Muhammad Bilal Hafeez’s research while affiliated with Gdansk University of Technology and other places

Natural convection is a complex environmental phenomenon that typically occurs in engineering settings in porous structures. Shear thinning or shear thickening fluids are characteristics of power-law fluids, which are non-Newtonian in nature and find wide-ranging uses in various industrial processes. Non-Newtonian fluid flow in porous media is a difficult problem with important consequences for energy systems and heat transfer. In this paper, convective heat transmission in permeable enclosures will be thoroughly examined. The main goal is to comprehend the intricate interaction between the buoyancy-induced convection intensity, the porosity of the casing, and the fluid’s power-law rheology as indicated by the Rayleigh number. The objective is to comprehend the underlying mechanisms and identify the ideal conditions for improving heat transfer processes.The problem’s governing equations for a scientific investigation are predicated on the concepts of heat transport and fluid dynamics. The fluid flow and thermal behavior are represented using the energy equation, the Boussinesq approximation, and the Navier–Stokes equations. The continuity equation in a porous media represents the conservation of mass. Finite Element Analysis is the numerical method that is suggested for this challenging topic since it enables a comprehensive examination of the situation. The results of the investigation support several important conclusions. The power-law index directly impacts heat transmission patterns. A higher Rayleigh number indicates increased buoyancy-induced convection, which increases the heat transfer rates inside the shell. The porosity of the medium significantly affects temperature gradients and flow distribution, and it is most noticeable when permeability is present. The findings show how, in the context of porous media, these parameters have complicated relationships with one another.

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In this review article, we investigate the dynamic nature of the Kozeny–Carman Model concerning permeability and its application in engineering contexts. Providing insights into the changing dynamics of permeability within mining, petroleum, and geotechnical engineering, among other engineering applications. While some are complex and require additional modifications to be applicable, others are simple and still function in specific situations. Therefore, having a thorough understanding of the most recent permeability evolution model would help engineers and researchers in finding the right solution for engineering issues for prospects. The permeability evolution model Kozeny–Carman (KC) put forth by previous and current researchers is compiled in this paper, with a focus on its features and drawbacks.

In this article, we will discuss the applications of the Spectral element method (SEM) and Finite element Method (FEM) for fractional calculusThe so-called fractional Spectral element method (f-SEM) and fractional Finite element method (f-FEM) are crucial in various branches of science and play a significant role. In this review, we discuss the advantages and adaptability of FEM and SEM, which provide the simulations of fractional derivatives and integrals and are, therefore, appropriate for a broad range of applications in engineering, biology, and physics. We emphasize that they can be used to simulate a wide range of real-world phenomena because they can handle fractional differential equations that are both linear and nonlinear. Although many researchers have already discussed applications of FEM in a variety of fractional differential equations (FDEs) and delivered very significant results, in this review article, we aspire to enclose fundamental to advanced articles in this field which will guide the researchers through recent achievements and advancements for the further studies.

The Spectral Finite Element Technique (SFEM) has Several Applications in the Sciences, Engineering, and Mathematics, which will be Covered in this Review Article. The Spectral Finite Element Method (SFEM) is a Variant of the Traditional Finite Element Method FEM that Makes use of Higher Order Basis Functions (FEM). One of the most Fundamental Numerical Techniques Employed in the Numerical Simulation is the SFEM, which Outperforms Other Techniques in Terms of Faster Convergence, Reduced Diffusion and Dispersion Errors, Simplicity of the Application as well as Shorter time of Computation. The Spectral Finite Element Technique Combines the Characteristics of Approximating Polynomials of Spectral Methods. The Approach to Discretizing the Examined Region Unique to the FEM is a mix of both Approaches. Combining These Techniques Enables Quicker (Spectral) Convergence of Solutions, Higher Approximation Polynomial Order, the Removal of Geometric Constraints on the Examined Areas, and much Lower Discretization Density Requirements. Spectral Element Methods used in Different Applications are Presented Along with a Statistical Overview of Studies During 2010–2022.

The goal of this study is to determine the maximum energy and solute particles' transportation growth in a 3D-heated region of Prandtl martial through a dynamic magnetic field. The effects of this field on the properties of solvent molecules and heat conduction are studied. A correctly stated functional method and a finite element approach are comparable to a certain type of differential equations. In order demonstrate the effects of various factors such as mass diffusion, heat generation, and thermal diffusivity on the investigation of the diffusion coefficient and thermal mass in a three-dimensional Newtonian flow, the study of viscous and heat conduction rates is presented. The results show that the comparisons of hybrid nanofluid 2 3 and 2 3 with base fluid and w.r.t Local skin friction coefficient, Nusselt number and Sherwood number.

In this paper, an extensive analysis of heat and mass transfer characteristics of a Casson fluid flow past a cylinder in a wavy channel has been performed. Due to the non-availability of analytical solution the model represented by coupled non-linear partial differential equations has been simulated by implementing higher-order Finite Element Method (FEM). For the approximation of velocity, temperature, and concentration profiles, a finite element space involving the cubic polynomial (P3) is selected whereas the pressure estimation is accomplished through a space of quadratic polynomial (P2). Such a choice gives rise to 10° of freedom for each of the velocity components, temperature, and concentration profile while 6° of freedom for the pressure. The Newton's method is used to linearize the systems of equations. The linearized inner system of equations are solved with a direct solver PARDISO. Computational results are demonstrated in the form of velocity, isotherms, isoconcentrations, and for several quantities of interest including the drag and lift coefficients. It has been observed that both drag and lift coefficients show a decreasing trend with Magnetic parater M. In addition, for all values of Bn, the drag coefficient has a linear growth profile as a result of fluid forces dominating at higher values of Bn. Furthermore, the concentration is high in the center of the channel and has a decreasing trend as we move towards the walls.