Thermal effect and optimal design of cooling pipes on mass concrete with constant quantity of water flow

References

• X. Z. Yu, J. Y. Chen, Q. Xu and Z. Zhou, “Research on the Influence Factors of Thermal Cracking in Mass Concrete by Model Experiments,” KSCE J. Civil Eng., vol. 22, no. 8, pp. 2906–2915, 2018. DOI: 10.1007/s12205-017-2711-2.
   Web of Science ®Google Scholar
• C. X. Qian and G. B. Gao, “Reduction of interior temperature of mass concrete using suspension of phase change materials as cooling fluid,” Construct. Build. Mater., vol. 26, no. 1, pp. 527–531, 2012. DOI: 10.1016/j.conbuildmat.2011.06.053.
   Web of Science ®Google Scholar
• T. S. Seo, S. S. Kim and C. K. Lim, “Experimental study on hydration heat control of mass concrete by vertical pipe cooling method,” J. Asian Architect. Build. Eng., vol. 14, no. 3, pp. 657–662, 2015. DOI: 10.3130/jaabe.14.657.
   Web of Science ®Google Scholar
• A. Tasri and A. Susilawati, “Effect of cooling water temperature and space between cooling pipes of post-cooling system on temperature and thermal stress in mass concrete,” J. Build. Eng., vol. 24, pp. 100731, 2019. DOI: 10.1016/j.jobe.2019.100731.
   Web of Science ®Google Scholar
• B. F. Zhu, “The equivalent heat conduction equation of pipe cooling in mass concrete considering influence of external temperature,” J. Hydraul. Eng., vol. 34, no. 3, pp. 49–54, 2003.
   Google Scholar
• J. K. Yang, Y. Lee and J. K. Kim, “Heat Transfer Coefficient in Flow Convection of Pipe-Cooling System in Massive Concrete,” ACT, vol. 9, no. 1, pp. 103–114, 2011. DOI: 10.3151/jact.9.103.
   Google Scholar
• Z. Y. Zhu, S. Qiang and W. M. Chen, “A new method solving the temperature field of concrete around cooling pipes,” Comput Concrete, vol. 11, no. 5, pp. 441–462, 2013. DOI: 10.12989/cac.2013.11.5.441.
   Web of Science ®Google Scholar
• A. T. Al-Sammarraie and K. Vafai, “Heat transfer augmentation through convergence angles in a pipe,” Numer. Heat Transf. Part A Appl. , vol. 72, no. 3, pp. 197–214, 2017. DOI: 10.1080/10407782.2017.1372670.
   Web of Science ®Google Scholar
• X. Liu, C. Zhang, X. Chang, et al., “Precise simulation analysis of the thermal field in mass concrete with a pipe water cooling system,” Appl. Therm. Eng., vol. 78, pp. 449–459, 2015. DOI: 10.1016/j.applthermaleng.2014.12.050.
   Web of Science ®Google Scholar
• X. H. Liu, Y. Duan, W. Zhou and X. L. Chang, “Modeling the Piped Water Cooling of a Concrete Dam Using the Heat-Fluid Coupling Method,” J. Eng. Mech., vol. 139, no. 9, pp. 1278–1289, 2013. DOI: 10.1061/(ASCE)EM.1943-7889.0000532.
   Web of Science ®Google Scholar
• R. Zhong, G. P. Hou and S. Qiang, “An improved composite element method for the simulation of temperature field in massive concrete with embedded cooling pipe,” Appl. Therm. Eng., vol. 124, pp. 1409–1417, 2017. CDOI: 10.1016/j.applthermaleng.2017.06.124.
   Web of Science ®Google Scholar
• G. R. Chen, X. F. Ding, M. X. Cai and W. Z. Qiao, “Analytical solution for temperature field of nonmetal cooling pipe embedded in mass concrete,” Appl. Therm. Eng., vol. 158, pp. 113774, 2019. DOI: 10.1016/j.applthermaleng.2019.113774.
   Web of Science ®Google Scholar
• J. Cheng, T. C. Li, X. Q. Liu and L. H. Zhao, “A 3D discrete FEM iterative algorithm for solving the water pipe cooling problems of massive concrete structures,” Int. J. Numer. Anal. Meth. Geomech., vol. 40, no. 4, pp. 487–508, 2016. DOI: 10.1002/nag.2409.
   Web of Science ®Google Scholar
• S. Qiang, Z. Q. Xie and R. Zhong, “A p-version embedded model for simulation of concrete temperature fields with cooling pipes,” Water Sci. Eng., vol. 8, no. 3, pp. 248–256, 2015. DOI: 10.1016/j.wse.2015.08.001.
   Web of Science ®Google Scholar
• S. Y. Reutskiy, “A meshless radial basis function method for 2D steady-state heat conduction problems in anisotropic and inhomogeneous media,” Eng. Anal. Bound. Elem., vol. 66, pp. 1–11, 2016. DOI: 10.1016/j.enganabound.2016.01.013.
   Web of Science ®Google Scholar
• M. Jamil and E. Y. K. Ng, “Evaluation of meshless radial basis collocation method (RBCM) for heterogeneous conduction and simulation of temperature inside the biological tissues,” Int. J. Therm. Sci., vol. 68, pp. 42–52, 2013. DOI: 10.1016/j.ijthermalsci.2013.01.007.
   Web of Science ®Google Scholar
• S. Q. Lyu, C. Wu and S. F. Zhang, “Application of the RBF Method to the Estimation of Temperature on the External Surface in Laminar Pipe Flow,” Math. Probl. Eng., vol. 2013, pp. 1–11, 2013. DOI: 10.1155/2013/205169.
   Web of Science ®Google Scholar
• G. M. Yao, C. S. Chen and H. Zheng, “A Modified Method of Approximate Particular Solutions for Solving Linear and Nonlinear PDEs,” Numer. Methods Partial Differential Eq., vol. 33, no. 6, pp. 1839–1858, 2017. DOI: 10.1002/num.22161.
   Web of Science ®Google Scholar
• A. H.-D. Cheng, M. A. Golberg, E. J. Kansa, et al., “Exponential convergence and HC c multiquadric collocation method for partial differential equations,” Numer. Methods Partial Differential Eq., vol. 19, no. 5, pp. 571–594, 2003., DOI: 10.1002/num.10062.
   Web of Science ®Google Scholar
• W. Chen, Y. Hong and J. Lin, “The sample solution approach for determination of the optimal shape parameter in the Multiquadric function of the Kansa method,” Comp. Math. Appl., vol. 75, no. 8, pp. 2942–2954, 2018. DOI: 10.1016/j.camwa.2018.01.023.
   Web of Science ®Google Scholar
• C. S. Liu, W. Chen and Z. Fu, “A multiple-scale MQ-RBF for solving the inverse Cauchy problems in arbitrary plane domain,” Eng. Anal. Bound. Elem., vol. 68, pp. 11–16, 2016. DOI: 10.1016/j.enganabound.2016.02.011.
   Web of Science ®Google Scholar
• C. S. Liu and C. W. Chang, “An energy regularization of the MQ-RBF method for solving the Cauchy problems of diffusion-convection-reaction equations,” Commun. Nonlinear Sci. Numer. Simul., vol. 67, pp. 375–390, 2019. DOI: 10.1016/j.cnsns.2018.07.002.
   Web of Science ®Google Scholar
• A. I. Tolstykh and D. A. Shirobokov, “On using radial basis functions in a” finite difference mode” with applications to elasticity problems,” Comput. Mech., vol. 33, no. 1, pp. 68–79, 2003. DOI: 10.1007/s00466-003-0501-9.
   Web of Science ®Google Scholar
• C. S. Chen and A. Karageorghis, “Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains,” CiCP, vol. 25, no. 1, pp. 41–67, 2019. DOI: 10.4208/cicp.OA-2018-0031.
   Google Scholar
• B. Fornberg and N. Flyer, “Solving PDEs with radial basis functions,” Acta Numer., vol. 24, pp. 215–258, 2015. DOI: 10.1017/S0962492914000130.
   Web of Science ®Google Scholar
• V. Shankar, G. B. Wright, R. M. Kirby and A. L. Fogelson, “A Radial Basis Function (RBF)-Finite Difference (FD) Method for diffusion and reaction-diffusion equations on surfaces ,” J. Sci. Comput., vol. 63, no. 3, pp. 745–768, 2016. DOI: 10.1007/s10915-014-9914-1.
   PubMed Web of Science ®Google Scholar
• L. D. Su, “A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem,” Appl. Math. Comput., vol. 354, pp. 232–247, 2019. DOI: 10.1016/j.amc.2019.02.035.
   Web of Science ®Google Scholar
• Y. X. Hong, J. Lu, J. Lin and W. Chen, “Numerical Simulation of Non-Linear Schrodinger Equations in Arbitrary Domain by the Localized Method of Approximate Particular Solution,” AAMM, vol. 11, no. 1, pp. 108–131, 2019. DOI: 10.4208/aamm.OA-2018-0026.
   Web of Science ®Google Scholar
• Y. X. Hong, J. Lin and W. Chen, “Simulation of thermal field in mass concrete structures with cooling pipes by the localized radial basis function collocation method,” Int. J. Heat Mass Transf., vol. 129, pp. 449–459, 2019. DOI: 10.1016/j.ijheatmasstransfer.2018.09.037.
   Web of Science ®Google Scholar
• Y. X. Hong, W. Chen, J. Lin, et al., “Thermal field in water pipe cooling concrete hydrostructures simulated with singular boundary method,” Water Sci. Eng., vol. 10, no. 2, pp. 107–114, 2017., DOI: 10.1016/j.wse.2017.06.004.
   Web of Science ®Google Scholar
• J. Slak and G. Kosec, “Adaptive radial basis function-generated finite differences method for contact problems,” Int. J. Numer. Methods Eng., vol. 119, no. 7, pp. 661–686, 2019. DOI: 10.1002/nme.6067.
   Web of Science ®Google Scholar
• Y. X. Hong, J. Lin, A. H.-D. Cheng, Y. Wang and W. Chen, “Thermal analysis of heat transfer in pipe cooling concrete structure by a meshless RBF-FD method combined with an indirect model,” Int. J. Therm. Sci., vol. 152, pp. 106296, 2020. DOI: 10.1016/j.ijthermalsci.2020.106296.
   Web of Science ®Google Scholar
• G. H. An, J. M. Park, S. L. Cha and J. K. Kim, “Development of a portable device and compensation method for the prediction of the adiabatic temperature rise of concrete,” Construct. Build. Mater., vol. 102, pp. 640–647, 2016. DOI: 10.1016/j.conbuildmat.2015.10.143.
   Web of Science ®Google Scholar
• P. R. Singh and D. C. Rai, “Effect of piped water cooling on thermal stress in mass concrete at early ages,” J. Eng. Mech., vol. 144, no. 3, pp. 04017183, 2018. DOI: 10.1061/(ASCE)EM.1943-7889.0001418.
   Web of Science ®Google Scholar