Thermophoretic transport of particles that act as volumetric heat sources in natural convection flow

The natural convection boundary layer with suspended heat generating aerosol particles adjacent to a cooled, isothermal, vertical wjiU was investigated for the following circumstances: laminar and turbulent flow, large temperature differences between the wall and the fluid, stable thermal stratification far from the wall, and fluid participation in thermal radiation heat transfer. The deposition of aerosol particles by thermophoresis was investigated.

A scaling analysis showed the negligible effect inside the boundary layer of the particulate heat source strengths of practical interest. Only the temperature of the fluid far from the wall is affected appreciably by the heat sources. The scaled boundary layer differential equations are transformed to a nonsimilarity form for numerical solution using two different methods.

An expression for the ratio of mass transfer to heat transfer coefficients was developed to simplify the computation of thermophoretic particle deposition at the wall for the case of constant temperature conditions far from the wall. Variable thermophysical property effects for the three gases of steam, air, and hydrogen were investigated. A dimensionless ratio of transfer coefficients for large temperature differences and turbulent flow was computed as a product of the laminar constant property results and a ratio of the known thermophysical properties at the wall and far from the wall. An approximation of the laminar constant property results for all three gases is developed in terms of the known wall and fluid temperatures, Prandtl number, and a thermo phoretic constant. This allows particle deposition to be computed from a known heat transfer coefficient without explicitly solving the particle conservation equation.

Very low heat source strengths result in a quadratic vertical temperature distribution far from the wall. As a result of this thermal stratification in the freestream, particle movement from outside the boundary layer toward the wall is blocked from reaching the wall at a point approximately halfway down the wall due to detraining outflow.

Thermophoretic particle deposition in the presence of participating thermal radiation was investigated using the diffusion or Rosseland approximation. A decreased temperature gradient caused by an increase in the effective thermal conductivity results in decreased thermophoretic particle deposition.