In remanufacturing, a vital segment of the sustainable, low-carbon circular economy, existing versions of the traditional unequal-areas facility layout problem (UA-FLP) model face significant limitations in designing layouts. To be specific, in the process of minimizing the material-handling cost (MHC), these models also alter departmental dimensions, often diverging from construction specifications. This poses a difficulty, as critical equipment required for remanufacturing, e.g., sorting and cleaning machines, have unalterable dimensions, which implies that departmental dimensions cannot be changed from specifications provided. To address this, a novel Flexible Envelope UA-FLP (FE-UA-FLP) model is proposed in this work for designing layouts wherein department dimensions and shapes are not altered while simultaneously the MHC is reduced. The new model offers two additional advantages in that (a) it diminishes the dead space between the departments, generating a visually appealing, compact layout, and (b) it uses an updatable interaction matrix, which allows it to be adaptable to changing demand, making the design process suitable for smart systems. Numerical testing with three meta-heuristics on simulated factory data demonstrates the effectiveness of the FE-UA-FLP model in achieving these objectives. The numerical results also highlight the model's ability to rapidly generate solutions, which is a key requirement for smart manufacturing. Future work can extend this model to three-dimensional optimization and job shop settings.