A mathematical model of three-dimensional fluid flow, heat transfer and solidification in thin slab casting is developed based on the enthalpy-porosity approach in a single-phase framework and used to analyze and compare the fluid flow and thermal behaviors in the funnel-type molds of Compact Strip Production (CSP^®) and Flexible Thin Slab Casting (FTSC^®) caster. An Electromagnetic Brake (EMBR) model is also incorporated into this coupled model to see the effects of EMBR on fluid flow and solidification in a CSP caster with EMBR system. The numerical treatments specific to the complex funnel-shaped mold boundaries are discussed. The obtained numerical results are partly validated by those available in literature and theoretical analyses. The fluid flow and thermal features of thin slab in CSP mold and FTSC mold are analyzed and their comparisons between them are made. It is found that the flow pattern, level fluctuation, superheat dissipation, temperature distribution and shell growth in both molds present different features. The structure of SEN strongly affects the flow pattern of the impinging jet from SEN ports, and then the dissipation mode of the melt superheat and the uniform growth of solidification shell. A four-port SEN^® with two small upper ports in FTSC mold is helpful to activate the meniscus flow and increase the meniscus temperature, but high level fluctuation may occur. The EMBR in a CSP mold can both suppress the meniscus flow and increase the meniscus temperature. A complete flow-control system including the design of SEN, EMBR and operational conditions is essential for thin slab production considering their individual flow and thermal features in the funnel-type molds of CSP and FTSC casters.