TY - JOUR
T1 - Analytical solution to heat transfer in compressible laminar flow in a flat minichannel
AU - Bao, Cheng
AU - Jiang, Zeyi
AU - Zhang, Xinxin
AU - Irvine, John T. S.
N1 - This work was supported by the Beijing Science and Technology Project [grant number Z181100004518004] and the Fundamental Research Funds for the Central Universities [grant number FRF-GF-17-B31]. CB thanks for the China Scholarship Council (CSC) fellowship support.
PY - 2018/12
Y1 - 2018/12
N2 - Heat transfer in compressible laminar flow in mini-/micro-channels, a classical and general topic in fields of fuel cells, electronics, micro heat exchanger, etc., is revisited. Based on a two-dimensional continuum flow model, analytical solutions of the dimensionless model are achieved in closed-form symbolic algebras of Whittaker eigenfunctions, corresponding to two kinds of boundary conditions with arbitrarily prescribed wall temperature or wall heat flux. As the eigenvalues and eigenfunctions are independent on the dimensionless quantities, which influence the along-the-channel behaviors, the algorithm reveals the common features of compressible laminar thermal flows. The algorithms do not require the assumption of a linear pressure distribution, which is proved to be untenable in some cases (e.g. constant wall heat flux). The algorithms are validated well by the exact (numerical) computations in exemplary cases of both small and moderate Reynolds number, Mach number and Eckert number of air. Although expressed in a series of eigenfunctions, only several terms (sometimes one or two terms) of solutions are required for a practical computation.
AB - Heat transfer in compressible laminar flow in mini-/micro-channels, a classical and general topic in fields of fuel cells, electronics, micro heat exchanger, etc., is revisited. Based on a two-dimensional continuum flow model, analytical solutions of the dimensionless model are achieved in closed-form symbolic algebras of Whittaker eigenfunctions, corresponding to two kinds of boundary conditions with arbitrarily prescribed wall temperature or wall heat flux. As the eigenvalues and eigenfunctions are independent on the dimensionless quantities, which influence the along-the-channel behaviors, the algorithm reveals the common features of compressible laminar thermal flows. The algorithms do not require the assumption of a linear pressure distribution, which is proved to be untenable in some cases (e.g. constant wall heat flux). The algorithms are validated well by the exact (numerical) computations in exemplary cases of both small and moderate Reynolds number, Mach number and Eckert number of air. Although expressed in a series of eigenfunctions, only several terms (sometimes one or two terms) of solutions are required for a practical computation.
KW - Minichannel
KW - Heat transfer
KW - Compressible laminar flow
KW - Analytical solution
KW - Whittaker function
U2 - 10.1016/j.ijheatmasstransfer.2018.08.084
DO - 10.1016/j.ijheatmasstransfer.2018.08.084
M3 - Article
SN - 0017-9310
VL - 127
SP - 975
EP - 988
JO - International Journal of Heat and Mass Transfer
JF - International Journal of Heat and Mass Transfer
IS - Part C
ER -