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A mathematical model comprising Darcy Forchheimer effects on the 3D nanofluid flow with engine oil as a base fluid containing suspended carbon nanotubes (CNTs) is envisioned. The CNTs are of both types i.e., multi-wall carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs). The flow is initiated by an exponentially stretched surface. The impacts of Cattaneo–Christov heat flux along with velocity and thermal slip conditions are key factors in the novelty of the defined model. The boundary layer notion is designed to convert the compact form of equations into the component shape. Appropriate transformations lead to differential equations with high nonlinearity. The final non-dimensional system is solved numerically by a “MATLAB” function known as bvp4c. For both CNTs, different graphical sketches are drawn to present the influence of arising parameters versus related profiles. The outcomes show that higher slip parameter boosts the axial velocity, whereas fluid temperature lowers for a sturdier relaxation parameter.

Due to the growing of the use of Internet and communication media, image encryption is rapidly increased. Image sharing through unsafe open channels is vulnerable for attacking and stealing. For protecting the images from attacks, encryption techniques are required. Recently, new and efficient chaos-based techniques have been suggested to develop secure image encryption. This study presents a novel image encryption framework based on integrating the chaotic maps and color codes. Three phases are involved in the proposed image encryption technique. Piecewise chaotic linear map (PWLCM) is used in the first phase for permuting the digital image. In the second phase, substitution is done using Hill cipher which is the mixing of color codes with the permuted image. The third phase is implemented by XORing, a sequence generated by the chaotic logistic map (CLM). The proposed approach enhances the diffusion ability of the image encryption making the encrypted images resistant to the statistical differential attacks. The results of several analyses such as information entropy, histogram correlation of adjacent pixels, unified average changing intensity (UACI), number of pixel change rate (NPCR), and peak signal-to-noise ratio (PSNR) guarantee the security and robustness of the proposed algorithm. The measurements show that the proposed algorithm is a noble overall solution for image encryption. Thorough comparison with other image encryption algorithms is also carried out.

In the last decade, the communication of images through the internet has increased. Due to the growing demands for data transfer through images, protection of data and safe communication is very important. For this purpose, many encryption techniques have been designed and developed. New and secured encryption schemes based on chaos theory have introduced methods for secure as well as fast communication. A modified image encryption process is proposed in this work with chaotic maps and orthogonal matrix in Hill cipher. Image encryption involves three phases. In the first phase, a chaotic Henon map is used for permuting the digital image. In the second phase, a Hill cipher is used whose encryption key is generated by an orthogonal matrix which further is produced from the equation of the plane. In the third phase, a sequence is generated by a chaotic tent map which is later XORed. Chaotic maps play an important role in the encryption process. To deal with the issues of fast and highly secured image processing, the prominent properties of non-periodical movement and non-convergence of chaotic theory play an important role. The proposed scheme is resistant to different attacks on the cipher image. Different tests have been applied to evaluate the proposed technique. The results of the tests such as key space analysis, key sensitivity analysis, and information entropy, histogram correlation of the adjacent pixels, number of pixel change rate (NPCR), peak signal to noise ratio (PSNR), and unified average changing intensity (UCAI) showed that our proposed scheme is an efficient encryption technique. The proposed approach is also compared with some state-of-the-art image encryption techniques. In the view of statistical analysis, we claim that our proposed encryption algorithm is secured.