Abstract
Transient forced convection for slug flow inside parallel-plate channels and circular ducts including conjugation to the walls is solved analytically and exactly for periodic variation of the inlet temperature. The periodic solution to the problem involved eigenfunctions and eigenvalues of a complex eigenvalue problem. The complex eigenvalue problem is solved by modifying the recently advanced Count Method, and benchmark results are presented for the eigenvalues in tabular form. The amplitude and phase lag of oscillations with respect to the conditions at the inlet are determined for the wall temperature, fluid bulk temperature and heat flux. The results for the cases of both parallel-plate channels and circular ducts are presented in the graphical form as a function of the axial position for different values of the parameters signifying the rate of energy storage in the walls. The effects of walls on damping the amplitude and altering the phase of temperature and heat flux oscillations along the duct are investigated.
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