Heat transfer coefficients of natural volcanic clasts

Heat transfer coefficients used in numerical simulations of volcanic eruptions are typically borrowed from industrial settings where the coefficients are well determined for non-permeable, machined (spherical) materials. Volcanic clasts, in contrast, are permeable and have irregular shapes. We performed a series of laboratory experiments to determine heat transfer coefficients for natural volcanic particles. We measured the surface and interior temperatures during cooling at wind speeds ranging from 0 to 10 m/s. We also measured the permeability and density of the particles. We find that the permeability of the particles has little effect on clast cooling. In the absence of any wind, heat loss occurs by free convection, and we find no relationship between the heat transfer coefficient and particle density. However, for non-zero Reynolds numbers (finite wind speed), the heat transfer coefficient decreases with increasing porosity. We obtain a correlation for the dimensionless heat loss, or Nusselt number, of the form Nu = 2 + aRe^1/2Pr^1/3 where a is a density dependent coefficient given by a = 0.00022ρ + 0.31, with ρ in kg/m³, and Re and Pr are the Reynolds number and Prandtl number, respectively. Compared with non-porous particles, heat transfer coefficients for natural pumice clasts are reduced by a factor of 2–3 for particles with similar Re. Numerical simulations show that this leads to an increase in depositional temperature by 50–90 °C.