We develop a radial basis function finite collocation method(RBF-FC)that utilises an adaptive quadtree dataset to cluster nodes around critical features in the domain,for the solution of transport processes occurring in moving boundary problems.An adaptive quadtree dataset is used to distribute an optimum set of solution centres in the domain around which local Hermitian collocation systems are formed.In these local systems,the governing PDE and boundary operators of the problem are enforced by collocation.Globally,the systems are linked via reconstruction of the solution variable in terms of the solution value at neighbouring nodes producing a sparse global matrix with a solution cost that scales linearly with the number of nodes in the domain.By generating an optimum set of nodal points with the quadtree dataset,we can reduce the global solution error in the RBF-FC method whilst maintaining low solution times.The proposed method is validated on a steady-state and transient convection-diffusion problem,simulating boundary layer capture and infinite Peclet number transport in a 2D domain.We then couple the method with an interface tracking technique to solve the transient heat transfer in a Hele-Shaw cell,demonstrating the effectiveness of the proposed method for the solution of convection dominated transport in moving boundary problems.