In this work, two models for calculating heat transfer through a cooled vertical wall covered with a running slag layer are investigated. The first one relies on a discretization of the velocity equation, and the second one relies on an analytical Solution. The aim is to find a model that can be used for calculating local heat flux boundary conditions in computational fluid dynamics (CFD) analysis of such processes. Two different cases where molten deposits exist are investigated: the black liquor recovery boiler and the coal gasifier. The results show that a model relying on discretization of the velocity equation is more flexible in handling different temperature viscosity relations. Nevertheless. a model relying on an analytical solution is the one Fast enough for a potential use as a CFD submodel. Furthermore. the influence of simplifications to the heat balance in the model is investigated. It is found that simplification of the heat balance can be applied when the radiation heat flux is dominant in the balance.