  In the solar corona and solar wind, electron heat conduction is an important
process that transports energy over large distances and helps determine the
spatial variation of temperature. High-density regions undergoing rapid
particle-particle collisions exhibit a heat flux described well by classical
Spitzer-Harm theory. However, much of the heliosphere is closer to a more
collisionless state, and there is no standard description of heat conduction
for fluid-based (e.g., magnetohydrodynamic) models that applies generally. Some
proposed models rely on electron velocity distributions that exhibit negative
values of the phase-space density. In this paper, we explore how
positive-definite velocity distributions can be used in fluid-based
conservation equations for the electron heat flux along magnetic-field lines in
the corona and solar wind. We study both analytic forms of skewed distributions
(e.g., skew-normal distributions, two-sided bi-Maxwellians, and
constant-collision-time electrostatic solutions) and empirical fits to
measurements of core, halo, and strahl electrons in interplanetary space. We
also present example solutions to a generalized conservation equation for the
heat flux in the solar wind, with some limiting cases found to resemble known
free-streaming approximations. The resulting values of the electron heat flux
vary as a function of radial distance and Knudsen number in ways that resemble
observed data. We note that this model does not include the effects of kinetic
instabilities (which may impose saturation limits when active), so for now its
regime of applicability is limited to collisionless heat-flux evolution away
from the known instability boundaries in parameter space.
