Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We consider the convection problem of a fluid with viscosity depending on temperature in either a bounded or an exterior domain Omega subset of R-N, N = 2, 3. It is assumed that the temperature is transported without thermal conductance (dissipation) by the velocity field which is described by the Navier-Stokes flow. This model is commonly called the Boussinesq system with partial viscosity. In this paper we prove the existence and uniqueness of strong solutions for the Boussinesq system with partial viscosity with initial data in W-2-2/p,W- p (Omega) x W-1,W-q (Omega). For a bounded domain Omega, we also analyze the inviscid limit problem when the conductivity in the fully viscous Boussinesq system goes to zero.112421439Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)