CFD Online Discussion Forums - Topology optimization of thermal coupled flow

Hi everyone,
I'm working on topology optimization of thermal coupled flow. Problem domain is attached. I derived adjoint equations and implemented them on OpenFoam by modifying adjointShapeOptimizationFoam.
Solution of adjoint variables (velocity and temperature) and primal temperature are reaching to enourmous numbers dramatically in earlier iterations, thus solution crashed.
I can share source code if anyone interested.

Flow and heat transfer equations :

$\nabla v = 0$

$\mu\nabla^{2}v + \alpha \rho v = \nabla p$

$\rho C_p v \nabla T + Q = k \nabla^{2} T$

where

is uniform heat source.

Adjoint equations:

$\nabla u = \partial J / \partial p$

$\rho C_{p} T_a$ $\nabla T + \partial J / \partial u$ = - $\nabla q+\mu \nabla^{2} u + \alpha \rho u$

$\rho C_{p} v$ $\nabla$ $T_{a} + k$ $\nabla^{2} T_{a}$ = $\partial$ $J / \partial T$

where

and

are adjoint velocity, pressure and temperature variables, respectively.

Is there anyone who has an idea about problem?