  For the solutions of Navier-Stokes-Boussinesq equations in a
three-dimensional thin tube with front like initial data, we derive some
uniform estimates on the burning rate and the flow velocity, which can be
interpreted as stability results for the laminar front. We also show that the
front-like datum admits a solution which will stay front-like in time. We
consider no-slip (Dirichlet) boundary condition for the flow, and no-flux
(Neumann) boundary condition for the reactant(temperature).
