Studies on the Convective Heat Transfer from Rotating Disk : 2nd Report, The Effect of Prandtl Number on the Laminar Heat Transfer from a Disk Rotating in Uniform Forced Stream

Abstract

A theoretical study on laminar heat transfer from a disk rotating in uniform forced stream was carried out for the fluid of any Prandtl number in the case when the surface temperature difference is expressed by the quadratic relation : t_ω-t_∞=a_o+a₂r². The results are summarized as follows. (1) The asymptotic solutions for P_r→o and P_r→∞ have an appropriate accuracy in P_r<0.01 and P_r>100. (2) The effect of radial heat conduction in a fluid of low Prandtl number was analized in the case of pure quadratic disk temperature, i.e. t_ω-t_∞=a₂r² and a criterion that the effects of radial heat conduction on the heat transfer coefficient reach 5% was established. According to this criterion, when the ratio of axial stream velocity to rotating velocity of a disk is larger than 0.25, the effect of radial heat conduction in P_r=0.01 may be negligible, even if the rotating Reynolds number decreases to the order of R_ewr=r²ω/ν&cong;10³.