Schmidt Number Research Articles

A multiple applications study of motile microorganisms past a vertical surface with double‐diffusive binary base fluid

AbstractThis study investigates the various uses of density of motile microorganisms in the context of the flow of a binary base fluid with double diffusion past a vertical surface. The research aims to comprehend the interactions between motile microorganisms and the fluid dynamics, as well as the heat and mass transport mechanisms in this system. The analysis involves mathematically constructing the governing equations, transforming them into dimensionless nonlinear ordinary differential equations using similarity transformations, and numerically solving them using the MATLAB bvp4c solver. An analysis of the influence of several parameters on the profiles of velocity, temperature, concentration, nanoparticle concentration, and density of motile microorganisms is conducted using graphical representation. The findings demonstrate that boosting the thermophoresis parameter intensifies the temperature profile. In addition, an increase in the nanofluid Schmidt number results in a larger concentration of nanoparticles, whereas a higher bioconvection Lewis number reduces the density of the motile microorganism profile. These findings may find use in biomedical engineering as well as industrial processes that include enhancing the efficiency of mass transfer and bioconvection. Numeric simulation prophesies 99.9% for both shear stress and heat transfer rate intensification for Prandtl values are noticed.

Influence of chemical reaction on transient natural convective flow in an infinite vertical cylinder packed with porous material

A study of mass and heat transport on fully developed laminar and transient free convective flow in a vertical cylinder containing a porous substance inside it. The Laplace Transform Method (LTM) is used to solve the governing equations with suitable boundary conditions. A compact form solution represented by using Bessel and modified Bessel functions. The numerical results were thoroughly scrutinized using graphs and tables to illustrate the effects of newly discovered fluid characteristics, including time, Grashof, mass Grashof, Schmidt, Prandtl, Darcy numbers, viscosity ratio on the concentration and the velocity profiles. The velocity and concentration profiles progressively increase with varying time values until reaching a steady state. Furthermore, it is found that the velocity profiles are decreased by the Prandtl, Schmidt number, and viscosity ratio. In contrast, the Darcy, Grashof, and mass Grashof numbers exhibit an opposite effect. The rate of mass transport, skin friction, and mass flux are presented in tables. The major finding of the current research is that the viscosity ratio parameter decelerates the skin friction and mass flux. This study has potential applications in innovative fields such as solar energy systems, chemical engineering processes, etc.

Numerical evaluation for the peristaltic flow in the proximity of double-diffusive convection of non-Newtonian nanofluid under the MHD

This article mainly studies the 2-D propagation of a non-compressible Eyring-Powell nanofluid flow through a stretched wedge under the Magneto-hydrodynamic effect. Equations for temperature, concentration, double-diffusive convection and momentum are taken into consideration. Since solving the dimensionless equations associated with our study is an uphill task, we utilize the MATLAB bvp4c solver to illustrate the graphical performance of different parameters. This manuscript may be significant in the projects in the field of industry and medicine. The manuscript's noteworthy features include the magnetic field, heat source-sink parameter, double diffusivity, and solar radiation process. The main finding is that the local fluid parameter k1 and magnetic field parameter M decelerate the velocity of nanofluid. Because different nanoparticles have different effects on fluids, the fluid's temperature exhibits multiple behaviors, therefore by escalating the Prandtl number initially, it increases and then decelerates due to the presence of nanoparticles. The concentration of fluid declines as the Schmidt number rises. The double diffusivity of Eyring-Powell nanofluid improves with magnification in the fluid's Schmidt number Sc and Prandtl number Pr.

Mixed convective magneto flow of nanofluid for the Sutterby fluid containing micro-sized selfpropelled microorganisms with chemical reaction: Keller box analysis

The current work aims to scrutinize the bioconvection Sutterby nanofluid flow of the Cattaneo-Christov heat and mass flux over a rotating disk. The effects of thermophoresis and Brownian motion receive considerable consideration. The process of analyzing heat and mass transfer phenomena involves taking into account the impacts of thermal radiation and chemical reactions that are susceptible to convective boundary conditions. Firstly, we reduce the PDEs of the physical model to ODEs through alter transformation and then numerically solved the transformed ODEs using Keller Box technique. An analysis of numerical data follows to ascertain the role of numerous flow variables on the flow profiles. Based on the findings, it is evident that an increase in the fluid variable Δ and the porous variable K leads a decrease in the, radial F'(ζ), axial F'(ζ) and tangential G(ζ) velocities. Furthermore, we find that the growing values of the thermal radiation Rd variable and the thermal Biot number B T greatly aid in raising the fluid’s temperature. Concentration profile shows decreasing behavior for rising values of Schmidt number Sc but upsurge for solutal Biot number B C . The microorganism is decayed with greater Lewis number Lb and Peclet number Pe.

Numerical simulation of heat and mass transfer through hybrid nanofluid flow consists of polymer/CNT matrix nanocomposites across parallel sheets

The hybrid nanofluid (Hnf) flow with heat and mass transmission under the magnetic field and activation energy consequences across parallel double-rotating surfaces has been studied. In order to synthesize the Hnf, polymer/CNT matrix nanocomposites (MNCs) are dissolved in water. Polymer/CNT MNCs are highly efficient and have exceptional properties. These MNCs are helpful in various applications, from engineering to biomedical research, because of their incredible thermophysical properties. Keeping in view the significant uses of the polymer/CNT MNC hybrid nanofluid flow, we have formulated the fluid flow in the form of the system of PDEs (partial differential equations), which are reformed into the non-dimensional form of ODEs (ordinary differential equations) and then solved numerically through the Matlab package (bvp4c). The numerical outputs for velocity, heat and mass profiles are compared with another numerical approach ND-solve. It has been determined that the outputs are precisely correct and reliable. Furthermore, the fluid velocity drops with the influence of suction/injection, Reynold number, and polymer/CNT MNC. The increasing quantity of polymer/CNT MNC in water reduces the energy and mass profiles. The energy field enhances with the upshot of the heat source term, whereas the concentration field falloffs with the effect of Schmidt number.

Soret Effect of Unsteady Parabolic Flow Past an Accelerated Vertical Plate with Constant Temperature and Mass Diffusion in t he Presence of Rotation

Objective: Circular force's detrimental effects on inhomogeneous parabola circulation over an upright slab that rapidly accelerates in uniform temperature and continuous mass dispersion are discussed. There is no electrical conductivity in the liquid in question. Methods: The solutions for the temperature, concentration, and velocity profiles were identified through the Laplace transformation methodology. Findings: Graphical drawings displaying several specifications, include the acceleration parameter, Schmidt value, Soret value, Hartmann number, thermal Grashof number are used to illustrate the results that were obtained. It is noted that as the values - thermal Grashof number -increase, speed also increases. Regarding Schmidt and Prandtl numbers, the tendency is the opposite. Novelty: The unique aspect of this work is its thorough analysis of the Soret Effect in an erratic, rotating, parabolic flow past an accelerating vertical plate with mass diffusion and constant heat. The work closes gap in the literature by addressing these particular conditions and offers insightful conclusions and useful techniques that may be used to a variety of scientific and engineering issues. This study investigates the impact of rotating effects and Soret impact on erratic convective movement in a vertical plate. Results show that Schmidt number and wall thickness increase over time, while temperature patterns rise with increasing Sr and Sc levels. The Prandtl number depends on air and water temperatures. The study fills a literature gap and provides valuable insights for various scientific and practical applications. Keywords: Soret effect, Turning, Mass dissemination, Parabolic, Vertical surface

IMPACT OF CHEMICAL REACTION ON MHD BOUNDARY LAYER FLOW OF NANOFLUIDS OVER A NONLINEAR STRETCHING SHEET WITH THERMAL RADIATION HAAR WAVELET COLLOCATION METHOD

In this paper, we investigate the effects of chemical reaction and thermal radiation on MHD boundary layer fluid flow of nanofluid moving over a nonlinearly stretching sheet through semi-numerical approach. The nanofluid physical model of the problem comprises with effects of thermophoresis, radiation and chemical reaction parameters. The mathematical model scrutinizes mass, momentum, heat transfer and concentration equations are reduced to couple nonlinear ordinary differential equations over infinite domain using proper similarity variables. Haar wavelet collocation method is used to solve the resulting equations. The obtained results are compared with available numerical findings and are comparable which confirms and verifies the wavelet method. The effects of various non-dimensional parameters on the rate of heat and mass transfer are depicted through tables and graphs. It predicts that, the local Sherwood number increases with increase in the parameters of Brownian motion and thermophoresis. For both temperature and volume fraction profiles decreases due to an increase in the Schmidt number.

Effect of chemical absorption on Jeffery Fluid Flow in saturated Porous Media with variable thermal conductivity

This study investigates the impact of species absorption of Jeffery fluid flow through a saturated permeable medium with variable thermal conductivity. The dimensional partial nonlinear derivative model controlling the chemical reacting fluid flow is transformed to invariant form. The resulting flow equations are computed numerically using an approximated finite implicit Crack-Nicolson. A chemical absorption of fluid reactant occurs in a boundless vertical device. Computations are performed for different parameters to examine their sensitivity under isothermal temperature conditions. The computed results are offered graphically for qualitative and quantitative insights into the flow behaviour. The obtained outcomes revealed that the fluid flow rate rises with an increasing values of the parameters and, and it damps with upsurge in the values of the parameters, and. The heat transfer field is reduced with enhancing values of the thermal source, viscous dissipation and time, but declines for a boosted value of the terms suction and Prandtl number. Also, the mass transfer field is higher when mass absorption and time are increased, and diminish with an elevate in the values of Schmidt number and chemical reactions.

Analysis of the tri-hybrid Maxwell nanofluid flow with temperature-dependent thermophysical characteristics on static and dynamic surfaces employing Levenberg-Marquardt artificial neural networks

Using the Levenberg-Marquardt Artificial Neural Network (LM-ANN) model, this study applies computational neuroscience to the analysis of flow, heat, and mass transport characteristics. The novel characteristics of MHD Maxwell tri-hybrid nanofluid passing through static and moving wedge with temperature-dependent thermophysical properties (thermal conductivity, viscosity, diffusivity, and electrical field) in permeable, radiative, and mixed convection processes are investigated in this paper. Nonlinear PDEs are transformed into nonlinear ODEs using similarity variables. A dataset for the LM-ANN is generated across various scenarios by varying parameters such as the temperature-dependent viscosity parameter ( 0.07 − 0.1 ) , variable diffusivity parameter ( 0.4 − 2.5 ) , thermal buoyancy parameter ( 0.1 − 0.5 ) , nonlinear thermal buoyancy parameter ( 0.2 − 0.5 ) , thermal radiation ( 1 − 1.5 ) , buoyancy ratio parameter ( 0.2 − 0.5 ) , chemical reaction parameter ( 1 − 3 ) , and Schmidt number ( 1 − 3 ) using the Bvp5c numerical algorithm. The testing, training, and validation procedure of LM-ANN is utilized to examine the estimated solutions of specific situations, and the proposed algorithm is then validated. After that, the proposed LM-ANN is validated using regression analysis, MSE, and histogram analysis. The prescribed approach impeccably mirrors the recommended and cited findings, evincing a precision level within the realm of 10−9. Results indicate that increasing the permeability parameter from 1 to 1.2 and the temperature-dependent thermal conductivity parameter from 0.4 to 2.5 enhances the Nusselt number. Additionally, increasing the chemical reaction parameter from 1 to 3 leads to an increase in the Sherwood number. The significance of this study lies in its potential applications in industries such as aerospace, chemical processing, and energy systems, where efficient heat and mass transfer processes are crucial. For instance, the findings can be applied to enhance cooling techniques in high-performance aerospace components, optimize reactor designs in chemical plants, and improve thermal management in power generation systems.

Heat and mass transfer conduct in an unsteady two- dimensional stream between parallel sheets

In the present research, an effort has been made to analytically solve heat and mass linear/ nonlinear as well as steady/ unsteady equations in a viscous nanofluid squeezed between parallel sheets. Using Python and the SymPy library, the nanofluid with viscous properties between parallel sheets has been analyzed to symbolically solve flow, heat, and mass transfer effects equations through the Homotopy Perturbation Method and Akbari-Ganji Method approaches. The two nanofluids selected to conduct this study are Copper as well as Al2O3, whose sizes are 29 nm and 47 nm respectively. The provided details encompass the outcomes of active variables on flow and the transfer of heat coupled with mass. The Homotopy Perturbation and Akbari-Ganji methods have resulted in top-of-the-line consequences compared to analytical and numerical approaches. This research study highlights a faster and more accurate computation to conduct the analytic section of the study. The outcome shows that the increase of the Prandtl number and the Eckert number will increase Nusselt. However, skin friction increases with the increase in the Schmidt number. Furthermore, a rise in Schmidt number and parameters related to chemical reactions leads to an elevated Sherwood number. The outcomes of the study presented here provide a more innovative and precise insight, and the comparison with the available literature also proves there is a well-agreed numerical calculation. Microchips in engineering and medical-related industries would enjoy the outcomes obtained from this study. This study proves that the maximum and minimum amounts of heat transfer in respect occur at η=0 and η=1. Moreover, the maximum and minimum amounts of error are equal to 0.0001 and 0.00001, respectively. The maximum and minimum amounts of concentration occur at η=1 and η=0 in order. Finally, the maximum and minimum amounts of error are equal to 0.000016 and 0.000002, respectively.

Implicit finite difference simulations for unsteady oscillating flow of Walters-B nanofluid with microbes using the Cattaneo–Christov model

The thermal importance of nanoparticles in different fields of engineering is still a developing issue that necessitates additional focused consideration. The suspension of non-Newtonian fluids with nonmaterials has various applications in areas such as enhanced thermal systems, energy processes, aerospace engineering, and chemical industries. Following such motivations, this work aims to analyze the heat and mass transfer flow of Walters-B nanofluid in the presence of microorganisms. The fluid motion is presumed to be nonsteady over a surface that undergoes periodic acceleration. The motivations for studying nanofluid’s oscillating flow are its use in effective mixing processes, combustion stability, and process efficiency. The text provides a detailed explanation of the saturation of porous media. A modified theory for heat and mass fluxes, known as the Cattaneo–Christov approach, suggests an extension in heat equations. Moreover, it supports the interaction of radiation phenomena for enhancing heat transfer. It is noteworthy that the entire problem is represented using extremely nonlinear partial differential equations (PDEs). The CFD study utilizing the renowned implicit finite difference method (FDM) has been effectively employed to propose a numerical solution for the problem. The numerical results are deemed valid and confirmed within certain limiting cases, based on the available data. The evaluation of velocity, skin friction coefficient, Nusselt number, and Sherwood number as a function of time has been demonstrated for various parameters. It is asserted that the wall shear force exhibited an oscillating pattern with a greater magnitude as a result of the viscoelastic parameter. The Nusselt number and Sherwood number exhibit slight acceleration as a result of changes in the Prandtl number and Schmidt number, respectively. The proposed model is specifically designed for use in heat exchangers, vibrational systems, compact designs, and vibration control.

Analysis of Darcy–Forchheimer flow of magnetized hybrid nanofluid (MoS 2+ZnO/E) with non-linear heat source and quartic autocatalytic chemical reaction

In this article, an effort is made to analyze the 3 − D flow of hybrid nanofluid over a rotating stretching sheet. The hybrid nanofluid contains engine oil as a base fluid amalgamated with nano-particles Mo S 2 and ZnO . The flow is assumed to pass through a Darcy–Forchheimer medium subjected to the influence of an inclined magnetic field. In addition, heat radiation, Joule heating, viscous dissipation, nonlinear heat source, and quartic autocatalytic chemical reaction are applied to discourse heat and mass transfer features. The PDEs representing the physical problem are converted to ODEs with the introduction of similarity transformations. The solution of the problem is determined numerically by using MATLAB built-in bvp4c method. The proposed mathematical model’s validation is ascertained by comparing it with an earlier study in limiting case. In this regard, an excellent consensus is accomplished. The current investigation reveals that the flow along axial direction gets retarded by enhancing the values of rotational parameter, inertial parameter, and magnetic parameter, whereas the flow along radial direction gets accelerated. The increasing value of angle of inclination admirably resists the motion of nanofluid and hybrid nanofluid. The concentration profile gets decreased under the increasing influence of inclination angle and Schmidt number while it enhances for homogeneous reaction parameter. The enhancing values of rotational parameter, solid volume fraction and temperature, and exponential dependent heat generation parameters enhance the value of Nusselt number.

REV-Scale study of miscible density-driven convection in porous media

Miscible density-driven convection in porous media has important implications for the long-term security of geological CO2 sequestration. In this study, a REV-scale lattice Boltzmann equation method based on the generalized Navier–Stokes equations was used to simulate density-driven convection in porous media, Thus, the effects of the Rayleigh number, the Darcy number, the Schmidt number, and the porosity of porous media can be discussed separately. The results show that density-driven convection only occurs when the Rayleigh–Darcy–Schmidt number RaD-S exceeds 102. The larger the Ra, the more disordered the concentration field, the earlier the convective phenomenon begins, and the more significant the convective mixing; The larger the Da, the finer the generated fingers. These findings provide important insights for the development of geological sequestration technologies.

Numerical investigation of the divergence-free constraint for the miscible fluids interaction in a lock-exchange arrangement

The present work scrutinizes the implementation of the divergence-free constraint in miscible fluids flow algorithms. In general, the flow solvers handling the interaction of the miscible fluid enforce the zero divergence condition, considering the fluids to be incompressible. In these algorithms, however, a convection-diffusion equation for the mass fraction, in conjunction with the Navier-Stokes equation, is solved for incorporating the mixing effects. This equation leads to a non-zero velocity field in the numerical modeling and the derived velocity divergence is a function of Reynolds and Schmidt numbers. Therefore, in this work, a quasi-incompressible formulation is presented for such flows wherein weak compressibility effects exist, but Mach numbers are very small. This novel approach is tested extensively in the classical lock-exchange setup where the effects of Reynolds and Schmidt numbers are analyzed. The role of density ratios is also investigated to realize whether the quasi-incompressible formulation generates a different mixing behavior or is similar to the conventional incompressible approach. The results demonstrate the convincing differences in these two formulations subjected to the specific combinations of Reynolds number, Schmidt number, and density ratio. A lenient criterion is also suggested by investigating the numerical tests carried out in this work, which may predict the possibilities of generating consistent results in both formulations.

Renormalization group model of turbulent bioconvection of gyrotactic microorganisms

The problems connected with processes of turbulent bioconvection are considered. These processes are typical for technologies of microbiological and other industries. The concept of using renormalization groups in the theory of turbulence is shown. A step-by-step algorithm for applying the renormalization methodology to deriving the equation for mass transfer in bioconvective processes, which includes renormalization of the turbulent diffusion coefficient, is presented. The dependence for the turbulent Schmidt number was obtained. It has been shown that turbulent Schmidt number is function of six parameters: molecular Schmidt number, turbulent viscosity, molecular viscosity, parameter of geometric shape of microorganisms, average velocity of motion of microorganisms relative to the fluid, orientation parameter. The turbulent Schmidt number enables closing the diffusion equation. The effect of the geometric shape of microorganisms on the development of turbulence in a bioconvective flow in the presence of gyrotactic microorganisms is analyzed. Analysis shows that microorganisms with spherical symmetry make a small contribution to the formation of turbulent mass transfer processes. The results of the analysis are in a good agreement with data from studies of the nonlinear hydrodynamic stability of bioconvective processes based on the Lorentz model.

Fractional analysis of unsteady magnetohydrodynamics Jeffrey flow over an infinite vertical plate in the presence of Hall current

The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field.

Unsteady flow of nanofluid over a sheet of variable thickness with nonlinear kinematics

The transport of heat in an unsteady flow of nanofluid has been discussed in this paper. The flow is maintained over a non-flat, variably porous, and moving sheet in the present simulation. Moreover, the sheet has both constant temperature and nanoparticle concentration at its surface. Unsteadiness in all field variables (i.e. the flow, temperature, and nanoparticles concentration) has been produced by the time-dependent quantities, specified at the surface of the sheet (i.e. kinematics of sheet). The well-known Buongiorno model of nanofluid has been undertaken in the present studies. Furthermore, the simulation includes the particular cases of uniform and linear (polynomial & algebraic functions) stretching/shrinking and injection/suction velocities. Besides that observations of the same nature have been recorded for the non-flat sheet. The boundary layer form of the governing PDEs has been utilized to evaluate the exact status of field variables in the flow domain. Appropriate conditions are imposed by considering the geometry of the flow problem. The problem at hand is simplified by introducing a new set of functions for the field variables because of boundary inputs. After this treatment, the system of boundary value ODEs, which contains several dimensionless numbers (parameters), has appeared, and the problem is solved numerically for various values of parameters, involved in it. More precisely, effects of unsteadiness, wall roughness, surface deformation parameters, Prandtl, Schmidt, thermophoretic, and Brownian motion numbers have been seen on profiles of four field variables. Besides that, the numerical results are also obtained for the skin friction coefficient, Nusselt, and Sherwood numbers. The present modelled problem and its solution are compared with classical models of that particular nature and with their solutions.

Influence of activation energy and multidiffusive quadratic convective nanoliquid flow past a cone and wedge

The present problem aims to examine the impact of quadratic buoyancy-driven flow nanofluid flow on two specific geometries such as cone and wedge in the presence of binary chemical reactions with activation energy, using liquid hydrogen species. This analysis is relevant for various industrial applications and are widely used in thermal energy storage devices for cooling or heating processes. The fluid flow model's governing equations are numerically solved using a fifth-order boundary value approach in matrix laboratory (MATLAB). In order to obtain the numerical solution, we initially transformed the coupled equations of the flow model and the partial differential equations into ordinary differential equations using similarity variables. The graphs and tables illustrate the importance of different physical factors that impact fluid flow and heat transfer. The quadratic combined convection parameter leads to an augmentation in fluid velocity while also inducing an elevation in frictional forces between the object's surface and the fluid. The increased in values of Schmidt number cause a decrease in mass diffusivity, which in turn leads to lower concentration profiles and improved mass transport efficiency. The activation energy is directly proportional to the decreased amplitude of the concentration profiles of liquid hydrogen species.

Mixed Convection Flow of MHD Casson Nanofluid over a Vertically Extending Sheet with Effects of Hall, Ion Slip and Nonlinear Thermal Radiation

This manuscript investigates the effects of viscous dissipation, Ohmic heating, nonlinear thermal radiation, chemical reactions, Hall current, and ion slip on the mixed convection flow of magnetohydrodynamic (MHD) Casson nanofluid over a vertically stretching sheet in a spongy medium. The strongly nonlinear ordinary differential equations (ODEs) derived from the governing equations are solved using a sixth-order, seven-stage Runge–Kutta (RK6) method in conjunction with the shooting technique. Numerical simulations are conducted using an open-source Python programming language. The study evaluates temperature, velocity, nanoparticle concentration, skin friction coefficients, Nusselt number (rate of heat transfer), and Sherwood number (rate of mass transfer) based on dimensionless parameters. Key findings reveal that increasing ion slip and Hall currents enhance the velocity profile in the x-direction, while the Casson parameter exerts a diminishing effect. The fluid temperature decreases with higher Hall current, Casson parameter, and ion slip values but increases due to nonlinear thermal radiation, the temperature ratio parameter, and the Eckert number. Furthermore, the chemical reaction parameter and Schmidt number reduce nanoparticle concentration within the boundary layer, with the Casson parameter amplifying this effect. The study also examines the rates of mass, heat, and momentum transfer near the surface under varying parameter influences, presenting results through comprehensive graphs and tables. To validate the numerical method, a comparative analysis is conducted against previous studies, demonstrating excellent agreement and thus confirming the reliability and accuracy of the computational approach.

Unsteady MHD‐radiative thin film flow with heat transfer over a stretching surface in porous media

AbstractThis study conducts a computational analysis to explore how magnetic fields, radiation, heat, and mass transfer collectively influence a horizontal stretching sheet within a porous medium. The research focuses on elucidating the dynamics of thin film flow through the formulation of time‐dependent equations and subsequent transformation of fluid flow equations into ordinary differential equations via similarity transformation. The numerical solution is attained employing the Runge–Kutta fourth‐order method coupled with a shooting technique. MATLAB software is utilized to generate graphs and numerical values, offering a detailed representation of engineering‐relevant physical quantities in tabular form. The investigation revealed notable trends associated with varying parameters. Increasing unsteadiness parameters lead to a reduction in velocity, temperature, and concentration fields, while the temperature distribution demonstrates a positive correlation with radiation parameters. Moreover, elevated Prandtl numbers and unsteadiness parameters correspond to augmented heat and mass flux, respectively. Of particular significance is the observed heightened heat transfer rate during the transition from a Prandtl number of 1 (representing air) to 2 (representing oil), alongside an increased mass transfer rate with the escalation in Schmidt number from 0.62 (representing hydrogen) to 0.78 (representing ammonia). A comparative analysis of the numerical findings with existing literature demonstrates excellent agreement, affirming the validity and relevance of the present study. These insights offer valuable implications for understanding and optimizing heat and mass transfer processes in porous media, with potential applications in various engineering and scientific domains.