Equilibrium temperature of a convex body in a free molecular shearing flow

It is shown that the equilibrium temperature T(w) of a high conductivity axially symmetric convex body in a simply shearing gas of temperature T is given by T(w)/T=1+(beta(a)/4)(p(xy)/p) sin(2)theta sin(2phi), theta,phi are polar angles of the axis of the body (z is the polar axis). a is a geometric shape factor of the body (which vanishes for a sphere) and beta takes the value 1 if only the lowest order Sonine term is retained. p is the pressure and p(xy) the viscous pressure. The body is assumed small compared to the mean free path, which is small compared to the length scale of the velocity field.