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The steady non-isothermal flow of an Eyring–Powell fluid in a pipe is investigated using both perturbation and numerical methods. The results are presented for two viscosity models, namely the Reynolds model and the Vogel model. The shooting method is employed to compute the numerical solution. Criteria for validity of perturbation solution are developed. When these criteria are met, it is shown that the perturbation solution is in good agreement with the numerical solution. The influence of various emerging parameters on the velocity and temperature field is also shown.

Purpose The main purpose of this study is to examine the effects of moving wall on the mixed convection flow and heat transfer in a right-angle triangular cavity filled with a micropolar fluid. Design/methodology/approach It is assumed that the bottom wall is uniformly heated and the right inclined wall is cold, whereas the vertical wall is adiabatic and moving with upward/downward velocity v0/−v0, respectively. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the Galerkin finite element method. The Penalty method is used to eliminate the pressure term from the momentum equations. To accomplish the consistent solution, the value of the penalty parameter is taken 107. The simulations are performed for a wide range of Richardson number, micropolar parameter, Prandtl number and Reynolds number. Findings The results are presented in the form of streamlines, isotherms and variations of average Nusselt number and fluid flow rate depending on the Richardson number, Prandtl number, micropolar parameter and direction of the moving wall. The flow field and temperature distribution in the cavity are affected by these parameters. An average Nusselt number into the cavity in both cases increase with increasing Prandtl and Richardson numbers and decreases with increasing micropolar parameter, and it has a maximum value when the lid is moving in the downward direction for all the physical parameters. Research limitations/implications The present investigation is conducted for the steady, two-dimensional mixed convective flow in a right-angle triangular cavity filled with micropolar fluid. An extension of the present study with the effects of cavity inclination, square cavity, rectangular, trapezoidal and wavy cavity will be the interest of future work. Originality/value This work studies the effects of moving wall, micropolar parameter, Richardson number, Prandtl number and Reynolds number parameter in a right-angle triangular cavity filled with a micropolar fluid on the fluid flow and heat transfer. This study might be useful to flows of biological fluids in thin vessels, polymeric suspensions, liquid crystals, slurries, colloidal suspensions, exotic lubricants, solar engineering for construction of triangular solar collector, construction of thermal insulation structure and geophysical fluid mechanics, etc.

Buoyancy-driven, incompressible, two-dimensional flow of a micropolar fluid inside an inclined porous cavity in the presence of magnetic field is investigated. The nonlinear partial differential equations are solved by employing a robust Galerkin finite element scheme. The pressure term in this scheme is eliminated by using the penalty method. The results are exhibited in the form of streamlines, isotherms, and local and average Nusselt numbers for two cases, namely, the constant and the sinusoidal heated lower wall of the conduit. In both cases, the side walls of the cavity are cold and the upper side is insulated. The main difference between the two cases is observed from temperature contours. For constant heated bottom wall a finite discontinuity appears in the temperature distribution at the corners of the bottom wall. In contrast, no such discontinuity appears in the temperature distribution for non-uniform heated bottom wall. The quantitative changes in temperature contours in different portions of the cavity are identified by comparing the results for both cases. The code is also validated and benchmarked with the previous numerical data available in the literature. It is found that the magnetic field inclined at a certain angle either suppresses or enhances the intensity of primary circulations depending on the inclination of the cavity. Further, the average Nusselt number at the bottom wall is higher when magnetic field is applied vertically irrespective of the inclination of cavity. The analysis presented here has potential application in solar collectors and porous heat exchangers.

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