Simultaneous effects of viscous and Darcy dissipation on mixed convection flow in an annulus partially filled with porous material: Analytical approach

The effect of thermal dissipation on a steady, fully developed, mixed convection viscous, incompressible fluid in an annulus partially filled with porous materials has been thoroughly examined in this work. Fluid flow begins within the annulus when a pressure gradient is applied abruptly in the flow direction. The fluid flow in the porous zone is characterized by the Brinkmann-extended Darcy model. The fluid is divided into transparent and porous parts by a minimal interface. By matching their velocities and considering the shear stress jump conditions at the interface, the clear fluid and the porous region are connected. Additionally, the viscous dissipation effect is considered while determining the energy equation in the clear fluid zone. However, in the porous area, the Darcy dissipation effects are considered in addition to the viscous dissipation influence. In the model, the results of various fluid parameters in the problem were addressed using line graphs and the homotopy perturbation method. The study found that when the porous region's thickness grows, heat transmission on the annular surface enclosing the clear fluid region increases while it decreases on the border surface close to the porous region. In addition, a thicker porous region requires a greater pressure gradient to propel the flow.     

Time-dependent natural convection fluid flow of stably stratified fluid in an asymmetrically heated vertical channel filled with an anisotropic porous material

This paper presents a theoretical analysis of the combined effects of anisotropic porous material and thermal stratification on the transient natural convection fluid flow in an asymmetrically heated vertical parallel channel. The solutions of the governing equations for the temperature and velocity fields are obtained using Laplace transform technique, Riemann sum approximation, and the D'Alembert method. The choice of the D'Alembert method is to provide a simple decoupling procedure for the coupled governing equations while still retaining their original orders. The research established that owing to the layering effect induced by the thermal stratification $(S)$, the temperature and the velocity distributions of the fluid are found to be attenuated with an increase in thermal stratification. It is also observed that the inclusion of anisotropic parameters in the transport equations aids in regulating the fluid velocity, temperature, Nusselt number, skin friction, and mass flow rate. In addition, by neglecting the anisotropic parameter and taking into account the adiabatic stratification of the fluid, the numerical values for the mass flow rate of the present research favorably compared with the numerical results obtained by Singh et al.     

Time-dependent pressure-driven flow in a horizontal cylinder filled with a bidisperse porous material

Some properties of time-dependent that modify Brinkman equations for fluid flow in a cylindrical tube filled with Bidisperse Porous Material are discussed in this article. The fluid velocities through the fracture and porous phases of the Bidisperse Porous Medium (BDPM) resulting from the application of pressure gradient are described by two coupled second-order partial differential equations. Laplace transform technique, D'Alembert and Riemann-Sum Approximation Methods are used to obtain a semianalytical solution for the model. The choice of the D'Alembert is made to systematically decouple the coupled governing equations without altering their initial orders. The role of the coupling parameter: The coefficient of momentum transfer $(\eta )$ in the flow formation is considered. Accordingly, three cases are analyzed: (a) weak coupling $(\eta =0)$ which described the fluid flow in the absence of the coupling parameter, (b) the strong coupling resulting from a large value of the coupling parameter $(\eta \to \infty )$, and (c) fluid momentum for any arbitrary value of $\eta$. It is observed that fluid stability is attained when ${\mathit{Da}}_f$ and ${\mathit{Da}}_p$ are decreased; a finding that agrees with the findings of Nield and Kuznetsov and Magyari. Also, the maximum velocity in the fracture phase of the BDPM is attained when the coefficient of momentum transfer is neglected $(\eta =0)$ while an opposing flow formation is demonstrated in the fracture and porous phases of BDPM as $\eta$ is increased.     

Run-up flow of MHD fluid between parallel porous plates in the presence of transverse magnetic field

This paper investigated the run-up flow of magnetohydrodynamics (MHD) incompressible, viscous, Newtonian fluid bounded by two parallel horizontal porous plates in the presence of transverse magnetic field. The fluid flow is initially due to constant pressure gradient, placed parallel to the plates. On attaining steady state, the pressure gradient is suddenly withdrawn and the lower porous plate is set into motion in its own plane, this phenomenon is termed as run-up flow. The transfer of momentum is as a result of the disturbances emanating from the boundary into the fluid. The initial value problem is solved using Laplace transform technique to obtain the closed-form solution for the velocity in the Laplace domain. Semi-analytical result is obtained by an inversion technique based on Riemann-sum approximation to invert the solution for velocity into its corresponding time domain. The mathematical simulation conducted shows that increasing the Hartmann number is observed to decrease the fluid velocity while increasing the pressure gradient is found to enhance the fluid velocity. Furthermore, the opposing effects of suction/injection parameter on the fluid velocity have been established in the research.