–24. https://doi.org/10.1016/j.applthermaleng.2017.03.030/ CrossRefGoogle Scholar
- Koga AA, Lopes ECC, Nova HFV, de Lima CR, Silva ECN (2013) Development of heat sink device by using topology optimization. Int J Heat Mass Transf 64:759–772. https://doi.org/10.1016/ijheatmasstransfer.2013.05.007 CrossRefGoogle Scholar
- Kondoh T, Matsumori T, Kawamoto A (2012) Drag minimization and lift maximization in laminar flows via topology optimization employing simple objective function expressions based on body force integration. Struct Multidiscip Optim 45:693–701. https://doi.org/10.1007/s00158-011-0730-z MathSciNetCrossRefzbMATHGoogle Scholar
- Kurnia JC, Sasmito AP, Mujumdar AS (2014) Laminar heat transfer performance of power law fluids in coiled square tube with various configurations. Int Commun Heat Mass Transfer 57:100–108. https://doi.org/10.1016/j.icheatmasstransfer.2014.07.016 CrossRefGoogle Scholar
- Li P, Zhang D, Xie Y, Xie G (2016b) Flow structure and heat transfer of non-Newtonian fluids in microchannel heat sinks with dimples and protrusions. Appl Therm Eng 94:50–58. https://doi.org/10.1016/j.applthermaleng.2015.10.119 CrossRefGoogle Scholar
- Li S-N, Zhang H-N, Li X-B, Li Q, Li F-C, Qian S, Joo SW (2017) Numerical study on the heat transfer performance of non- Newtonian fluid flow in a manifold microchannel heat sink. Appl Therm Eng 115:1213–1225. https://doi.org/10.1016/j.applthermaleng.2016.10.047 CrossRefGoogle Scholar
- Martinez DS, Garcia A, Solano JP, Viedma A (2014) Heat transfer enhancement of laminar and transitional Newtonian and non-Newtonian flows in tubes with wire coil inserts. Int J Heat Mass Transf 76:540–548. https://doi.org/10.1016/j.ijheatmasstransfer.2014.04.060 CrossRefGoogle Scholar
- Oignet J, Hoang HM, Osswald V, Delahaye A, Fournaison L, Haberschill P (2017) Experimental study of convective heat transfer coefficients of CO2 hydrate slurries in a secondary refrigeration loop. Appl Therm Eng 118:630–637. https://doi.org/10.1016/j.applthermaleng.2017.02.117 CrossRefGoogle Scholar
- Okkels F, Bruus H (2007) Scaling behavior of optimally structured catalytic microfluidic reactors. Phys Rev E 75. https://doi.org/10.1103/PhysRevE.75.016301
- Pizzolato A, Sharma A, Maute K, Sciacovelli A, Verda V (2017a) Design of effective fins for fast PCM melting and solidification in shell-and-tube latent heat thermal energy storage through topology optimization. Appl Energy 208:210–227. https://doi.org/10.1016/j.apenergy.2017.10.050 CrossRefGoogle Scholar
- Shojaeian M, Karimzadehkhouei M, Kosar A (2017) Experimental investigation on convective heat transfer of non-Newtonian flows of Xanthan gum solutions in microtubes. Exp Thermal Fluid Sci 85:305–312. https://doi.org/10.1016/j.expthermflusci.2017.02.025 CrossRefGoogle Scholar
- Singh A, Kishore N (2018) Laminar mixed convection of non-Newtonian nanofluids flowing vertically upward across confined circular cylinders. J Therm Sci Eng Appl 10:14Google Scholar
- Yaji K, Yamada T, Kubo S, Izui K, Nishiwaki S (2015) A topology optimization method for a coupled thermal-fluid problem using level set boundary expressions. Int J Heat Mass Transf 81:878–888. https://doi.org/10.1016/j.ijheatmasstransfer.2014.11.005 CrossRefGoogle Scholar
- Zhao X, Zhou M, Sigmund O, Andreasen CS (2018) A “poor man’s approach” to topology optimization of cooling channels based on a Darcy flow model. Int J Heat Mass Transf 116:1108–1123. https://doi.org/10.1016/j.ijheatmasstransfer.2017.09.090 CrossRefGoogle Scholar