Display omitted •Conformal cooling channels are designed via thermal fluid topology optimization.•Temperature difference and pressure drop be decreased up to 2.20 K and 25.40%.•Thermal-load-based design strategy reduce the average temperature up to 1.45 K.•Special-shaped cylindrical castings be studied via 2D topology optimization.. Conformal cooling technology is widely used in the thermal management for injection molding process. However, the overall design of cooling channel layout needs to be optimized due to non-uniform thermal load, limited design freedom and other factors. This paper presents a novel procedure for conformal cooling channel design by using thermal-load-based topology optimization. Unlike previous approaches that focused on optimizing the channel configuration or geometric parameters, the current work applies multiphysics topology optimization on the entire cooling area. The objective is to obtain the optimal channel layout with both low pressure drop and high heat transfer rate. A serious of optimized planar results are converted to three-dimensional channels that conform to the specific injection casting and are applied to injection molding process in a simulation software environment. For a given thin-plate casting, compared with the conventional parallel cooling process, the steady state average temperature and maximum temperature difference are decreased by 0.53 K and 2.20 K, respectively, and the pressure drop of coolant is decreased by 25.40%. For castings where non-uniform thermal loads are considered, the average temperature and pressure drop are decreased up to 1.45 K and 27.55%, respectively. The results for both sheet castings and cylindrical castings have demonstrated the stability, flexibility, and rationality of the proposed procedure. In addition, the conceptual design of cooling channels based on thermal load is expected to be applied to more potential thermal engineering fields.