Convective Boundary Condition Research Articles

Cattaneo–Christov heat and mass flux model and thermal enhancement in three‐dimensional MHD Jeffrey hybrid nanofluid flow over a bi‐directional stretching sheet with convective boundary conditions

AbstractInspired by the progressive relaxation characteristics of the Jeffrey model and its applied advantages in the rheological modeling of various dynamic fluids, the current study is focused to investigate the heat and mass transfer of magnetohydrodynamic (MHD) Jeffrey hybrid nanofluid flow over bi‐directional stretching sheet with convective boundary conditions. Additionally, the Cattaneo–Christov model of heat and mass flux is employed to take into consideration the time relaxation effects. The energy and concentration equation are taken into account to explore the effects of thermophoresis and Brownian motion. Homotopy analysis method (HAM) is employed for the solution of the current problem. Solution methodology is verified by comparing present results with those already published in open literature. The physical aspects of obtained graphical and numerical results are explained in detail to justify acquired trends. From the investigation, it is inferred that the magnetic and viscoelastic factors have a reducing influence on the flow profile along primary and secondary directions, while the stretching parameter has an increasing behavior on the flow profile in the secondary direction. Furthermore, the Brownian motion, magnetic parameter, and thermophoretic parameter have an escalating behavior on thermal distribution; however, the Brownian motion has a declining consequence on the concentration profile. The larger Biot number heightens the thermal and concentration distributions.

Nanoparticle aggregation kinematics and nanofluid flow in convectively heated outer stationary and inner stretched coaxial cylinders: Influenced by linear, nonlinear, and quadratic thermal radiation

The consequence of nanoparticle aggregation and convective boundary condition on the nanofluid stream past the co-axial cylinder with radiation impact is investigated in the present examination. The influence of linear, nonlinear, and quadratic thermal radiation on the nanofluid flow is analyzed. The outer cylinder stays stable, while the inner cylinder deforms horizontally in the axial direction, allowing fluid to flow. By using similarity variables, the governing equations are transformed into ordinary differential equations (ODEs). Subsequently, the Runge–Kutta–Fehlberg fourth-fifth order (RKF-45) method is employed to solve the reduced ODEs. The upshot of several nondimensional terms on the temperature and velocity profiles is displayed with graphical representation. The comparison of linear, quadratic, and nonlinear thermal radiation on the thermal profile is illustrated. The upsurge in curvature parameter increases velocity and thermal profile. The increase in radiation parameter intensifies the temperature profile. The thermal profile improves with a rise in the values of radiation parameter. The radiation parameter generates thermal energy in the flow zone, which is why the temperature field has improved. The thermal Biot number exhibits an increasing response with temperature and thermal boundary layer thickness. The linear thermal radiation shows better heat transfer compared to quadratic and nonlinear thermal radiation.

Lattice Boltzmann simulation of effects of realistic boundary conditions on volumetric radiation‐conduction melting of a novel cylindrical enclosure filled with phase change materials

AbstractIn this research, a novel solar latent heat thermal energy storage (LHTES) system, including the cylindrical enclosures filled with a phase change material (PCM), is proposed, which can be installed on the building windows to alleviate the drawbacks of traditional PCM‐filled double‐glazed windows, such as daylight hindrance and leakage. The lattice Boltzmann method (LBM) is used to simulate the volumetric radiation‐conduction melting of the PCM within a single cylinder of the proposed LHTES system with considering more realistic conditions such as convective boundary condition, shadow effect, and variable solar radiation angle compared with the available works in the literature. As such, several boundary conditions are assessed, and parameters such as cylinder diameter, extinction coefficient, scattering albedo, solar angle, shadow effect, and natural convection heat transfer coefficient are studied on the time history of the melting fraction and charging time. The results revealed that considering the applied conditions, such as convection heat loss to the environment and shadow, significantly affects the charging time of the system. It is shown that the charging time for convective boundary condition with , , and increases, respectively, by 11%, 30%, and 50% relative to a case with the insulated boundary condition without the shadow effect and 38%, 91%, and 175% compared with the insulated case with a 90° shadow.

Tangent hyperbolic nanofluid flow through a vertical cone: Unraveling thermal conductivity and Darcy–Forchheimer effects

Purpose: This paper demonstrates the way tangent hyperbolic nanofluid flow through a vertical cone is influenced by varying viscosity and varying thermal conductivity. This study also seeks to illustrate the impact of convective boundary conditions on a fluid. The mathematical modeling also takes the Darcy–Forchheimer effect into account. Methodology: Using the appropriate similarity transformation, the fluid problem is reduced into a set of nonlinear ordinary differential equations. These systems of differential equations are evaluated numerically by applying the Optimal Homotopy Asymptotic Method. Findings: The nature of emergent parameters is examined in relation to the temperature distribution, nanoparticle concentration profile, and velocity profile. An increase in variable viscosity corresponds to a decrease in fluid velocity, while enhanced thermal conductivity results in elevated fluid temperature. The skin friction coefficient, Sherwood, and Nusselt numbers are numerically examined for active concerned parameters. These findings can be put into practice in a variety of fields such as polymer cooling systems and medication. Originality: Existing literature has yet to explore the combination of tangent hyperbolic nanofluids with varying viscosity and thermal conductivity under convective boundary conditions.

Simulation of hybrid boiling nano fluid flow with convective boundary conditions through a porous stretching sheet through Levenberg Marquardt artificial neural networks approach

In the domain of artificial neural networks, the Levenberg-Marquardt technique stands out for its innovative approach and convergent stability. It generates a numerical approach for the progression of a hybrid Cu–Al2CO3/water nanofluid on a porous stretched sheet (HNF-PSS), employing regression plots, state transition measures, histogram representations, and mean squared errors. This work explores the analysis of the fluid flow problem associated with HNF-PSS, introducing a novel application of an intelligent computing system that utilizes the effectiveness of neural networks trained by the Levenberg-Marquardt algorithm (NN-TLMA). The initial mathematical expression, expressed in terms of partial differential equations (PDEs) for HNF-PSS, undergoes transformation into dimensionless nonlinear ordinary differential equations (ODEs). The collection of data for the envisioned NN-TLMA involves parameters influencing the velocity of the HNF-PSS system model, generated using the Lobatto IIIa formula. The efficacy of the suggested NN-TLMA for solving the HNF-PSS is robustly verified by examinations of state transition dynamics, regression analyses, mean square error, and error histogram studies. The consistent alignment of the obtained results with corresponding solutions attests to the legitimacy of the structure, achieving a high level of accuracy within the range of 10–6 to 10–8. Insightful findings demonstrate that the thermal Biot number contributes significantly to an upsurge in fluid temperature. Furthermore, an augmentation in nanofluid concentration and thermal profile is found to increase the porosity strength of the medium. Nevertheless, an attenuation in the velocity profile is noted under these conditions. The application of this simulation work can be found in optimizing the designs of heat exchanger, in biomedical application and in renewable energy processes.

Unsteady tetra hybrid nanofluid in MHD flow between two parallel rotating stretchable disks under chemical reaction and activation energy effects

This article aims to investigate the dynamics of unsteady tetra hybrid nanofluid magnetohydrodynamic (MHD) flow occurring between two parallel rotating stretchable disks with convective boundary conditions. The study employs blood as the base fluid, incorporating quadrant hybrid nanoparticles comprising ZrO2, MoS2, MWCNTs, and UO2. The influence of parameters such as shape factor, chemical reaction, and activation energy on the flow characteristics is examined. By employing similarity transformations, the governing partial differential equations are converted into a set of ordinary differential equations. Analytical solutions are obtained utilizing the differential transform method (DTM) and validated against results obtained through the HAM-package and numerical techniques (Explicit Runge-Kutta Method). Velocity profiles in the axial, radial, and tangential directions, as well as temperature and concentration profiles, are scrutinized across various fluid parameters. The tetra hybrid nanofluid demonstrates a higher Nusselt number compared to other fluid compositions. However, it is noted that skin friction is also elevated for the tetra hybrid nanofluid, underscoring the importance of carefully considering optimal nanoparticle utilization in engineering applications. This study offers valuable insights into the behavior of hybrid nanofluids within MHD flow systems and their potential industrial applications.

Enhanced numerical modeling of natural heat convective phase change for generalized non-Newtonian fluids at high Rayleigh number

Numerical modeling of convective heat transfer employing non-Newtonian fluids is a key issue and represent an interesting challenge in many engineering applications. For this reason, this work develops an enhanced numerical model to predict fast and accurately the convective phase change for generalized non-Newtonian fluids. The strongly thermally coupled model is solved by an improved pressure-correction algorithm (SIMPLERnP) and the Finite Volume Method with accuracy of the third order for the transient terms and second order for the convective boundary conditions and the velocity gradients that allows to calculate the apparent viscosity. The study examines the natural heat convective solidification of the ternary Al-27 %Cu-5.25 %Si alloy with the Herschel-Bulkley rheology at a high Rayleigh number (>107). In addressing the main problem, four crucial aspects are discussed: the validation of the numerical scheme with numerical and experimental results; the modeling of the non-linear temperature variation of the liquid phase change fraction; the non-Newtonian effects of the power index (0.1 ≤ n ≤ 1.9) and yield stress (0≤τ0≤5 Pa) on the heat transfer mechanisms; and finally, the time of computation with the high-order numerical scheme and the enhanced pressure-correction algorithm. The main finding is that FVM/SIMPLERnP provides a significant reduction in the time of computation compared to reliable pressure-correction schemes (SIMPLER and IDEAL), being a robust, accurate and efficient scheme to solve complex natural heat convective phase change problems involve generalized non-Newtonian fluids at high-Rayleigh numbers.

Couple-stress nanofluid flow comprising gyrotactic microbes subject to convective boundary conditions: Numerical solution

Couple-stress nanofluids have multiple potential applications in numerous industrial and engineering sectors, such as energy production, medical diagnostics, thermal control systems, and the aerospace industry. Couple-stress nanofluids have the ability to improve the heat exchange properties and elevate the performance of nuclear power plants, solar panels, and other renewable energy sources. Therefore, in the current analysis, a non-homogeneous nanofluid model is considered to examine the non-Newtonian Casson nanofluid flow across a prolonging sheet. The flow has been studied under the significance of generalized Fourier’s and Fick’s laws, convective boundary conditions, and the heat source/sink. The modeled equations are simplified into a dimensionless lowest-order system of ordinary differential equations by using similarity transformation. The numerical outcomes are achieved by using the “ND-Solve” approach. It has been noticed that the energy field decreases because of the Prandtl number’s impacts, whereas it increases with the increase in the heat radiation parameter. The couple-stress nanoliquid’s velocity decreases vs increasing values of the magnetic field and mixed convection parameter. The influence of thermal relaxation and couple-stress parameters falls off the energy field. Furthermore, the intensifying effect of Rayleigh number and buoyancy ratio increases the fluid temperature.

Entropy production on mixed convection stagnation point flow of nonlinear radiative fourth-grade hybrid nanofluid through a stretchable Riga surface

The purpose of the current study is to inspect entropy generation, mixed convective stagnation point flow, and thermal transfer features of nonlinear radiative fourth-grade hybrid nanofluid (NF) confined by a convectively heated Riga surface. The heat transport is examined with the existence of two disparate heat source modulations, variable thermal conductivity, and viscous dissipation. The original flow equations are first transmuted using appropriate transformations into non-dimensional ordinary differential equations, which are then solved via an overlapping grid-based spectral collocation scheme. The upshots of various pertinent parameters on velocity, temperature, entropy generation, and valuable engineering quantities are deliberated. Pivotal results obtained reveal that speedily flow of fluid and skin friction can be accelerated by strong magnetic force, rising mixed convection, and material parameters. Also, convective boundary conditions, along with nonlinear radiation and fluctuating thermal conductivity, are recommended for boosting fluid temperature, rates of entropy generation and heat transport. Thermal mechanism in hybrid NF is dominant over simple NF, which implies that performance of hybrid NF is better than that of simple NF. The outcomes of this study can be useful in enriching thermal performance of the working fluid, assisting in diagnosing causes of incompetency in thermal systems, and discovering suitable means of minimizing entropy generation with the intention of mitigating the loss of useful and scarce energy resources.

Lie group analysis on EMHD Jeffrey nanofluid flow with exponential heat source: Heat transfer optimization using RSM

The present research examines the behavior of a Jeffrey nanofluid flow across a stretching sheet under the effect of electric and magnetic fields. It comprises the Buongiorno model as well as an exponential heat source. The impact of chemical reaction has also been taken into consideration. While assuming no mass flux, the study considers boundary conditions for thermal convection and velocity slip. Lie group transformations are employed to transform the set of governing equations into a dimensionless system and later simulated using the finite difference scheme. It is found that the velocity profile rises as the Deborah number is enhanced whereas the ratio of relaxation to retardation time parameter has an inverse effect on the velocity profile. It is noted that per unit change in the Deborah number descends the drag coefficient by 31.29%. In this study, the response surface methodology and sensitivity analysis have been conducted by choosing heat transport as the dependent variable and the electric-field parameter ( 0.01 ≤ E ≤ 0.03 ) , exponential heat source parameter ( 0.02 ≤ Qe ≤ 0.06 ) , and Biot number ( 0.15 ≤ Bi ≤ 0.25 ) as the independent variables. The Nusselt number escalates when the Bi number is increased and drops as the E values are raised. In the instance of the Biot number, the Nusselt number exhibits the maximum sensitivity.

Numerical study of heat and mass transfer of williamson hybrid nanofluid (CuO/CNT's-water) past a permeable stretching/shrinking surface with mixed convective boundary condition

The present paper deals with the hybrid nano fluid, for this we have used Single and Multi-wall carbon nano tubes along with CuO and Water. The inclined magneto-hydrodynamics is considered along with Hall effect, soret and dufour for the impact on Williamson fluid flowing through porous medium over stretching/shrinking lamina having suction and injection in consideration. Heat and mass convective boundaries are taken to solve the nonlinear problem using shooting method and bvp4c MATLAB solver. The study shows the comparison between nanofluid (Cuo-Water, SWCNT-Water and MWCNT-Water) and found that the hybrid carbon nanotubes possess excellent result in skin friction and local Nusselt number compared to the SWCNT-water and MWCNT-water.Then the effect of different parameters are analysed through graphical representation and data tables.

Enhancing thermal efficiency in MHD kerosene oil-based ternary hybrid nanofluid flow over a stretching sheet with convective boundary conditions

The increasing demand for thermal management due to the high heat density heat exchangers for different technological and industrial processes draw the attention of researchers in heat transfer analysis to investigate the simultaneous solution to this problem. Keeping this in mind, the current work addressed the utilization of ternary hybrid nanofluid, a mixture of graphene oxide with silver and copper, to examine the heat and mass transfer enhancement of MHD Maxwell fluid. In the current model, the author discussed heat and mass transfer analysis of Maxwell MHD ternary hybrid nanofluid flow across a porous medium over an extending sheet. The energy and concentration equations are expressed to include the effects of Brownian motion and thermophoretic diffusion. Additionally, the effects of thermal radiation, activation energy, chemical reactions, and convective boundary conditions are considered. The similarity transformations are used to convert the nonlinear PDEs into ODEs. The impact of embedded factors on velocity, temperature, and concentration profiles is perceived graphically and mathematically by using the HAM technique. The convergence of computed solutions is ensured by h-curves. The significant outcomes from the analysis expressed that the flow distribution increases with slip and suction/injection factors. The concentration of the ternary hybrid nanofluid increases with an increase in thermophoretic diffusion (0.1–0.5), thermal biot number, and solutal biot number (0.1–0.5), however, a declining behavior is perceived with rising quantity of Schmidt number (0.6–0.8) and Brownian motion (0.1–0.5) parameters. Nusselt number shows a dominant behaviour with a higher magnetic factor. Similarly, the skin friction increases with an increase in thermal biot number and thermophoresis factor. It is revealed that the skin friction along x− direction increases from (0.78138, 0.833702, 0.897022, and 0.972526) for ternary hybrid nanofluid. Nusselt number increases from 2 to 5% (0.208936, 0.214288, 0.219799, 0.22555) when the volume fraction varies from 0.01 to 0.04 respectively.

Mathematical Simulation for MHD Casson Convective Nanofluid Flow Induced by 3D Permeable Sheet with Chemical Effect

Objectives: Current manuscript focuses on examination of chemical reaction and heat generation impacts on 3D MHD non-Newtonian nanofluid flow with convective boundary conditions induced by permeable sheet. Additionally, Brownian motion, non-Newtonian heating and thermophoretic processes as used for this study. Methods: A computational programme, MATLAB has been used for solving the system of O.D.Es with the help of ODE45 solver. The Runge Kutta Fehlberg approach is implemented to calculate the answer to the expression for temperature, velocity, and nanoparticle concentration after the shooting process. Findings: For a variety of fluid parameters, the temperature, concentration of nanoparticles, and dimensionless velocities are shown and examined, including permeability parameter , magnetic , stretching ratio parameter , Lewis number , Brownian motion and Prandtl number , thermal Biot number , Casson fluid parameter , chemical reaction parameter . The temperature is found to increase with an enhance in the thermal Biot number and to reduce with a greater Prandtl number and stretching ratio parameter. Novelty: Although the immense significance and frequent use of nanofluids in industries and technology, no effort has been made to explore the chemical influence on MHD Casson fluid flow using a three-dimensional permeable sheet. Through similarity transformations, the Runge-Kutta Fehlberg technique converts mass, momentum, and energy conservation equations into ODEs and incorporates boundary conditions. Skin friction and the heat transmission rate past an extending surface, which have an impact on technology and production, can be predicted using the results of this study. Keywords: Chemical reaction, Buongiorno's model, Nanofluid, Biot numbers, 3D permeable sheet

Quasi-one-dimensional approach to heat transfer: General formulation and its application to transformer windings

A quasi-one-dimensional approach to conduction heat transfer with convective boundary conditions is developed for bodies of variable geometry. The novelty of the method is demonstrated on the windings in oil-filled distribution transformers with partial cooling ducts. We obtain analytical solution for the windings average temperature rise and tangential temperature distribution and find them in an excellent agreement with the FEM simulation, numerically confirming the validity of the reduction from 2D to 1D. When the quasi-one-dimensional approach is applied to calculation of temperature rise for the low and high voltage windings in industrial setting we obtain 1% and 5% discrepancy with the industrial tests respectively. Hence, the method offers reliable estimates of the temperature rise, and temperature distribution in a chosen direction, in bodies of variable geometry.

Linear stability analysis of a solidification process with convection in a bounded region of space

The morphological/dynamic instability of crystallization process in a bounded region in the presence of intense convection in liquid is studied. The paper considers a linear theory of morphological instability with a flat solid-liquid interface on the example of molten metal and magma. The mathematical model includes heat transfer equations and convective type boundary conditions at the interface. The equations for perturbations of the temperature field and interfacial boundary are found, allowing to obtain the dispersion relation. Its analysis has shown the existence of morphological instability of the flat interfacial boundary for a wide range of wavenumbers. Dynamic perturbations (perturbations of the quasi-stationary crystallization velocity) were also analyzed and two solutions for the perturbation frequency were obtained. One of them is stable and the other one is unstable. The system selects one of them depending on the action of convection. The result of morphological and dynamic instability is the appearance of a two-phase region in front of a flat solid-liquid interface. Therefore, the paper also considers the dynamic instability of stationary crystallization with a two-phase region replaced by a discontinuity surface. In this case, the dynamic instability was also found for a wide range of crystallization velocities.

Dynamics of methanol conveying mono and hybrid nanoparticles to optimization of heat transfer across stretching cylinder

This manuscript investigates the comparative analysis of SiC and SiC − Ag with methanol-base fluid. The nano species are more important in many fields such as medicine, catalysis, energy-based research, imaging, and environmental sciences. The present study includes theoretical and numerical studies of the Prandtl hybrid nanofluid flow model, which takes into account the effects of heat radiation across a stretched cylinder, inclined magnetohydrodynamics (MHD), and Darcy-Forchheimer. The cylinder’s surface is subjected to the convective slip boundary condition as part of the study. The main aim of this study is to enhance heat transformation. The flow problem is formulated in a system of nonlinear partial differential equations. By employing a similarity transformation, a nonlinear system of partial differential equations can be converted into a linear system of ODEs. A feasible numerical technique Bvp4c is used to solve the reduced system of ODEs through MATLAB software. The results of temperature, concentration, and velocity profiles are discussed graphically. In section and injection scenarios, the velocity profile of both fluids decreased with increasing inputs of magnetic and Darcy-Forchheimer parameters. The heat transmission improved for higher inputs of Prandtl and thermal radiation parameters for both section and injection cases. Furthermore, our findings align with the body of current literature. The conclusions are supported by a careful comparison with pertinent research that has been published in earlier publications.

Thermodynamic survey of a reactive MHD couple stress fluid through saturated porous substances with convective boundary conditions

This study explores the thermodynamic behavior of a reactive hydromagnetic liquid flowing through permeable materials, with convective cooling applied to the walls. This study holds practical significance in optimization of thermal management systems and it is crucial for enhancing the efficiency of controlling thermal runaway. The flow is modeled as a system of partial differential equations which are numerically solved. The modified Adomian Decomposition Method and Pade approximation technique are utilized in solving the equations. The results acquired for velocity and temperature distributions are thereby employed to estimate entropy generation rate with critical values over numerous effects of various boundaries over improvement of thermal runaway utilizing Pade approximation technique to show the significant impact of convective cooling term (Biot number) and other thermophysical parameters on the fluid flow. The outcomes show that fluid velocity continuously increases with rising values of inverse couple stress and fluid temperature increases Biot number.

Effects of thermal boundary conditions on Stokes' second problem

In this investigation, an infinite flat plate is employed to examine the flow behavior of Casson fluid and the associated heat transfer phenomena. The plate undergoes an initial acceleration with a constant velocity until it eventually decelerates to rest. The energy equation incorporates the effects of viscous dissipation. An appropriate similarity transformation transforms the governing equations into coupled nonlinear ordinary differential equations (ODEs). A closed-form solution for the velocity profile is obtained, while the energy equation is solved using the built-in function NDSOLVE in Mathematica. The study investigates the influence of governing parameters on dimensionless velocity, temperature, skin friction, and local heat transfer rate under two thermal boundary conditions: Newtonian heating and convective boundary conditions. The fluid's thermophysical properties remain constant throughout the study, with the surface temperature of the plate assumed to be fixed at a constant value. A graphical analysis examines the flow behavior and temperature distribution, revealing the impact of non-dimensional parameters. This study reveals that thermal boundary conditions significantly influence heat transfer rates, with Newtonian heating leading to an increase and convective heating causing a decrease. This is attributed to the direct application of heat at the boundary in Newtonian heating, which enhances thermal energy transfer. In contrast, convective heating disperses heat through fluid motion, limiting transfer rates.

Optimizing heat transfer rate and sensitivity analysis of hybrid nanofluid flow over a radiating sheet: Applications in solar-powered charging stations

In a solar collector system, absorbing radiation through solar panel and transforming it into heat, the role of nanofluid is vital. However, the combined effect of CuO and Cu water hybrid nanofluid efficiently carries the fascinated heat away from the solar collector. Further, it helps improve in efficiency of the thermal solar thermal system by enhancing heat transfer and thermal losses. Based upon the advanced properties, the study aims at the behavior of a conducting hybrid nanofluid comprised of CuO and Cu nanoparticles through a nonlinear stretching surface filled with a porous matrix. Essentially, the use of thermal radiation with dissipative heat and convective heat transfer boundary conditions are important in enhancing heat transfer properties. The assemble of diversified similarity rules is useful for the transformation of the governing equations into dimensionless form. Further, numerical technique with the help of built-in function bvp4c in MATLAB is employed for the solution of the designed model equipped with different constraints. A robust statistical analysis i.e. response surface methodology (RSM) combined with analysis of variance (ANOVA) is used to optimize the heat transfer rate. Sensitivity analysis for the associated factors united to the response of heat transfer is obtained and presented briefly. Finally, the parametric behavior is important to describe following the pattern of the graph. Further, the important outcomes are; the enhanced volume fraction of the nanoparticles augments the fluid velocity as well as the temperature significantly. Thermal radiation has influential behavior in enhancing the heat transport phenomenon of hybrid nanofluid.

Study of Nano-Powell-Erying fluid flow past a porous stretching sheet by the effects of MHD, thermal and mass convective boundary conditions

AbstractThe 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.