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A numerical method for the solution of the Navier‐Stokes equations is developed using an integral representation of the conservation equations. The velocity‐vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundary‐domain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. The boundary‐domain integral formulation is developed and tested for natural convection flows in closed cavities with complex geometries.

This paper aims to describe the 2D meshless local boundary integral equation (LBIE) method for solving the Navier–Stokes equations.

The velocity–vorticity formulation is selected to eliminate the pressure gradient of the equations. The local integral representations of flow kinematics and transport kinetics are derived. The integral equations are discretized using the local RBF interpolation of velocities and vorticities, while the unknown fluxes are kept as independent variables. The resulting volume integrals are computed using the general radial transformation algorithm.

The efficiency and accuracy of the method are illustrated with several examples chosen from reference problems in computational fluid dynamics.

The meshless LBIE method is applied to the 2D Navier–Stokes equations. No derivatives of interpolation functions are used in the formulation, rendering the present method a robust numerical scheme for the solution of fluid flow problems.

The main purpose of this study is to investigate the natural convection of micropolar fluid in a square cavity with two orthogonal heaters placed inside. The study of natural convection in a two-dimensional enclosure determines the effect of non-uniform heated plate on certain micropolar fluid flows which are found in many engineering applications. Therefore, because of its practical interest in the engineering fields such as building design, cooling of electronic components, melting and solidification process, solar energy systems, solar collectors, liquid crystals, animal blood, colloidal fluids and polymeric fluids, the topic needs to be further explored.

The dimensionless governing equations have been solved by finite volume method of the second-order central difference and upwind scheme.

The effects of the Rayleigh number, nonuniformity parameter and vortex viscosity parameter on fluid flow and heat transfer have been analyzed. The rate of heat transfer increases with an increase in the aspect ratio of the heated plates for all the values of Rayleigh number and vortex viscosity parameter. The heat transfer rate is reduced with an increase in the vortex viscosity parameter. It is predicted that the non-uniform of the baffle gives better heat transfer than uniform heating.

The present numerical results were tested against the experimental work. The present results have an excellent agreement with the results obtained by the previous experimental work.

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.

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.

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.

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.

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.

This paper aims to develop a multidomain boundary element method (BEM) for modeling 2D complex turbulent thermal flow using low Reynolds two‐equation turbulence models.

The integral boundary domain equations are discretised using mixed boundary elements and a multidomain method also known as a subdomain technique. The resulting system matrix is an overdetermined, sparse block banded and solved using a fast iterative linear least squares solver.

The simulation of a turbulent flow over a backward step is in excellent agreement with the finite volume method using the same turbulent model. A grid consisting of over 100,000 elements could be solved in the order of a few minutes using a 3.0 Ghz P4 and 1 GB memory indicating good efficiency.

The paper shows, for the first time, that the BEM is applicable to thermal flows using k‐ε.

The purpose of this paper is to study steady natural convection flow and heat transfer in a triangular cavity filled with a micropolar fluid.

It is assumed that the left inclined wall is heated, whereas the other walls are cooled and maintained at constant temperatures. All four walls of the cavity are assumed to be rigid and impermeable. The micropolar fluid is considered to satisfy the Boussinesq approximation. The governing equations and boundary conditions are solved using the finite difference method of the second order accuracy over a wide range of the Rayleigh number, Prandtl number, vortex viscosity parameter and two values of micro-gyration parameter, namely, strong concentration (n = 0) and week concentration (n = 0.5).

The results are presented in the form of streamlines, isotherms, vorticity contours and variations of average Nusselt number and fluid flow rate depending on the Rayleigh number, Prandtl number, vortex viscosity parameter and micro-gyration parameter. The flow field and temperature distribution in the cavity are affected by these parameters. The heat transfer rate into the cavity is decreasing upon the raise of the vortex viscosity parameter.

This work studies the effects of vortex viscosity parameter and micro-gyration parameter in a 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; for the design of solar collectors, room ventilation systems and electronic cooling systems; and so on.

Science, Technology, Engineering, and Mathematics (STEM) education, its importance, and its difficulties have been defined. This chapter seeks to present the digital tools that have been used during the pandemic period and that have been focused on promoting STEM education at different levels. The efforts made by educational organizations worldwide are mentioned. Different regions are shown presenting the best experiences of digital tools that enhance the elements of STEM and can be extended to different levels of education from elementary school to university. On the other hand, successful experiences of the use of technological tools from the teachers' point of view are shown, depicting the tools that have worked the most during the process of adapting to online classes to devise a much better educational plan that continues to take advantage of digital tools for STEM education.

Vorticity formulations for the incompressible Navier‐Stokes equations have certain advantages over primitive‐variable formulations including the fact that the number of equations to be solved is reduced through the elimination of the pressure variable, identical satisfaction of the incompressibility constraint and the continuity equation, and an implicitly higher‐order approximation of the velocity components. For the most part, vorticity methods have been used to solve exterior isothermal problems. In this research, a vorticity formulation is used to study the natural convection flows in differentially‐heated enclosures. The numerical algorithm is divided into three steps: two kinematic steps and one kinetic step. The kinematics are governed by the generalized Helmholtz decomposition (GHD) which is solved using a boundary element method (BEM) whereas the kinetics are governed by the vorticity equation which is solved using a finite element method (FEM). In the first kinematic step, vortex sheet strengths are determined from a novel Galerkin implementation of the GHD. These vortex sheet strengths are used to determine Neumann boundary conditions for the vorticity equation. (The thermal boundary conditions are already known.) In the second kinematic step, the interior velocity field is determined using the regular (non‐Galerkin) form of the GHD. This step, in a sense, linearizes the convective acceleration terms in both the vorticity and energy equations. In the third kinetic step, the coupled vorticity and energy equations are solved using a Galerkin FEM to determine the updated values of the vorticity and thermal fields. Two benchmark problems are considered to show the robustness and versatility of this formulation including natural convection in an 8×1 differentially‐heated enclosure at a near critical Rayleigh number.

This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non‐Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non‐linear terms is converted into equivalent boundary integrals by the multi‐domain dual reciprocity method (MD‐DRM) in each subdomain. Augmented thin plate splines interpolation functions are used for the approximation of field variables. The iterative numerical formulation is achieved by viewing the material as divided into small elements and on each of them the integral representation formulae for the velocity and temperature are applied and discretised using linear boundary elements. The final system of non‐linear algebraic equations is solved by a modified Newton's method. The numerical examples include non‐Newtonian problems with viscous dissipation, temperature‐dependent viscosity and natural convection due to bouyancy forces.

The main objective of this paper is to investigate the response of human skin to an intense temperature drop at the surface. In addition, this paper aims to evaluate the efficiency of finite difference and finite volume methods in solving the highly nonlinear form of Pennes’ bioheat equation.

One-dimensional linear and nonlinear forms of Pennes’ bioheat equation with uniform grids were used to study the behavior of human skin. The specific heat capacity, thermal conductivity and blood perfusion rate were assumed to be linear functions of temperature. The nonlinear form of the bioheat equation was solved using the Newton linearization method for the finite difference method and the Picard linearization method for the finite volume method. The algorithms were validated by comparing the results from both methods.

The study demonstrated the capacity of both finite difference and finite volume methods to solve the one-dimensional and highly nonlinear form of the bioheat equation. The investigation of human skin’s thermal behavior indicated that thermal conductivity and blood perfusion rate are the most effective properties in mitigating a surface temperature drop, while specific heat capacity has a lesser impact and can be considered constant.

This paper modeled the transient heat distribution within human skin in a one-dimensional manner, using temperate-dependent physical properties. The nonlinear equation was solved with two numerical methods to ensure the validity of the results, despite the complexity of the formulation. The findings of this study can help in understanding the behavior of human skin under extreme temperature conditions, which can be beneficial in various fields, including medical and engineering.