This paper deals with the MHD peristaltic flow of Williamson fluids through a porous medium between two joint cylinders. The fluid flow was considered to be that of a non-Newtonian fluid, i.e., a Williamson fluid. The inner tube was uniform, while the flexible outer tube had a Sine wave moving down its wall. The analytical solutions for velocity and temperature were obtained as functions (Bessell functions of the first and second types). The solution for velocity profile, temperature, and concentration distribution were obtained as functions of the physical parameters of the problem (Darcy number, magnetic parameter, Grasoff thermal number, Reynolds number, Prantl number, and Schmidt number) along with other physical parameters. The effect of the physical parameters was discussed graphically. A comparison with previously published graphical results was also carried out. The ambition of the present paper is to contribute to practical applications in geographical and physiological fluid dynamics, such as on sandstone, in the human lungs, on beach sand, on limestone, and in the bile duct. This study is based on theoretical research and can be helpful in the fields of fluid mechanics and mathematics.

Various industrial operations involve frequent heating and cooling of electrical systems. In such circumstances, the development of relevant thermal devices is of extreme importance. During the development of thermal devices, the second law of thermodynamics plays an important role by means of entropy generation. Entropy generation should be reduced significantly for the efficient performance of the devices. The current paper reports an analytical study on micropolar fluid with entropy generation over a stretching surface. The influence of various physical parameters on velocity profile, microrotation profile, and temperature profile is investigated graphically. The impact of thermal radiation, porous medium, magnetic field, and viscous dissipation are also analyzed. Moreover, entropy generation and Bejan number are also illustrated graphically. Furthermore, the governing equations are solved by using HAM and code in MATHEMATICA software. It is concluded from this study that velocity and micro-rotation profile are reduced for higher values of magnetic and vortex viscosity parameter, respectively. For larger values of Eckert number and thermal radiation parameters, Bejan number and entropy generation are increased, respectively. These findings are useful in petroleum industries and engineering designs.

The calculus in the absence of limits is known as quantum calculus. With a difference operator, it substitutes the classical derivative, which permits dealing with sets of functions that are non-differentiations. The theory of integral inequality in quantum calculus is a field of mathematics that has been gaining considerable attention recently. Despite the fact of its application in discrete calculus, it can be applied in fractional calculus as well. In this paper, some new Anderson type q-integral and h-integral inequalities are given using a Feng Qi integral inequality in quantum calculus. These findings are highly beneficial for basic frontier theories, and the techniques offered by technology are extremely useful for those who can stimulate research interest in exploring mathematical applications. Due to the interesting properties in the field of mathematics, integral inequalities have a tied correlation with symmetric convex and convex functions. There exist strong correlations and expansive properties between the different fields of convexity and symmetric function, including probability theory, convex functions, and the geometry of convex functions on convex sets. The main advantage of these essential inequalities is that they can be converted into time-scale calculus. This kind of inevitable inequality can be very helpful in various fields where coordination plays an important role.

A combined immersed boundary–lattice Boltzmann approach is used to simulate the dynamics of the fluid–structure interaction of a hollow sealing strip under the action of pressure difference. Firstly, the multiple relaxation times LBM model, hyper-elastic material model and immersed boundary method were deduced. According to the strain characteristics of hyper-elastic materials and the specific situation of friction between the elastic boundary and solid boundary, the internal force and the external force on the immersed boundary were discussed and deduced, respectively. Then, a 2D calculation model of the actual hollow sealing strip system was established, during which technical problems such as the equivalent wall thickness of the sealing strip and the correction of the stiffness of the contact corner were solved. The reliability of the model was verified by comparing results of FEM simulation of quasi-static deformation. Following this, the simulation results of three typical cases of sealing strips were presented. The results show that when the sealing strip fails, there will be a strong coupling phenomenon between the flow field and the sealing strip, resulting in the oscillation of the flow field and the sealing strip at the same frequency.

A major issue for human growth is the energy crisis. In the current study, circular pipes are considered an energy-efficient technology viable in all seasons. It uses non-constant soil temperature and water flow in coldest regions. This model reports the thermal performance of pipes with different results in hot and cold climates. To degree thermal performance, pipe version changed into advanced and simulated with ANSYS 18.1 Fluid Flow (Fluent). Data was collected from two modelled summer and winter seasons. Continuity, momentum, and energy equation have been used for the simulation. Comparison analysis is also being carried out about the obtained results with previously published articles. The effects of summer and winter temperature and speed on performance were also evaluated. Further, the graphical interpretation is also carried for velocity and pressure distribution. The study highlights a drastic drop in temperature and velocity near the inlet and outlet region while Pressure is inversely proportional to velocity in these regions. It is also obtained from the simulation that the temperature pressure and velocity remain uniform in the fully develop region.