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This analysis theoretically investigates the transport phenomena of mixed convection flows in an enclosure of rectangular geometry saturated with a permeable medium filled with an electrically conducting nanofluid. An inclined magnetic field is taken into consideration. Buongiorno's model is utilized to characterize the nanoliquid. The enclosure has adiabatic walls and hot slits. A uniform cold temperature is maintained at the enclosure's lower and upper walls. The enclosure's vertical walls are thermally insulated with hot slits at the center of the walls. This kind of analysis on mixed convective, electrically conducting nanofluid flows in enclosures finds applications in smart nanomaterial processing systems and hybrid electromagnetic nanoliquid fuel cells. The Marker-And-Cell (MAC) method is utilized to solve the transformed nondimension system of governing equations subject to the fitted boundary conditions. The effects of key physical parameters on streamlines, isotherms, iso-concentration contour plots and the heat transmission rate are examined. The simulations demonstrate that the Richardson number has a predominant impact on the thermo-solutal features of nanofluid flow in the rectangular enclosure. Variations in magnetic field and buoyancy ratio parameters exert a notable influence on the iso-concentrations and isotherms. An increase in the Darcy number values exhibits a tendency to magnify the local heat transfer rate. Higher Grashof number values reduce the local Nusselt number profiles. The effect of porous parameter is significant in the streamlines, isotherms and iso-concentrations. Thus, the porous medium can significantly control the transport phenomena in the enclosure. The concentration, temperature and velocity contours are strongly modified by the variations in the Grashof number. [ABSTRACT FROM AUTHOR]

The present paper investigates the thermal mixing and cooling processes in a passive micromixer, which is applicable for the cooling of electronic devices. Employing a porous block and testing different configurations for the mixing channel is considered to enhance the mixing process and cooling performance. A 2D lattice Boltzmann thermal model is utilized to investigate the thermal performance of a T-micromixer with a porous block. Two different types of mixing channel configurations, including a step-shaped and a zigzag-shaped channel, are considered, and the obtained results are compared with those of the simple mixing channel. The thermal mixing and cooling of two miscible fluids, at 50 and 25°C entering the micromixer, are investigated. The results show that changing the mixing channel configuration may create a chaotic laminar flow, which enhances the heat transfer rate between the mixed flow and the channel wall. Whatever the Reynolds number, the step-shaped mixing channel exhibits better mixing performance than the zigzag-shaped one. For the T-micromixer with a zigzag-shaped and step-shaped mixing channel, the cases with h/H = 0.5 and h/H = 0, respectively, exhibit better thermal mixing and cooling performance. [ABSTRACT FROM AUTHOR]

In this analysis, we have considered heat transmission in two-dimensional steady laminar nanofluid flow past a wedge. Magnetohydrodynamic (MHD), Brownian motion, viscous dissipation and thermophoresis effects are considered over the porous surface. Similarity transformations have been used to change the governing partial differential equations (PDEs) into nonlinear higher-order ordinary differential equations (ODEs). Governing ODEs with boundary conditions are then converted to the system of first-order initial value problem. After that the modeled system is solved numerically by RK4 technique. Impact of the magnetic number, Eckert number, Prandtl number, Lewis number, Brownian motion, thermophoresis and permeability parameters on the flow domain is analyzed graphically as well as in tabular form. It is noted that magnitude of Nusselt number for the flow regime increases with the increase of nondimensional parameter P r , N b , N t while opposite behavior is observed in case of R. [ABSTRACT FROM AUTHOR]

Inspired by the numerous applications of non-Newtonian nanomaterials in science and industries, the two-dimensional convective hydromagnetic movement in a micropolar nanofluid within an expanding permeable surface with the existence of binary chemical reaction and convective boundary constraints is examined in this study. Thermal radiation, energy generation, and activation energy interactions are employed to handle the nanofluid flow. The underlying equations are transformed via the similarity transitions into an array of non-linear ODE. The BVP4C MATLAB package is applied to solve the system of equations numerically. The necessary outcomes of the micropolar fluid velocity, micro-rotation, temperature, concentration, friction factor, mass transfer, and heat transfer rates are shown graphically and thoroughly analyzed quantitatively. The micropolar nanofluid's mobility is reduced by the heating and solutal Grashof numbers. It is noted that the magnetic coefficient decreases velocity, it has the opposite impact on the degree of temperature. The plotted outcomes also show that the temperature increases as the increase in stimulation radiation variable. Meanwhile, the thermal field exhibits strengthen as the intensity of Biot number and Eckert number responses enhances. The growth of the activation energy leads to a noticeable enrichment in the concentration profile. [ABSTRACT FROM AUTHOR]

In this study, entropy production in flow along with heat transport of non-Newtonian fluid via porous medium, is analyzed. For fluid flow via porous medium, a modified Darcy resistance term, is taken in the momentum equation for third-grade fluid. Temperature-dependent viscosity is considered using Vogel's model viscosity. Using adequate transformations, the momentum and heat transport equation are reduced to non-dimensional form and solved analytically invoking homotopy analysis method on MATHEMATICA software. Effects of parameters arising in the study are depicted by graphs on velocity distribution, temperature distribution, and entropy production with Bejan number and discussed. For validity of current findings, the values of velocity and temperature are computed for particular values of the parameters and equated with previously published results, excellent agreement achieved. Furthermore, skin-friction coefficient and Nusselt number values are expressed in tabular form for various values of relevant parameters and discussed. It is noticed that slip parameters (γ) and (β) reduce the entropy generation number (NS). Also noticed that skin friction coefficient upsurges with rising velocity slip parameter (γ) value while, effect of temperature slip parameter (β) is observed to lessen Nusselt number in the absolute sense. [ABSTRACT FROM AUTHOR]

This paper investigates the effects on the behavior of a saturated porous material of an evolving microstructure induced by the mass exchange between the solid and the fluid phases saturating the porous network, using two-scale asymptotic expansions. A thermodynamically consistent model of the fluid physics flowing through the porous network is proposed first, describing microstructure variations to be captured implicitly via the level set method. The two-scale asymptotic expansions method is then applied to obtain an upscaled model capable to account for mass transfer. This last is proven to depend not only on the gradient of the macroscopic forces, such as the fluid pressure and the chemical potential, but also on the average velocity of the solid–fluid interface. Numerical simulations are carried out using the finite element method in order to evaluate the relative weight of the new terms introduced. [ABSTRACT FROM AUTHOR]

This paper investigates magnetohydrodynamic (MHD) boundary layer slip flow with heat transfer over a bullet shaped object. The study addresses a significant problem in fluid dynamics and heat transport with applications in various engineering and industrial domains, including aerospace, material processing, and energy systems. The governing equations are resolved using the bvp4c, an inbuilt MATLAB tool, and the arithmetic computation for the momentum and thermotic equations are executed. The results are exhibited graphically. Numerical outcomes are graphically depicted with the aid of velocity and temperature profiles for several model variables. The achieved results exhibit a promising agreement with the previously established findings available in the open literature. The heat transfer processes and fluid flow are remarkably influenced by means of the ratio of surface thickness and stretching potential. The results obtained designated that the Mixed convection parameter λ increases momentum BL thickness, whereas the temperature profile diminishes. Furthermore, momentum and temperature profile improve for surface thickness parameter s $s$. The current investigation highlights the potential utility of heat transport rate and friction factor in the industrial divisions for regulating cooling rates and enhancing the quality of end products. [ABSTRACT FROM AUTHOR]

This study examines the impacts of thermal stratification and chemical reaction on magnetohydrodynamic (MHD) free convective flow along an accelerated vertical plate with variable temperature and exponential mass diffusion, set within a porous medium. Analytical solutions, utilized, are obtained through the Laplace transform technique to accurately represent the flow's physical mechanism. The research employs advanced mathematical models to analyze the intricate interplay between MHD and convective processes under varying thermal and exponential mass diffusion conditions, offering insights into fluid dynamics that closely simulate real‐world conditions. The study draws a significant conclusion by contrasting the effects of thermal stratification with a nonstratified environment. It has been noted that when stratification is applied to the flow, the steady state is achieved more quickly. The study reveals that thermal stratification reduces fluid velocity and temperature but increases skin friction and the Nusselt number, diverging from nonstratified conditions. It also shows that parameters, like, Gr,Gc,Sc,M,Da $Gr,Gc,Sc,M,Da$, and Kc ${K}_{c}$ significantly influence velocity, temperature, and concentration in fluid dynamics. This research could be driven by a need to enhance the understanding of fluid flow in various engineering and environmental contexts, where such conditions are prevalent, including geothermal energy extraction, thermal management, chemical processing industries, and environmental control technologies. This novel approach enhances understanding of flow processes in both natural and engineered porous environments. [ABSTRACT FROM AUTHOR]

The current article deals with the steady behavior of a fully developed viscous electrically conducting and compressible Jeffrey fluid via infinitely parallel porous vertical microchannel in the sight of a transverse magnetic field. The fluid flow problem is modeled using Napier–Stokes and energy conservation equations. To analyze the problem, the leading equations are reformulated into dimensionless forms. These dimensionless transformed equations are described by nonlinear‐coupled ordinary differential equations and are eliminated utilizing the shooting method based on the fourth‐order Runge–Kutta technique through the boundary conditions; this represent slip velocity and temperature‐jump situations on the fluid–fence interface. The model equations are numerically solved with MATLAB's built‐in routine "bvp4c." The behavior of Jeffrey fluid is described through graphs. The significance of model parameters is scrutinized and discussed in detail through graphs. Various significant impacts are examined in these simulations, such as radiation, magnetic field and viscous dissipation. Furthermore, the essential results of this investigation are the effects illustrated graphically and discussed quantitatively concerning various influencing parameters corresponding to the magnetic parameter, interaction parameter, buoyancy parameter, Darcy parameter, wall ambient temperature ratio, and the fluid‐wall relationship. We noticed that both walls are heated, that is, ξ=1 $\xi =1$ the velocity decreases with a rising Jeffrey parameter. [ABSTRACT FROM AUTHOR]

This study investigated the effects of magnetic field on pressure drop and heat transfer enhancement of nanofluid in a pipe containing porous medium by a 2D simulation. The study involves modeling the flow of nanofluid as a single-phase flow and simulating fluid flow through the porous medium using the Darcy–Brinkman–Forchheimer equation. A constant uniform heat flux around the pipe is used as the thermal boundary condition. The simulations evaluate the effect of several parameters, such as Reynolds number, porosity, thermal conductivity of the porous medium, and nanofluid material. The findings show that utilizing a magnetic field increases heat transfer in nanofluid. Based on the simulations, both pressure drop and heat transfer rates increase with increasing Reynolds number. The rate of heat transfer increases as the thermal conductivity of porous medium increases, and among the selected materials, Ag has the greatest impact on heat transfer, followed by copper, gold, aluminum, and steel. By comparison of metallic ( Al , Cu ) and metallic oxide ( Si O 2 , Ti O 2 , CuO ) nanoparticles it is observed that using Al provides the highest heat transfer. Moreover, increasing porosity (0.8–0.98) decreases heat transfer coefficient. The performance evaluation criteria (PEC) are also examined as a determinant term to select the desirable condition. (The aluminum water nanofluid that is subjected to a magnetic field and moves through a silver-porous medium with a porosity of 0.9 has the highest PEC.) [ABSTRACT FROM AUTHOR]

We investigate the temporal stability analysis of a two-layer flow inside a channel that is driven by pressure. The channel consists of a fluid layer overlying an inhomogeneous and anisotropic porous layer. The flow contains a Couette component due to the movement of the horizontal impermeable upper and lower walls binding the two layers. These walls of the channel move at an identical speed but in opposite directions. The flow dynamics for the porous medium are modelled by the Darcy-Brinkman equations, and the Navier-Stokes equations are employed to describe the motion within the fluid layer. The hydrodynamic instability of infinitesimal disturbance is investigated using Orr-Sommerfeld analysis. The corresponding eigenvalue problem is derived and solved numerically using the Chebyshev polynomial-based spectral collocation method. Results reveal that stability features are strongly affected by the axial and spatial permeability variations of the porous medium. Further, the ratio of the depth of the fluid layer to the porous layer and the strength of the Couette component play a crucial role. The destabilization of the perturbed system is noticed by strengthening the Couette flow component. The combined impact of increasing the anisotropy parameter and depth ratio, decreasing Darcy number, and reducing the inhomogeneity factor stabilizes the system. This facilitates us to have greater control over the instability characteristics of such fluid-porous configuration by suitably adjusting various flow parameters. The outcome will be beneficial in relevant applications for enhancing or suppressing the instability of perturbation waves, as preferable. [ABSTRACT FROM AUTHOR]

The ferromagnetic flow of Maxwell nanoliquid past a stretching surface is the focus of this endeavor. The flow is modeled in a porous medium obeying Darcy's law and is also subjected to the effects of magnetic dipole, nonlinear radiative heat flux, and activation energy. Using proper transformation, the governing system of partial differential equations (PDEs) transforms into ordinary differential equations (ODEs). The solution process employs a shooting approach. For nanofluid concentration, temperature, velocity, skin fraction, Sherwood number, and Nusselt number, the effects of relevant non-dimensional flow parameters and numbers are explored. The results show that the porosity, elastic, and ferromagnetic parameters all reduce nanofluid velocity. The nanofluid temperature drops as the ferromagnetic and Prandtl numbers increase, while the nanofluid temperature rises to enhance the temperature ratio and radiative heat parameters. The nanofluid concentration profile rises due to the non-dimensional activation energy and falls as the Schmidt number increases. [ABSTRACT FROM AUTHOR]

The aim of this study is to present forced convective nanofluid flow over a moving plate embedded in an absorbent medium. Following Darcy law's for porous medium, the flow analysis is explored in attendance of warmth basis/drop. The main objective of this study is to explore the effects of Brownian motion and thermophoresis. The plate is considered to move in both directions: in the way of movement of fluid and in the opposite route of fluid movement. Similarity alterations have been applied to alter the leading partial differential equations (PDEs) to ordinary differential equations (ODEs). Numerical solutions have been obtained with the help of MATHEMATICA software. Dual solutions have been obtained when the plate and liquid go in reverse ways. Wall shear stress, Nusselt and Sherwood numbers all are found to rise with the rising permeability parameter of absorbent medium. For Nusselt and Sherwood numbers, ranges of dual solutions diminish by the mounting values of permeability parameter K. The critical values for porosity parameter K = 0. 0 1 , 0.02, 0.03 are R c 1 = 1. 8 7 2 9 0 9 , R c 2 = 1. 9 2 7 2 1 1 , R c 3 = 1. 9 8 2 4 2 8 4 , respectively. For decreasing values of s, range of dual solutions decreases. For s = − 0. 4 5 , dual solutions exist in the range (1. 1 9 , 1. 2 0). [ABSTRACT FROM AUTHOR]

Fluids with microstructures and microinertia play a vital role in microfluidics and nanfluidics system. One of such significant fluid is micropolar fluid. The characteristic behavior of micropolar fluid flow in conduit/pipe, etc. filled with porous medium helps us understand the flow behavior of biological fluids in porous media, groundwater flow in aquifiers, rotatory machines or viscometer. To understand such real-world problems, it is necessary to get into the mathematical model of such flow models. One such model with wide number of application is presented in this paper. This work investigated the flow of two micropolar fluids between the region formed by two concentric cylinders. Authors have considered inner cylinder to be at rest and outer cylinder rotating at a constant angular velocity. The region between two concentric cylinder is filled with an isotropic porous material. A slip condition at the outer wall and continuity conditions at interface of two fluids has been utilized to obtain an analytical solution for the proposed model. The numerical solution of the obtained solution for present problem is used to graphically analyze the motion of immisicble micropolar fluids rotating in an annulus filled with the porous medium. It is found that an outer cylinder has a notable influence on the flow behavior of immiscible micropolar fluids, contrary to the effect observed within the inner region. An analytical approach of this work not only helps us obtain precise results and analysis of the flow, but it also serves as a useful validation for future approximations within the scope of this work. [ABSTRACT FROM AUTHOR]

Apples are preserved in cold storage within standard size crates to avoid injury during handling and are stacked in a specific manner to promote adequate air circulation. This research builds an air flow and heat transfer model of a cold room (5.75 m × 3.83 m × 3.75 m) with apple filled crates (0.55 m × 0.37 m × 0.3 m) modeled as a porous media and uses CFD simulation to study how alternate stacking impacts airflow distribution and product temperature. The conventional arrangement of crates, termed CS1, was simulated, and the resulting temperature distribution data were used to validate the model with published experimental data, a root mean square error of 1.13 °C indicates good match. The model is extended to examine temperature distribution for two additional arrangements of crates (CS2 and CS3) with changed orientations and spacing, in accordance with a specific strategy. CS3, featuring larger spacing along the z-direction, showed higher average air velocity compared to CS2 and CS1 by 7.4% and 3.7% respectively. CS3 also improved cooling rate by 25.2% and increased the number of chilled crates by 20% within 40 h, along with a reduced temperature heterogeneity (3.59 °C). The model could predict hot spots in various stacking configurations, aiding in optimal arrangement. [ABSTRACT FROM AUTHOR]

The application of fluid flow through a rotating disk in a solar thermal power plant can help in increasing energy production, reduce costs, and improve the overall efficiency of the system. The concentrated solar power (CSP) technology can help in assisting solar energy for sustainable power generation. This work explores the heat transfer assessment of magnetized tangent hyperbolic fluid flowing over a porous rotating disk under the effects of thermal radiation, convective heating, Ohmic heating and viscous dissipation. The solution of transformed ODEs is obtained by the Legendre wavelet collocation method (LWCM). To visualize the impact of acting variables, the results are portrayed by graphs and tables. From the outcomes, it is noted that the rate of heat transfer is enhanced up to 84.79% with an increase in radiation parameter. Moreover, the radial velocity enhances as the rotation parameter is accelerated. The dual behavior in temperature outlines is obtained due to escalated values of the porosity parameter. For the validation of the present results, a tabular comparison is shown with earlier work. [ABSTRACT FROM AUTHOR]

This study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity Ω. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamics (MHD) have numerous engineering and biomedical applications such as sensors, MHD pumps, magnetic medications, MRI, cancer therapy, astronomy, cosmology, earthquakes, and cardiovascular devices. In view of these applications and current developments, we investigate the magnetohydrodynamic MHD electro-osmotic flow of Casson nanofluid during peristaltic movement in a non-uniform porous asymmetric channel. The effect of thermal radiation, heat source, and Hall current on the Casson fluid peristaltic pumping in a porous medium is taken into consideration. The effect of chemical reactions is also considered. The mass, momentum, energy, and concentration equations were constructed using the proper transformations and dimensionless variables to make them easier for non-Newtonian fluids. A lubricating strategy is used to make the system less complicated. The Boltzmann distribution of electric potential over an electric double layer is studied using the Debye–Huckel approximation. The temperature and concentration equations are addressed using the homotopy perturbation method (HPM), while the exact solution is determined for the velocity field. The study examines the performance of velocity, pressure rise, temperature, concentration, streamlines, Nusselt, and Sherwood numbers for the involved parameters using graphical illustrations and tables. Asymmetric channels exhibit varying behavior, with velocity declining near the left wall and accelerating towards the right wall while enhancing the Casson fluid parameter. The pumping rate boosts in the retrograde region due to the evolution of the permeability parameter value, while it declines in the augment region. The temperature profile optimizes as the value of the heat source parameter gets higher. The concentration profile significantly falls as the chemical reaction parameter rises. The size of the trapped bolus strengthens with a spike in the parameter for the Casson fluid. [ABSTRACT FROM AUTHOR]

In recent days, entropy generation has attracted the attention of several researchers due to its applications in manufacturing electronic devices, heat exchangers, conservation of energy, and generation of power. Further, activation energy is an essential requirement in automobile and chemical industries, nuclear reactors, and so on. This paper investigation aims to examine the entropy generation and the mass and energy transfer in the magneto-hydro dynamic movement of convective Carreau-Yasuda nano liquid past a porous stretching sheet with the consequences of activation energy, energy source, and binary chemical reaction. Also, the analysis of the impact of viscous and Joule dissipation in the presence of suction/injection into the Buongiorno model is an essential objective of this study. By introducing a similarity variable, the partial differential equations are altered into a system of ordinary differential equations. Numerical solutions to the modified equations are determined by utilizing a BVP5C MATLAB package. The findings are presented visually for several relevant flow characteristics and explained carefully. The thermophoresis parameter and activation energy parameter optimize the concentration of nanoparticles. These outcomes further indicate that as the larger Brinkmann and permeability parameters the entropy generation is broadened. It is discovered that an augmentation in thermal and solutal Grashof numbers is associated with greater velocity distribution. [ABSTRACT FROM AUTHOR]

In this research, the influences of quadratic Boussinesq approximation and quadratic thermal radiation on the heat transfer analysis of magnetized Sisko nanofluid flow with Cattaneo–Christov heat flux through stretching surfaces are studied. The formulated mathematical model is solved by the finite difference technique, and heat transfer rate and skin friction coefficients are computed for acting parameters, i.e., magnetic field, Eckert number, Forchheimer parameter, thermal relaxation parameter, radiation parameter, porosity parameter and Biot number. For sensitivity analysis, the response surface method (RSM) with a face-centered central composite design is utilized. The RSM is elucidated by applying nonlinear regression, analysis of variance and goodness of fit. The results indicate that the friction coefficient and Nusselt number have positive sensitivities for the Forchheimer parameter. The heat transfer rate decreases with an increase in magnetic field, Biot number and thermal relaxation parameter values for shear thickening (n > 1) and shear thinning (n < 1). Further for n < 1, a one unit increase in A1 leads to a 33% drop in SFC and 48% in LNN; and an increase of 8 units in Fr leads to a 67.18% rise in LNN. [ABSTRACT FROM AUTHOR]

The purpose of this work is to determine transferred heat features and irreversible transport peristaltic of nanomaterial fluid through a porous medium with an inclined symmetric channel. Expression of the basic velocity, pressure gradient, temperature, and stream function profiles within the boundary layer are plotted and discussed in detail via various values of the distinct parameters. Nanoparticles of hybrid nanomaterial impacts are also used. In the present article, water is used as a base liquid while nanoparticle contain polystyrene and graphene oxide. Over time, it is observed that there are distinct factors and effects such as magnetic field and porosity parameters. Mathematica software is used for estimating the exact solutions of axial velocity and temperature profiles. Additionally, the resolution of equations are considered under the small Reynolds number and large wavelength approximation. Results with plotting graph access via MATHEMATICA (11) are listed. [ABSTRACT FROM AUTHOR]

Effects of nanoparticle and steam injection on the extraction of Iranian American Petroleum Institute (API) 14 heavy oil from a model porous medium at temperatures of 110, 150, and 200 °C were investigated. Nanoparticle content was 1 %, 3 %, and 5 %, and injection flow rates were 0.018, 0.036 and 0.072 mL h−1. In short‐term injection, increasing the injection temperature to 200 °C and the flow rate to 0.072 mL h−1 resulted in the highest recovery. In the mid‐term injection, the highest recovery factor was at a temperature of 150 °C and flow rate of 0.036 mL h−1, while the results of the long‐term injection predicted a non‐monotonic effect of flow rate. The effect of alumina content on the recovery factor is less than that of temperature and flow rate. Interestingly, alumina content also has non‐monotonic effects on the recovery factor. [ABSTRACT FROM AUTHOR]

The study investigates the heat and mass transfer of mixed peristaltic Casson fluid flow through a porous medium in the presence of electroosmosis. It uses the lubrication LWL-LRN analytical technique to transform flow-control equations into ordinary differential equations. The equation is simplified using a numerical solver, bvp4c, in MATLAB software. The study analyses the behaviour of momentum, thermal, solutal, and nanoparticle concentration using parameters such as the magnetic field parameter, porous, electroosmotic, Prandtl, thermal Grashof number, and solutal concentration. Comparing this work with the existing investigation reveals a high level of concordance regarding the impact of thermophoresis and Brownian variables on momentum fields. The study's novelty is the double-diffusive effects of Casson fluid, which provides a more accurate characterisation of its flow behaviour with convective boundary conditions over an inclined surface. Such observations are useful in real-life applications to capture the shear and stress-thinning properties and flow of synovial fluid in joints, as well as to understand blood flow in several physiological conditions. [ABSTRACT FROM AUTHOR]

In the present investigation, the radiative MHD flow of an incompressible viscous electrically conducting non-Newtonian Casson hybrid nanofluidover an exponentially accelerated vertical porous surface has been considered. Under the influence of slip velocity in a rotating frame, it takes Hall and ion slip impacts into account. Water and ethylene glycol mixture is considered a base Casson fluid. A steady uniform magnetic field is applied under the postulation of a low magnetic Reynolds number. The ramped temperature and time-altering concentration at the surface are considered. First-order consistent chemical reaction and heat absorption are also regarded. Silver and Titania nanoparticles are disseminated in base fluid water and ethylene glycol combination should be formed by a hybrid nanofluid. The Laplace transformation technique is employed on the non-dimensional governing equations to ensure closed-form analytical solutions. The graphical representations scrutinize the effects of physical parameters on the significant flow characteristics. The expression for non-dimensional shear stress, heat transfer rate and mass transfer are also evaluated. They are tabulated with different variations in implanted parameters. For uniform and ramped wall temperatures, the resultant velocity grows by an increase in Hall and ion slip parameters. The resultant velocity increases by an increase in volume fractions of nanoparticles with uniform wall temperature, and a reverse effect is observed with ramped wall temperature. The temperature of Casson hybrid Ag-TiO2/WEG nanofluid is relatively superior to that of Casson Ag-WEG nanofluid. Species concentration of Casson hybrid Ag-TiO2/WEG nanofluid decreases with an increase in Schmidt number and chemical reaction parameters. The heat absorption increases the Nusselt number near the surface, while Ag and TiO2 nanoparticle volume fractions tend to lessen it. [ABSTRACT FROM AUTHOR]

Motivated by studying emerging nanofluid‐based magnetic fuel cells and hybrid direct absorber solar collectors, a numerical study is presented for buoyancy‐driven flow in a vertical enclosure containing a porous medium saturated with magnetized nanofluid flow under a transverse static magnetic field. The enclosure features adiabatic side walls and vertical heat slits, ensuring consistent cold temperatures on the lower and upper bounded walls. The side walls of the regime are insulated, and the hot slits are centrally located on these walls. The finite difference method (FDM) is applied to employ the transformed dimensionless vorticity–stream function (VSF) formulation of the transport equations. The impact of pertinent parameters on isotherm, streamline, iso‐concentration, and average Nusselt and Sherwood numbers are visualized with contour plots and graphs. Increasing Darcy number values tend to amplify the isotherm magnitudes. Higher Hartmann (magnetic) number values, on the other hand, lead to a reduction in local Nusselt number profiles but do not significantly modify the local Sherwood number. The porous medium permeability, as simulated via the Darcy number, has a strong impact on streamlines, thermal contours, and iso‐concentrations. A reduction in Darcy's number suppresses local Nusselt and Sherwood numbers, whereas an elevation in Rayleigh's number enhances them. Increasing the Buongiorno nanoscale Brownian motion parameter enhances local Nusselt and Sherwood numbers at both cold walls of the enclosure. The simulations provide a deeper insight into enclosure flows involving electrically conducting nanofluids in advanced processing systems for nanomaterials and hybrid fuel cells utilizing electromagnetic and liquid fuel technologies. [ABSTRACT FROM AUTHOR]

The high surface area of porous media enhances its efficacy for evaporative cooling, however, the evaporation of pure substances often encounters issues including local overheating and unstable heat transfer. To address these challenges, a volume of fluid (VOF) model integrated with a species transport model was developed to predict the evaporation processes of ternary mixtures (water, glycerol, and 1,2-propylene glycol) in porous ceramics in this study. It reveals that the synergistic effects of thermal conduction and convective heat transfer significantly influence the mixtures evaporation, causing the fluctuations in evaporation rates. The obtained result shows a significant increase in water evaporation rates with decreasing the microcolumn size. At a pore size of 30 μm and a porosity of 30%, an optimal balance between capillary forces and flow resistance yields a peak water release rate of 96.0%. Furthermore, decreasing the glycerol content from 70% to 60% enhances water release by 10.6%. The findings in this work propose the approaches to optimize evaporative cooling technologies by controlling the evaporation of mixtures in porous media. [ABSTRACT FROM AUTHOR]

In the current work, inclined magnetic field, thermal radiation, and the Cattaneo-Christov heat flux are taken into account as we analyze the impact of chemical reaction on magneto-hydrodynamic Casson nanofluid flow on a stretching sheet. Modified Buongiorno's nanofluid model has been used to model the flow governing equations. The stretching surface is embedded in a porous medium. By using similarity transformations, the nonlinear partial differential equations are transformed into a set of dimensionless ordinary differential equations. The numerical solution of transformed dimensionless equations is achieved by applying the shooting procedure together with Rung-Kutta 4th-order method employing MATLAB. The impact of significant parameters on the velocity profile , temperature distribution , concentration profile , skin friction coefficient , Nusselt number and Sherwood number are analyzed and displayed in graphical and tabular formats. With an increase in Casson fluid , the motion of the Casson fluid decelerates whereas the temperature profile increases. As the thermal relation factor expands , the temperature reduces, and consequently thermal boundary layer shrinks. Additionally, by raising the level of thermal radiation the temperature profile significantly improves, and an abrupt expansion has also been observed in the associated thermal boundary with raise thermal radiation strength. It was observed that higher permeability hinders the acceleration of Casson fluid. Higher Brownian motion levels correspond to lower levels of the Casson fluid concentration profile. Moreover, it is observed that chemical reaction has an inverse relation with the concentration level of Casson fluid. The current model's significant uses include heat energy enhancement, petroleum recovery, energy devices, food manufacturing processes, and cooling device adjustment, among others. Furthermore, present outcomes have been found in great agreement with already published work. [ABSTRACT FROM AUTHOR]

The features of the magnetic susceptibility of a magnetic fluid with a non-magnetic filler were experimentally studied. It was determined that the dependence of the magnetic susceptibility on the concentration of the non-magnetic filler has features. The explanation of the detected effects is based on the assumption of the influence of surface forces on the processes of relaxation of the magnetic moment of magnetic particles. It was also found that the dependences of the magnetic susceptibility of a magnetic fluid with a non-magnetic filler on the strength of the external magnetic field differ from similar dependences for the magnetic fluid without a filler. [ABSTRACT FROM AUTHOR]

This research employs a neural network, specifically the Levenberg–Marquardt algorithm, to characterize the entropy optimization performance in the electro-magneto-hydrodynamic flow of a Casson tetra-hybrid nanofluid over a rotating disk. The problem was formulated mathematically using equations for momentum, continuity, and temperature. This study converts ordinary differential equations (ODEs) into partial differential equations (PDEs) by a self-similarity transformation. The equations are resolved via the fourth-order Runge-Kutta method in combination with a shooting technique for obtaining the required datasets. Using the Levenberg-Marquardt algorithm (LMA), these datasets are characterised as training, testing, and validation. The proposed outcomes are presented in multiple tables and graphs. This trained neural network is then utilized to predict the heat flow velocity and Nusselt number of the rotating disk. The developed model was evaluated using mean square error, error analysis, and regression analysis, thereby confirming the consistency, accuracy, and reliability of the designed technique. The best validation performance for skin friction and the Nusselt number for the Casson tetra-hybrid nanofluid flow across a rotating disk is 8752e-05 at epoch 95 and 0.00033239 at epoch 37. Training, validation, testing, and all performance metrics of the artificial neural network model are close to unity. As magnetic field strength increases, temperature profiles rise in di-hybrid, ternary-hybrid, and tetra-hybrid nanoparticle scenarios. Tetra-hybrid nanofluids are considered superior fluids when compared to di-hybrid, ternary-hybrid, and tetra-hybrid nanofluids. This optimization method holds promise for diverse applications in biotechnology, microbiology, and medicine, offering significant potential for various fields. [ABSTRACT FROM AUTHOR]

The present study explores the dynamics of a two-dimensional, incompressible nanofluid flow through a stretching curved sheet within a highly porous medium. The mathematical model is formulated by including external forces such as viscous dissipation, thermal radiation, Ohmic heating, chemical reactions, and activation energy by utilizing a curvilinear coordinate system. The viscosity and thermal conductivity of the nanofluids are examined using the Koo–Kleinstreuer–Li model. The choice of |$Al_{2}O_{3}$| and |$CuO$| nanoparticles in this model stems from their distinct thermal properties and widespread industrial applicability. By non-dimensionalizing the governing partial differential equations, the physical model is simplified into ordinary differential equations. BVP-5C solver in MATLAB is utilized to numerically solve the obtained coupled non-linear ordinary differential equation. Graphical results are presented to investigate the velocity, temperature, and concentration profiles with entropy generation optimization under the influence of several flow parameters. The artificial neural network backpropagated with Levenberg–Marquardt method (ANN-BLMM) used to study the model. The performance is validated using regression analysis, mean square error and error histogram plots. The outcome illustrates that the velocity and temperature profiles increase with increasing the Forchhiemer parameter. Also, the velocity profile increases with increasing curvature parameter, while, reverse effect is observed for temperature profile. This research augments our comprehension of nanofluid dynamics over curved surfaces, which has implications for engineering applications. The insights gained have the potential to significantly contribute to the advancement of energy-efficient and environmentally sustainable cooling systems in industrial processes. [ABSTRACT FROM AUTHOR]

This study investigates analytically the influence of nanoparticle shapes on an unsteady mixed convective viscoelastic MHD nanofluid flow in a horizontal channel with oscillating walls in a saturated porous medium. The effect of radiation is also considered in the energy equation. The considered NPs are Cu, Ag, Al2O3, TiO2, and Fe3O4, with base fluids H2O and C2H6O2. The considered different shapes of NPs are cylinder, platelet, blade, and brick. The study examines three flow situations based on physical boundary conditions. The perturbation method is employed to solve the flow governing equations for three different flow situations based on physical boundary conditions: Case (i) flow in a horizontal channel with both lower and upper walls stationary; Case (ii) the upper wall of the channel is in oscillation while the lower one is constant; Case (iii) both walls of the channel are in oscillatory motion. The velocity and temperature distributions, as well as the skin friction coefficient and heat transfer rate, are analyzed through graphs and tables to assess the impact of various governing parameters. From the results, it is found that brick-shaped NPs exhibit more strength to the velocity and temperature distributions, followed by cylinder, platelet, and blade for both water-based and EG-based NF. [ABSTRACT FROM AUTHOR]

This paper presents an investigation of magnetohydrodynamics (MHD) Casson nanofluid flow along a stretchable surface through a permeable medium. The modeling of the physical phenomena is considered with impact of thermal radiation, heat generation, slip conditions and suction. Transformations of the governing set of mathematical equations for the physical model are carried out into nonlinear ordinary differential equations (ODEs) with appropriate similarity variables. The nonlinear ODE solutions are carried out using the optimal homotopy analysis technique (OHAM), and the findings are presented for determining the influences of the emerging important parameters. The results indicate that velocity field increases in respect of porosity parameter, Casson fluid parameter and magnetic parameter while it declines for enhancing velocity slip and suction parameters. The temperature profile shows rising behavior for heat source, Prandtl number, thermophoresis, radiation and Brownian motion parameters while it declines for enhancing thermal slip parameter. Moreover, the concentration profile enhances for rise in Brownian motion parameter while it reduces for Schmidt number and nanoparticle parameter. We also showed the accuracy of the present results by indicating that skin friction values for varied magnetic parameters agree with earlier findings in the literature. [ABSTRACT FROM AUTHOR]

This study examines the flow dynamics and heat transfer characteristics of Maxwell fluid in a channel influenced by magnetohydrodynamics (MHD), Joule heating, thermal radiation, and boundary layer suction/blowing effects. The governing partial differential equations (PDEs) for momentum, energy, and concentration are transformed into ordinary differential equations (ODEs) using similarity transformations. The boundary value problem (BVP) is solved numerically using the bvp4c solver in MATLAB, yielding accurate solutions for velocity, temperature, and concentration profiles under various parameters. Key findings reveal that the porous parameter decreases the velocity profile but increases the temperature profile for both suction and blowing effects. Additionally, the MHD, Deborah, and Eckert numbers significantly influence the velocity and temperature profiles differently under these conditions. This study highlights the crucial role of integrating MHD, thermal, and boundary control effects to optimize performance and efficiency in engineering systems involving Maxwell fluids, with applications in polymer processing, biomedical engineering, electronics cooling, oil recovery, and chemical processing. [ABSTRACT FROM AUTHOR]

Predicting the long‐term success of endovascular interventions in the clinical management of cerebral aneurysms requires detailed insight into the patient‐specific physiological conditions. In this work, we not only propose numerical representations of endovascular medical devices such as coils, flow diverters or Woven EndoBridge but also outline numerical models for the prediction of blood flow patterns in the aneurysm cavity right after a surgical intervention. Detailed knowledge about the postsurgical state then lays the basis to assess the chances of a stable occlusion of the aneurysm required for a long‐term treatment success. To this end, we propose mathematical and mechanical models of endovascular medical devices made out of thin metal wires. These can then be used for fully resolved flow simulations of the postsurgical blood flow, which in this work will be performed by means of a Lattice Boltzmann method applied to the incompressible Navier–Stokes equations and patient‐specific geometries. To probe the suitability of homogenized models, we also investigate poro‐elastic models to represent such medical devices. In particular, we examine the validity of this modeling approach for flow diverter placement across the opening of the aneurysm cavity. For both approaches, physiologically meaningful boundary conditions are provided from reduced‐order models of the vascular system. The present study demonstrates our capabilities to predict the postsurgical state and lays a solid foundation to tackle the prediction of thrombus formation and, thus, the aneurysm occlusion in a next step. [ABSTRACT FROM AUTHOR]

The movement of bile inside ducts in a diseased state is investigated using a mathematical model that takes into account heat transport and chemical interactions. Bile is considered as a viscous fluid, geometry of ducts is assumed as finite length asymmetric channel and the flow is induced by peristaltic wave along the length of channel walls. Under the presumption of a long wave length and a low Reynolds number, the formulas for axial velocity, pressure gradient, volume flow rate, stream function, pressure increase, shear stress, and heat transfer coefficient are produced. In the end, a plot and discussion are made of how different emergent factors affect the relevant physical quantities. [ABSTRACT FROM AUTHOR]

This current investigation involves an experimental inspection of adding porous medium and phase change material (PCM) above the absorber surface to enhance the performance of a single slope and single basin solar water distiller system. To demonstrate the effectiveness of adding porous medium and PCM, the performance of the modified system and conventional system is compared under similar operating conditions. The system that uses porous medium and PCM is called MSS‐FPP, whereas the conventional system is called MSS‐F. Rectangular fins are fixed above the absorber plate for both models. For MSS‐FPP model, three different types of porous medium (stones, nuts, and black glass balls) are used in addition to paraffin wax filled inside circular tubes as a PCM. The data are collected in November and December 2023 in Mosul City, Iraq. The experiments are carried out under different water depths. The findings confirm that the performance of MSS‐FPP model is better than MSS‐F model by 41.32% (for water depth 3 cm) and 30.61% (for water depth 5 cm). The results also indicated that the water productivity of MSS‐FPP model is higher than MSS‐F model by 41.67% (for water depth 3 cm) and 30.65% (for water depth 5 cm). For MSS‐FPP model, the maximum water productivity and efficiency are obtained when using black glass balls as compared to nuts and stones types, where the highest water temperature and water productivity values are found equal 54°C and 1.01 kg/m2 for water depth 3 cm. The enhancement in the performance of modified solar water distiller system (MSS‐FPP) shows that using a porous medium and PCM has considerable impacts on the evaporation rate, heat exchange, and rate of heat transfer. [ABSTRACT FROM AUTHOR]

In porous water filters, the transport and entrapment of contaminants can be modeled as a classic mass transport problem, which employs the conventional convection–dispersion equation to predict the transport of species existing in trace amounts. Using the volume-averaging method (VAM), the upscaling has revealed two possible macroscopic equations for predicting contaminant concentrations in the filters. The first equation is the classical convection–dispersion equation, which incorporates a total dispersion tensor. The second equation involves an additional transport coefficient, identified as the adsorption-induced vector. In this study, the aforementioned equations were solved in 1D for column tests using 3D unit cells. The simulated breakthrough curves (BTCs), using the proposed micro–macro-coupling-based VAM model, are compared with the direct numerical simulation (DNS) results based on BCC-type unit cells arranged one-after-another in a daisy chain manner, as well as with three previously reported experimental works, in which the functionalized zeolite and zero-valent iron fillings were used as an adsorbent to remove phosphorous and arsenic from water, respectively. The disagreement of VAM BTC predictions with DNS and experimental results reveals the need for an alternative closure formulation in VAM. Detailed investigations reveal time constraint violations in all the three cases, suggesting this as the main cause of VAM's failure. [ABSTRACT FROM AUTHOR]

The current study investigates the three-dimensional radiative and convective Casson hybrid nanofluid flow and heat transfer with the Cattaneo–Christov heat flux model over an inclined spinning and extending disk subjected to an applied magnetic field. Additionally, the study considers the impacts of Joule’s heating and viscous dissipation. Mathematical modelling of the nanofluid flow problem containing Ag and multiwalled carbon nanotubes (MWCNT) nanoparticles with water as the base fluid in a Darcy medium is done using a cylindrical coordinate system. The simplified system of equations is subjected to the spectral quasilinearisation method (SQLM) approach for the graphical and tabular representations. Examining key parameters, such as magnetic field, Bejan number, angle of inclination, disk movement parameter and disk rotation reveals interesting results on velocity and temperature profiles. The research concludes that the Bejan number increases with higher values of temperature ratio, radiation and magnetic parameters, while it decreases with increasing Casson parameter and Brinkman number. Radial wall friction decreases with improved magnetic field, temperature ratio, stretching and porosity parameters, but tangential wall friction increases. The present results are compared with the one already existing in literature to validate the numerical scheme and the results are found to agree well with the previously published work. The application of hybrid nanofluid flow over rotating and stretching disks is widespread in various fields, including rotating machinery, electronic devices, patient treatment instruments, crystal growth method, etc. [ABSTRACT FROM AUTHOR]

In this paper, an analytical approach combined with a two-dimensional computational fluid dynamics (CFD) model is pursued to simulate the fluid flow in a monopropellant thruster for satellite propulsion systems. The thruster utilizes hydrogen peroxide (H2O2) as a green propellant at a concentration of 87.5%, with a catalytic bed based on spherical silver particles. Through a parametric analysis of particle diameter, we aim to optimize the design of a monopropellant thruster capable of generating a thrust of 20N. For this purpose, a program in CFD code in the commercially available ANSYS Fluent software is used to solve the energy, momentum, mass transfer, and species transport equations governing the thruster system. The local thermal non-equilibrium (LTNE) approach is used to describe the heat transfer occurring through both the solid and fluid phases within the catalyst bed. The results demonstrate that particle size significantly affects the thermal behaviour, species mass fraction, and exit velocity. An optimum diameter of 0.65mm exhibits the optimal performance of the monopropellant thruster, ensuring efficient decomposition of H2O2 at 968K and providing the required level of thrust force with a specific impulse of about 120s. [ABSTRACT FROM AUTHOR]

The current article covers the unsteady Williamson fluid flow towards vertical parallel porous plates through porous media. The Cartesian coordinate system is utilised to model the flow equations. Along with thermal radiation, the effect of the applied magnetic field is also taken into account. Furthermore, the vertical walls of the channel are employed to achieve velocity slip and temperature jump conditions. Convection is applied to assume that the stable plates swap heat with an outer fluid. The mathematical model is numerically solved via the bvp4c shooting technique in the computer software MATLAB. For various values - 1 , 0, 1 of the ratio of the fluid temperature to the wall temperature, the impacts of numerous physical characteristics affecting temperature and velocity profile including Weissenberg number, magnetic permeability, Prandtl number, suction parameter, Knudsen number, Radiation parameter, frequency of oscillation, magnetic parameter and the fluid–wall conversation parameter are discussed graphically. The concluding results suggest that the fluid velocity at the solid–fluid interface is influenced by the magnetic field, alterations in suction or injection parameters and specific values of velocity slip coupled with temperature jump conditions. [ABSTRACT FROM AUTHOR]

The object of this research is to examine the combined effects of mass and thermal Biot numbers on the properties of a Powell-Erying fluid flow that is two-dimensional, constant, viscous, incompressible, and non-Newtonian. In the direction of the flow is an extending sheet encircled by a porous medium. Further consideration is given to the existence of a chemical reaction, thermophoresis, Brownian motion, and velocity lapse, among other factors. Utilizing the Powell-Erying Cauchy non-Newtonian model, the viscoelastic effect is accounted for. When establishing concentration and temperature boundary conditions, thermal and mass Biot numbers are incorporated. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge–Kutta method. Furthermore, the Nusselt number, Skin-friction, and Sherwood number coefficients are evaluated and shown in a tabular format utilizing the same parameters. In the end, the numerical outcomes obtained from this investigation are substantiated and considered to be highly consistent with the findings that were previously documented. [ABSTRACT FROM AUTHOR]

Abstract Low-frequency shadows beneath gas reservoirs can be regarded as a time delay relative to the reflection from the reservoir zone, but they cannot be reasonably explained by the high-frequency attenuation or velocity dispersion observed in normal P-waves. According to the new asymptotic theory for porous media, seismic P-waves undergo multiple conversions between fast and slow modes during seismic waves passing through layered permeable reservoirs at low frequencies, and changes in the velocity and amplitude (i.e., energy) of slow P-waves can lead to low-frequency shadows. In this study, a forward analysis was performed on the dispersion and attenuation of fast and slow P-waves within the seismic frequency band based on the asymptotic theory for porous media; the results revealed that fast P-waves do not undergo frequency dispersion and attenuation within the seismic frequency band and that slow P-waves are the primary contributor of dispersion and attenuation. In addition, methods used to calculate the frequencies at which low-frequency shadows occur were analyzed and are discussed. Finally, S-transform time-frequency analysis method was used to calculate and analyze the low-frequency shadows of three-dimensional seismic data acquired from work area M in Sichuan. The low-frequency shadow anomalies determined by this method were found to be highly consistent with those identified based on the data acquired from wells in the target reservoir. These results indicate the good application performance of this method.

Abstract Apples are preserved in cold storage within standard size crates to avoid injury during handling and are stacked in a specific manner to promote adequate air circulation. This research builds an air flow and heat transfer model of a cold room (5.75 m × 3.83 m × 3.75 m) with apple filled crates (0.55 m × 0.37 m × 0.3 m) modeled as a porous media and uses CFD simulation to study how alternate stacking impacts airflow distribution and product temperature. The conventional arrangement of crates, termed CS1, was simulated, and the resulting temperature distribution data were used to validate the model with published experimental data, a root mean square error of 1.13 °C indicates good match. The model is extended to examine temperature distribution for two additional arrangements of crates (CS2 and CS3) with changed orientations and spacing, in accordance with a specific strategy. CS3, featuring larger spacing along the z-direction, showed higher average air velocity compared to CS2 and CS1 by 7.4% and 3.7% respectively. CS3 also improved cooling rate by 25.2% and increased the number of chilled crates by 20% within 40 h, along with a reduced temperature heterogeneity (3.59 °C). The model could predict hot spots in various stacking configurations, aiding in optimal arrangement.

The propagation of a pressure wave in a porous medium with a fractured porous zone was numerically investigated. The study used a two-velocity model of a porous medium and a three-velocity model of a fractured porous medium. The problem was examined in a twodimensional formulation, considering cases when a porous medium has a free surface or is unbounded. The fractured porous zone was shown to have either an ellipseor rectangle-shaped boundary. The influence of such inhomogeneities on the propagation of pressure perturbations was analyzed.

Abstract The drainage and imbibition processes are critical mechanisms in petroleum engineering. These processes in a porous medium are controlled by surface forces and pressure gradients. The study of these processes in the pore scale by common simulators always has limitations in multiphase flow modeling. Also, obtaining relative permeability curves through laboratory analysis requires expensive equipment. Additionally, these laboratory experiments are quite expensive and may introduce significant uncertainties. For this purpose, this study investigated the creation of relative permeability curves and their effect on oil production. Initially, single-phase fluid and two-phase droplet flow within a fracture with both soft and rough surfaces were utilized to validate the formulation of the Smoothed Particle Hydrodynamics (SPH) method. Then, by using three randomly constructed porous medium models, the imbibition and drainage processes have been studied. Finally, sensitivity study has been carried out on critical parameters related to fluid flow dynamics in the porous environment, including pressure changes, wettability, and heterogeneity in drainage and imbibition processes. The simulation results were consistent with current theories; therefore, it is reasonable to consider SPH to characterize the fluid flow dynamic during the drainage and imbibition processes. According to sensitivity studies, pressure gradient (residual saturation of displaced fluid is about 5.65% and 8.44%) and heterogeneity (the residual saturation of the displaced fluid was 4.04% and 2.98%) have the largest impact on flow modeling in both drainage and imbibition processes and wettability (the residual saturation became 36.62% and 5.12%) has significant effect on the drainage process through porous medium. In general, fluid flow dynamic studies can be performed using the SPH method to model fluid flow in simple and complex porous medium under various flow conditions. The SPH method can also be used as an applicable tool to investigate the hydrocarbon fluids flow within larger geometries in the future.

This work analyzes the impact of viscous dissipation on an unstable stretching surface in a porous medium with heat generation and thermal radiation—an important factor for numerous engineering applications like cooling baths and plastic sheets. Using MATLAB's Runge-Kutta fourth-order approach, the controlling partial differential equations are converted into highly nonlinear ordinary differential equations that can be solved numerically. The findings show that a decrease in the skin friction coefficient, temperature profiles, velocity, and Nusselt number occurs when the unsteadiness parameter is increased. In contrast to the Prandtl number, which rises with temperature profile and reduced Nusselt number, the Eckert number rises with a dimensionless temperature profile and reduced Nusselt number. Reduced Nusselt number and temperature profile affect the heat generation parameter; a decrease in skin friction coefficient and velocity profile correlate with the porosity parameter. Furthermore, the radiation parameter rises as the temperature distribution and Nusselt number decrease.