This study aims to present a novel approximate analytical solution for laminar heat and mass transfer in a conical gap (rotating cone and a fixed disk, conicity angles up to 4°) at high Prandtl numbers.
The recently proposed improved asymptotic expansion method for energy equation was used. The Reynolds number of rotation Re was equal to 0.1, 0.5 and 1.0, whereas the Prandtl number Pr was increasing from 1 to 3·106. The disk temperature was constant or varied according to the quadratic law along the radius. The solution was obtained again using a dimensionless number SvT = Re2Δ2Pr (that serves as an expansion parameter).
The thermal boundary layer on the cone with the relative thickness Δ is much thinner than the gap height. The exponents at the Pr and Re numbers are 1/3 and 2/3, respectively. The validity range of the solutions is SvT = 7..7.65 (Pr = 700). The solution for moderate Prandtl numbers is valid up to Sv = 25 until the onset of the thermal boundary layer on the cone (Pr = 2,000).
The solution is valid for high Prandtl/Schmidt numbers depending on the Reynolds number.
The new analytical solutions are applicable for heat transfer in polymer melts, mineral oils and glycerin and for convective diffusion in electrochemistry and medical applications.
The study can help design more effective heat and mass transfer devices in medicine to improve blood treatment.
The empirically corrected novel analytical solutions for the Nusselt numbers and Δ for the isothermal rotating cone agree well with the self-similar solution and fully coincide with the solutions for the rotating isothermal disk with a fixed cone.
