The thermal constitutive behavior of suspensions
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in /pdf document. The bulk thermal constitutive behavior of flowing, neutrally buoyant suspensions is considered theoretically and experimentally. A general theoretical expression relating the mac...
| Summary: | NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in /pdf document.
The bulk thermal constitutive behavior of flowing, neutrally buoyant suspensions is considered theoretically and experimentally. A general theoretical expression relating the macroscopic heat flux in the suspension to microscale velocity and temperature distributions on the length scale of the particles is derived from statistical considerations of the microstructural configuration of the suspension. Evaluation of the relation for specific conditions is discussed with particular attention given to the role of random Brownian motions of the particles. Constraints imposed by simple shear flow are considered, and it is seen that the flowing suspension may not be described by a complete effective conductivity tensor [...].
The effective conductivity transverse to the flow of a dilute suspension of slightly deformed droplets is calculated in the limit of small particle Peclet number for the undisturbed bulk shear, [...], and the linear bulk temperature field, [...]. Two distinct cases of small deformation are considered; deformation dominated by interfacial tension forces, and deformation dominated by viscous forces in the drop. The microscale velocity and temperature fields are obtained as regular, asymptotic expansions in the small deformation parameter, [...], the governing thermal energy equation is then solved for small Peclet number using the methods of matched asymptotic expansions. The results obtained display the possible fundamental change in the dominant flow contribution to the effective conductivity due to the deformation in shape of the particles.
The bulk heat flux of a dilute suspension of rigid prolate spheroids is evaluated in the limit of small particle Peclet number for the undisturbed shear flow, [...], and the linear bulk temperature fields [...]. Microscale velocity fields near the particle are calculated from the Stokes equations for small particle Reynolds number for arbitrary orientation and rotation of the particles, and temperature distributions for the small, but non-negligible Peclet number by the methods of matched asymptotic expansions. The components of the effective conductivity tensor for a stationary suspension is obtained, and the bulk heat flux due to the temperature gradients orthogonal to the flow evaluated for the case of significant rotational Brownian motion of the particles.
A rotating cylinder apparatus designed for the investigation of the bulk heat flux transverse to the flow of a suspension undergoing simple bulk shear flow is described, with special consideration given to describing and minimizing secondary effects such as natural convection, particle migration, viscous dissipation, and Taylor instability of the flow. Results obtained for the effective conductivity of suspensions of spherical polystyrene particles suspended in a Newtonian fluid are presented and compared to the theoretical prediction of Leal (1973) for the effective conductivity of dilute suspensions of spherical particles at low particle Reynolds and Peclet numbers. |
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