An amalgamation of blockchain technology and the Internet of Things (IoT) has presented notable concerns regarding scalability, security, and privacy, particularly in IoT contexts with limited resources. Conventional blockchains, including traditional consensus mechanisms like Proof of Work (PoW) and Proof of Stake (PoS), meet challenges in handling many transactions, meeting energy efficiency standards, and addressing privacy issues in blockchain-based IoT networks. This work presents a new fog-based blockchain paradigm that integrates the benefits of Proof of Authority (PoA) and Delegated Proof of Stake (DPoS) consensus mechanisms and a proxy re-encryption approach to guarantee improved efficiency and system security. The proposed architecture integrates three essential operational algorithms: Fog Node Operation, Blockchain Node Operation, and Privacy Preservation Mechanism. These algorithms manage data processing, ensure secure transactions, and maintain privacy. Fobsim is used to conduct a series of simulations to evaluate the performance of PoA, DPoS, PoW, and PoS. The results indicate that PoA and DPoS provide better transaction speed, energy efficiency, and scalability than conventional consensus. As illustrated in the results, PoA stands out for its deficient energy consumption, making it an ideal fit for IoT applications. This research addresses the pressing concerns of scalability, privacy, and energy efficiency in blockchain-enabled Internet of Things (B-IoT) systems. The results lay the foundation for the future advancement of integrated B-IoT systems that can enable extensive, real-time IoT applications.