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In this paper, a mathematical relationship between particle melting rate and its surface heat flux is established to solve the problem of melting of elliptical particle sedimentation based on the direct numerical simulations of particle sedimentation when taking account of thermal convection within the framework of the arbitrary Lagrangian-Eulerian technique. The elliptical particle with different initial angles is released in a mesoscale channel under gravity. Compared with the isothermal elliptical particle sedimentation, the melting elliptical particle shows large differences in moving trajectories, the forces exerting on the particle and velocities, which come from the consideration of fluid convection, mass loss, and shape change. More specifically, 1) in the case of isothermal elliptical particle sedimentation, the velocity, the horizontal trajectory, and the force vary periodically. However, the amplitude recedes gradually, and finally becomes zero in the case of the melting elliptical particle, which is caused by the mass lost and shape change. 2) The equilibrium position of the major axis will finally be perpendicular to the direction of sedimentation. So, the initial angle of slope (θ) usually affects the sedimentation in the beginning, and vanishes after a period of time. 3) The downward convection induced by the cold fluid accelerates the velocity of the melting particle. The angular velocity, force and horizontal amplitude of the melting particle become smaller than those of the isothermal particle, and finally recedes to zero. In our study, the investigation of coupled heat transfer, fluid-solid system and shape change is carried out, and some new features are found out.
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Keywords:
- mesoscale /
- melting /
- elliptical particle /
- direct numerical simulation
[1] Kong G, Braun R D, Dewhirst M W 2000 Cancer Res. 60 4440
[2] Taylor R A, Otanicar T, Rosengarten G 2012 LSA 11
[3] Choi S U S 1995 ASME FED 231 99
[4] Keblinski P, Eastman J A, Cahill D G 2005 Mater. Today 8 36
[5] Liu H T, Liu M B, Chang J Z, Su T X 2013 Acta Phys. Sin. 62 064705 (in Chinese) [刘汉涛, 刘谋斌, 常建忠, 苏铁熊 2013 物理学报 62 064705]
[6] Liu M, Meakin P, Huang H 2006 Phys. Fluids 18 017101
[7] Liu M B, Chang J Z, Liu H T, Su T X 2011 Int. J. Comp. Meth. 8 637
[8] Mackie A D, Bonet D, Avalos J B, Navas V 1999 Phys. Che. Chem. Phys. 1 2039
[9] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 7556 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 7556]
[10] Chang J Z, Liu H T, Su T X, Liu M B 2011 Int. J. Comp. Meth. 8 851
[11] Qiu Y, You C F, Qi H Y, Xu X C 2003 Advances in mechanics 33 507[仇轶, 由长福, 祁海鹰, 徐旭常 2003力学进展 33 507]
[12] Gan H, Chang J Z, James J. Feng, Howard H. Hu 2003 J. Fluid Mech. 481 385
[13] Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮 2013 物理学报 62 084703]
[14] Yu Z S, Shao X M, Wachs A 2006 J. Comp. Phys. 217 424
[15] Qi D W 2000 Int. J. Multiphase Flow 26 421
[16] Xia Z H, connington K W, Rapaka S, Yue P T, Feng J J, Chen S Y 2009 J. Fluid Mech. 625 249
[17] Liu H T, Tong Z H, An K, Ma L Q 2009 Acta Phys. Sin. 58 6369 (in Chinese) [刘汉涛, 仝志辉, 安康, 马理强 2009 物理学报 58 6369]
[18] Gray D D, Giorgin A 1976 Int. J. Heat Mass Transfer 19 545
[19] Gan H, Feng J J, Hu H H 2003 Int. J. Multiphase flow 29 751
[20] Liu H T, Chang J Z 2013 Acta Phys. Sin. 62 084401 (in Chinese) [刘汉涛, 常建忠 2013 物理学报 62 084401]
[21] Tong Z H, Liu H T, Chang J Z, An Kang 2012 Acta Phys. Sin. 61 024401 (in Chinese) [仝志辉, 刘汉涛, 常建忠, 安康 2012 物理学报 61 024401]
[22] McLeod P, Riley D S, Sparks R S J. 1996 J. Fluid Mech. 327 393
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[1] Kong G, Braun R D, Dewhirst M W 2000 Cancer Res. 60 4440
[2] Taylor R A, Otanicar T, Rosengarten G 2012 LSA 11
[3] Choi S U S 1995 ASME FED 231 99
[4] Keblinski P, Eastman J A, Cahill D G 2005 Mater. Today 8 36
[5] Liu H T, Liu M B, Chang J Z, Su T X 2013 Acta Phys. Sin. 62 064705 (in Chinese) [刘汉涛, 刘谋斌, 常建忠, 苏铁熊 2013 物理学报 62 064705]
[6] Liu M, Meakin P, Huang H 2006 Phys. Fluids 18 017101
[7] Liu M B, Chang J Z, Liu H T, Su T X 2011 Int. J. Comp. Meth. 8 637
[8] Mackie A D, Bonet D, Avalos J B, Navas V 1999 Phys. Che. Chem. Phys. 1 2039
[9] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 7556 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 7556]
[10] Chang J Z, Liu H T, Su T X, Liu M B 2011 Int. J. Comp. Meth. 8 851
[11] Qiu Y, You C F, Qi H Y, Xu X C 2003 Advances in mechanics 33 507[仇轶, 由长福, 祁海鹰, 徐旭常 2003力学进展 33 507]
[12] Gan H, Chang J Z, James J. Feng, Howard H. Hu 2003 J. Fluid Mech. 481 385
[13] Mao W, Guo Z L, Wang L 2013 Acta Phys. Sin. 62 084703 (in Chinese) [毛威, 郭照立, 王亮 2013 物理学报 62 084703]
[14] Yu Z S, Shao X M, Wachs A 2006 J. Comp. Phys. 217 424
[15] Qi D W 2000 Int. J. Multiphase Flow 26 421
[16] Xia Z H, connington K W, Rapaka S, Yue P T, Feng J J, Chen S Y 2009 J. Fluid Mech. 625 249
[17] Liu H T, Tong Z H, An K, Ma L Q 2009 Acta Phys. Sin. 58 6369 (in Chinese) [刘汉涛, 仝志辉, 安康, 马理强 2009 物理学报 58 6369]
[18] Gray D D, Giorgin A 1976 Int. J. Heat Mass Transfer 19 545
[19] Gan H, Feng J J, Hu H H 2003 Int. J. Multiphase flow 29 751
[20] Liu H T, Chang J Z 2013 Acta Phys. Sin. 62 084401 (in Chinese) [刘汉涛, 常建忠 2013 物理学报 62 084401]
[21] Tong Z H, Liu H T, Chang J Z, An Kang 2012 Acta Phys. Sin. 61 024401 (in Chinese) [仝志辉, 刘汉涛, 常建忠, 安康 2012 物理学报 61 024401]
[22] McLeod P, Riley D S, Sparks R S J. 1996 J. Fluid Mech. 327 393
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