This paper deals with a multi-physics topology optimization problem in an asymmetrically heated channel, considering both pressure drop minimization and heat transfer maximization. The problem is modeled under the assumptions of steady-state laminar flow dominated by natural con-vection forces. The incompressible Navier-Stokes equations coupled to the convection-diffusion equation through the Boussinesq approximation are employed and are solved with the finite volume method. In this paper, we first propose two new objective functions: the first one takes into account work of pressures forces and contributes to the loss of mechanical power while the second one is related to thermal power and is linked to the maximization of heat exchanges. In order to obtain a well-defined fluid-solid interface during the optimization process, we use a sigmoid interpolation function for both the design variable field and the thermal diffusivity. We also use adjoint sensitivity analysis to compute the gradient of the cost functional. Results are obtained for various Richardson (Ri) and Reynolds (Re) number such that 100 < Ri < 400 and Re ∈ {200, 400}. In all considered cases, our algorithm succeeds to enhance one of the phenomenon modelled by our new cost functions without deteriorating the other one. We also compare the values of standard cost functions from the litterature over iteration of our optimization algorithm and show that our new cost functions have no oscil-latory behavior. As an additional effect to the resolution of the multi-physics optimization problem, we finally show that the reversal flow is suppressed at the exit of the channel.