Flow and heat transfer of couple stress fluid in a porous channel with expanding and contracting walls

In this paper, an incompressible laminar flow of a couple stress fluid in a porous channel with expanding or contracting walls is considered. Assuming symmetric injection or suction along the uniformly expanding porous walls and using similarity transformations, the governing equations are reduced to nonlinear ordinary differential equations. The resulting equations are then solved numerically using quasilinearization technique. The graphs for velocity components and temperature distribution are presented for different values of the fluid and geometric parameters.     

Combined effects of variable thermal conductivity and induced magnetic field on convective Jeffrey fluid flow with nth order chemical reaction

This study addresses the impact of variable thermal conductivity and induced magnetic field on an unsteady two‐dimensional channel flow of an incompressible laminar mixed convective and chemically reacted Jeffrey fluid embedded in a non‐Darcy porous medium with an appropriate convective type boundary conditions. The suction/injection velocity distribution has been assumed to be in an exponential form. The set of transport equations is reduced into coupled ordinary differential equations by using appropriate similar variables, which are solved by shooting technique with Runge‐Kutta fourth‐order algorithm. The investigation is carried out for various emerging nondimensional parameters on the axial, radial velocities, temperature distribution, concentration, and induced magnetic fields and also with skin friction coefficient are discussed through graphs. The value of the local Sherwood and Nusselt numbers are analyzed numerically. We noticed that the effect of the induced magnetic field is increased with Strommer's number while it decreases for high magnetic Reynolds number.     

Influence of homogeneous‐heterogeneous reactions and induced magnetic field on the nonlinear thermal convective radiative Jeffrey liquid flow with heat source/sink

An analysis has been carried out to investigate the effect of homogeneous‐heterogeneous reactions and induced magnetic field on the unsteady two‐dimensional incompressible nonlinear thermal convective velocity slip flow of a Jeffrey fluid in the presence of nonlinear thermal radiation and heat source/sink. We assumed that the flow is generated due to injection at the lower plate and suction at the upper plate. We obtained a numerical solution for the reduced nonlinear governing system of equations via the shooting technique with fourth‐order Runge‐Kutta integration. We plotted the graphs for various nondimensional parameters, like Deborah number, heat source/sink parameter, nonlinear convection parameter, nonlinear radiation parameter, magnetic Reynolds number, Strommer's number, velocity slip parameter, strengths of homogeneous, heterogeneous reaction parameters and skin friction over the nondimensional flow, temperature, concentration profiles and magnetic diffusivity fields. Also, we calculated the numerical values of boundary properties, such as the skin friction and heat transfer rate. We noticed that the temperature of the fluid is enhanced with the radiation parameter, whereas the concentration decreases with increase of the magnetic Reynolds number. The present results have good agreement with published work for the Newtonian case.     

Attribute-based authentication on the cloud for thin clients

We propose two new authentication schemes for the cloud that support private attribute-based authentication services. The basic scheme is non-anonymous attribute-based authentication scheme. The extended scheme of the basic scheme is fully anonymous attribute-based authentication scheme to realize full anonymity and unlinkability services. In the proposed schemes, a user is authenticated by the remote server if the intersection of the set of his/her assigned attributes and the server’s required attributes exceeds a satisfactory predefined level. Unlike existing attribute-based encryption and signature schemes that require the user to perform significant amount of elliptic curve bilinear pairings and modular exponentiations, and require the user to hold a significantly long decryption/signature key, in our schemes the user is not required to perform any bilinear pairings. With a fixed length private key, independent of the number of attributes, the cloud user performs only few exponentiations by which he/she is able to authenticate himself/herself to the remote server and establish a session key with the server with the condition that he/she satisfies a predefined level of the server’s attributes requirement. Therefore, our schemes are suitable for implementation on devices with limited resources. We provide the rigorous security of the proposed schemes and complexity analysis of our schemes. Finally, the security and performance comparisons of our schemes with the existing related schemes show that our schemes outperform other existing schemes.     

Effects of double stratification on MHD chemically reacting second‐grade fluid through porous medium between two parallel plates

The present study focuses on the study of heat transfer in a magnetohydrodynamic double stratification fluid flow through porous channel. In getting the solution of Navier‐Stokes equations, we have adapted the similarity transformation technique to convert the partial differential equations into a coupled system of nonlinear ordinary differential equations. We further applied the fourth‐order Runge‐Kutta method with shooting technique to solve the problem numerically. The results are exhibited via graphs, and the analysis has been addressed for various flow characteristics with respect to the parameters concerned. It is found that thermal stratification enhances both temperature and heat transfer rates, and solutal stratification enhances concentration and mass transfer rates. Concentration decreases with increasing chemical reaction and it increases with stratification. A significant variation is observed between concentration profiles in the presence of stratification.     

Second law analysis for chemically reacting natural convective second‐grade fluid flow between porous parallel plates with Hall and Ion slip

In this article, we performed the entropy generation of free convective chemically reacting second‐grade fluid confined between parallel plates in the influence of the Hall and Ion slip with heat and mass fluxes. Let there be a periodic suction/injection along with the plates, the governing flow field equations are reduced as a set of coupled nonlinear ordinary differential equations by using appropriate similarity transformations then solved numerically with shooting method based on Runge‐Kutta 4th order scheme. The results are analyzed for velocity in axial and radial directions, temperature distribution, concentration distribution, entropy generation number, Bejan number, mass and heat transfer rates with respect to distinct geometric, and fluid parameters and shown graphically and tables. It is observed that the entropy generation is enhanced with Prandtl number, whereas decreases with a second‐grade parameter, the effects of Hall and Ion slip parameters on velocity components, temperature and entropy generation number are the same. The entropy generation number the fluid is enhanced with the suction‐injection parameter whereas, the concentration of the fluid decreases with the increasing of chemical reaction parameter.     

Numerical investigation of induced magnetic field and variable mass diffusivity on double stratified Jeffrey fluid flow with heat and mass flux boundary conditions

The investigation explores the influence of the induced magnetic field and variable mass diffusivity on an unsteady incompressible mixed convective double stratified and chemically reactive flow of Jeffrey fluid through a porous medium with heat, and mass flux boundary conditions. The system of flow field nonlinear partial differential equations is reduced into coupled nondimensional ordinary differential equations using appropriate similar variables, then worked out a numerical solution via shooting technique along with Rung-Kutta fourth-order scheme. The results are analyzed for various physical flows, heat and mass transfers, induced magnetic field, and skin friction against disparate prominent parameters via graphs and tables. It is recognized that the temperate of the fluid is enhanced with thermal stratification; however, the concentration of the fluid is decreased with magnetic Reynold's number. The comparison of numerical values of skin friction with the existing literature for limiting sense.     

Entropy generation analysis of natural convective chemically reacting squeezing flow of Casson fluid between parallel disks with Hall and Ion slip currents

This paper concerns the second law analysis of free convective squeezing flow of a chemically reacting Casson fluid confined between two parallel disks with Hall and Ion slip effects. The upper one is impermeable and the lower disk is porous. The linear momentum, energy balance and mass partial differential equations converted as system of ODEs by similarity transformations and tackled with shooting method via fourth order Runge‐Kutta scheme. The impact of various dimensionless geometric and fluid parameters on the velocity fields, temperature and concentration fields, entropy generation and Bejan numbers are studied and presented in the form of pictorially. The present results are correlated with already published outcomes for viscous case and found to be good agreement. The Bejan number of the fluid enhances with Ion slip parameter, whereas the concentration profile of the fluid is decreases with increasing of the Casson fluid parameter. The entropy generation of the fluid is enhanced with Eckert number whereas the Bejan number is decreased with suction/blowing parameter     

Entropy generation analysis of free convection radiative MHD Eyring–Powell fluid flow between porous parallel plates with Soret and Dufour effects

In this present study, we have investigated the entropy generation analysis and Dufour and Soret impacts on unsteady incompressible free convective radiative MHD Eyring–Powell fluid flow between parallel plates with periodic injection and suction. The governing PDEs are converted into nondimensional coupled nonlinear ordinary differential equations by using similarity variables then numerically solved by Runge–Kutta fourth-order scheme with shooting technique. The results are discussed in detail for different flow, mass, and heat transfer profiles corresponding to various active parameters and presented in tables and graphs. Also, it is noticed that the temperature profiles are enhanced with the fluid parameter, whereas the concentration profiles are decreased with the Prandtl number. The validations of present results with the existing outcomes for the viscous case of skin friction are included and have found to be in good agreement. The present numerical study is useful for the enhancement of heat transfer in various industrial and chemical processes.