Mixed Convection Stagnation Point Flow Research Articles

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.

Analysis of mixed convective stagnation point flow of hybrid nanofluid over sheet with variable thermal conductivity and slip Conditions: A Model-Based study

This research looks at the stagnation point flow of MHD Al2O3-Cu/H2O hybrid nanofluid against a permeable, vertically extending surface that uses thermal radiation and how different models of thermal conductivity affect it. This study is unique because it looks at how changes in thermal conductivity, mixed convection, and the slip velocity of hybrid nanofluids affect the stretching surface. It also looks at how changes in temperature, skin-friction coefficient, Nusselt number, and velocity affect convective thermal boundary conditions. With the use of boundary layer approximations, the complicated system of PDEs is simplified. The dimensionality of these PDEs and the boundary conditions they include are eliminated by applying certain modifications. Combining a local non-similarity approach up to the second truncation level with MATLAB's built-in finite difference code (bvp4c), one can obtain the results of the updated model. The research demonstrates and analyzes the impact of different factors on fluid flow and heat transfer characteristics in the studied flow situations. This is done by comparing the computed data with available literature and presenting the findings in graphical form. Tables are generated to present the numerical fluctuations of the drag coefficient and Nusselt number. This study shows how important thermal conductivity is in the mixed convection of hybrid nanofluids and looks into what happens when the thermal conductivity parameter is changed. Significantly, an augmentation in this parameter results in an elevation in the temperature distribution of the hybrid nanofluid while simultaneously reducing the rate of heat transfer across various models. Furthermore, increasing the nanoparticle volume fraction parameter leads to higher temperature and Nusselt number profiles while reducing skin friction. The mixed convection parameter has a notable impact on increasing the friction coefficient on the stretched vertical surface. However, because these elements function as regulating variables, it decreases when the magnetic, mass suction, and velocity slip parameters are present. The results also demonstrate notable discrepancies in the mean Nusselt values generated by various thermal conductivity models. According to the analysis, the Hamilton-Crosser model has the lowest average Nusselt numbers, followed by the Yamada-Ota model and the Xue model, in that order.

Effect of viscous dissipation and induced magnetic field on an unsteady mixed convective stagnation point flow of a nonhomogenous nanofluid

In the study, we investigate the numerical investigation of variable viscous dissipation and source of heat or sink in mixed convective stagnation point flow the unsteady non-homogeneous nanofluid under the induced magnetic parameter. Considering similarity conversions, the governing of fundamental boundary of layer non-linear PDEs are transformed to equations of the non-linear differential type that, under appropriate boundary conditions, are numerically solved, and the MATLAB function bvp4c is considered to solve the resulting system. The obtained results are calculated numerically for non-dimensional velocity, temperature, and volume fraction and displayed graphically. Further, numbers of Nusselt and Sherwood and local Skin of friction have been produced and displayed by graphs. A comparison with previous results obtained neglecting the new parameters has been made to show the impact of new external parametes on the phenomneon. The obtained findings agree with those introduced by others if the magnetic field and viscous dissipation are neglected. The results obtained have an important applications in diverse field as chemical engineering, agriculture, medical science, and industries.

Mixed convective flow of nanofluid across exponential surface: A numerical assessment of the impact of Darcy-Forchheimer and nanoparticle aggregation

Improving heat transmission is a modern difficulty faced in a multitude of areas, incorporating but not limited to electronics, heat exchangers, biochemical reactors, and other similar areas. In their capacity as cutting-edge heat transfer fluids, nanofluids have the promise of becoming a useful instrument in the pursuit of greater energy transfer efficiency. So, the focus of this work is on how it is possible to enhance heat transmission by using nanofluids. Using a stretched exponentially accelerating surface, this analysis investigates the effect that nanoparticle aggregation with thermal radiation has on the nanofluid of mixed convective stagnation point flow through Darcy-Forchheimer porous surfaces. The aggregation of nanoparticles may be assessed using modified Krieger-Dougherty and Maxwell-Bruggeman models. By using the right similarity transformations, the controlling equations of this problem were turned into a numerical model that can be unraveled. Mathematica was used to resolve the issue numerically by using the shooting with Runge-Kutta (RK-IV) procedure. nanoparticles with base fluid under aggregation effect boost heat transfer performance. A diversity of parameter estimates, including the mixed convection, mass suction, solid volume fraction of nanoparticles, thermal radiation, and stretching, were used to provide solutions for heat transfer and lower skin friction coefficients, as well as velocity and temperature curves. In addition to the findings, there were graphs and tables with explanations. The increase in heat transfer rates was 6.7021% when the suction parameters were set between 2.0 to 2.5 with =0.01. When the amount of nanoparticles volume fraction went from 0% to 1% by volume, the ineptitude of heat transfer went by an average of 4.249%. Aggregation models are often favored over non-aggregation models due to their ability to provide more accurate velocity and skin fraction profiles. Because of their superior precision, they are often used in situations where accuracy is paramount.

Effect of an inclined magnetic field on unsteady mixed convective stagnation point flow over a permeable stretching sheet with radiative heat transfer

In this study, we analyzed the time-dependent, 2D, inclined magnetohydrodynamics mixed convection stagnating point flow of nanoparticle toward a permeable stretchable surface with radiative heat effect. Four different types of water-based nanomaterials, namely titanium dioxide copper aluminum oxide and copper oxide are analyzed in this investigation. Numerous engineering disciplines, including energy systems, material processing, thermal management, and environmental engineering, can benefit greatly from research in mixed convection, MHD, and nanofluids. The boundary layer representations of the dominating partial differential equations PDEs are converted into strong nonlinear ordinary differential equations ODEs utilizing similarities approach. The ODEs are computed numerically employing 4th order Runge–Kutta methodology-based shooting scheme. Few special situations, a remarkable alignment is determined between the present study and the outcomes obtained in the existing research. The impact of numerous pertinent variables on the prominent quantities such as velocity, temperature and concentration distributions, drag friction coefficient and heat transport are demonstrated graphically. It is noticed that the velocity and thermal curve decrease as the nanoparticle volume friction factor increases. Moreover, it is analyzed that higher values of nanoparticle concentration diminishes the velocity and temperature distributions.

Entropy generation due to nanofluid flow in porous media over radiative permeable exponentially surface with nanoparticle aggregation effect

In recent years, energy scarcity has emerged as a serious problem for manufacturing since most of the power produced is lost as heat during transportation. Due to the irreversible nature of heat transfer processes, it is crucial to minimize the development of entropy during nanofluid flow and heat transmission. Therefore, the purpose of this study is to inquire entropy generation on viscous TiO2−C2H6O2 nanofluid through a permeable exponentially surface with porous media and effect that nanoparticle aggregation with thermal radiation, mixed convective stagnation point flow. The controlling partial differential equations were simplified by using an appropriate similarity transformation, resulting in a set of ordinary differential equations. After that, we used Mathematica's shooting technique and fourth order Runge-Kutta integration to get a numerical answer to these equations. The current study showed that increasing the volume percentage of nanoparticles, the porosity of the nanofluid, the mass suction, and the mixed convection parameters all led to an increase in the skin friction coefficient. The heat transfer rates increased by 6.7021% points when the suction settings were set to values between 2.0 and 2.5 and the nanoparticle volume fraction was set to 1%. The average reduction in heat transfer efficiency for the aggregation model was around 4.249% for the range of 0–1% nanoparticle volume fraction. Since aggregation models may provide more accurate velocity and skin friction profiles, they are often preferred over homogeneous models. The growing use of aggregation models may largely be attributed to their improved profile prediction accuracy. Improving Ω's values is known to lessen the onset of entropy. An increase in Ec is shown to be beneficial to the entropy inception field. Increasing the Brinkman number accelerates the entropy production rate.

Comparative analysis of analytical and numerical approximations for the flow and heat transfer in mixed convection stagnation point flow of Casson fluid

A mathematical description of non-Newtonian mixed convective Casson fluid stagnation point flow and transfer of heat exists in terms of partial differential equations. We considered the same to study it further under the effects of unsteadiness and varied film thickness parameters. For inclusion of these parameters in the flow model study we modified the available similarity transformations. The governing equations with three independent variables are converted into ordinary differential equations by employing the modified invertible transformations. For the mass and heat transfer in the mixed convection stagnation point unsteady flow of Casson fluid over a stretching sheet, a detailed comparative analysis is carried out in this paper, of the analytical and numerical approximation techniques. The Homotopy Analysis Method is applied for the analytical solutions while the Runge-Kutta with a Shooting Method (RKF45) and Finite Difference Method are used for obtaining the numerical solutions. With these solution schemes we present an analysis of velocity and temperature profiles under the effects of embedded parameters such as the Casson fluid parameter, unsteadiness parameter, mixed convection parameter, Prandtl number, Eckert number, and stretching ratio. The results are presented in both graphical and tabulated forms and they illustrate the dependence of mass and heat transfer characteristics of Casson fluid upon the embedded parameters. Further, we have shown an agreement between the analytical and the approximate solutions for the considered flow and heat transfer which reflects a validation of the results presented here.

Mathematical investigation of nanoparticle aggregation and heat transfer on mixed convective stagnation point flow of nanofluid over extendable vertical Riga plate

The purpose of this study is to evaluate the effects that aggregation of nanoparticles has on mixed convective stagnation point flow and porous media across a permeable stretched vertical Riga plate in the occurrence of a heat source or sink for ethylene glycol-based nanofluids. It is possible to evaluate nanoparticle aggregation with modified versions of the Krieger-Dougherty and Maxwell-Bruggeman models. To obtain numerical solutions to the mathematical model of the present issue, the Runge–Kutta (RK-IV) with shooting technique in Mathematica was used. Figures in the proposed mixed convection and suction variables along a boundary surface in the stagnation point flow towards a permeable extending Riga plate identify and explain heat transfer processes and interrupted flow occurrences. By combining titania (TiO 2) nanoparticles with ethylene glycol as the base fluid, improved heat transmission is possible. The effects of different inputs on temperature and velocity profiles, skin friction coefficient, and local Nusselt number were graphically shown using tables and graphs. The heat transmission and skin friction rates both increased when the suction parameter was given larger values. Increases in both skin friction and the Nusselt number may be attributed to variations in the volume percentage of nanoparticles. Heat source parameter increased the temperature profile and reduced the Nusselt number. Aggregation models provide more accurate velocity and skin fraction profiles than homogeneous models, which is why they are more often used. The findings were confirmed by comparing the most up-to-date research with previously published results for the same situation. Results indicated that the two sets of data were consistent with one another.

Mathematical analysis of mixed convective stagnation point flow over extendable porous riga plate with aggregation and joule heating effects

It is still not quite apparent how suspended nanoparticles improve heat transmission. Multiple investigations have demonstrated that the aggregation of nanoparticles is a critical step in improving the thermal conductivity of nanofluids. However, the thermal conductivity of the nanofluid would be greatly affected by the fractal dimension of the nanoparticle aggregation. The purpose of this research is to learn how nanoparticle aggregation, joule heating, and a heat source affect the behavior of an ethylene glycol-based nanofluid as it flows over a permeable, heated, stretched vertical Riga plate and through a porous medium. Numerical solutions to the present mathematical model were obtained using Mathematica's Runge-Kutta (RK-IV) with shooting technique. In the stagnation point flow next to a permeable, heated, extending Riga plate, heat transfer processes and interrupted flow phenomena are defined and illustrated by diagrams in the proposed mixed convection, joule heating, and suction variables along a boundary surface. Data visualizations showed how different variables affected temperature and velocity distributions, skin friction coefficient, and the local Nusselt number. The rates of heat transmission and skin friction increased when the values of the suction parameters were raised. The temperature profile and the Nusselt number both rose because of the heat source setting. The increase in skin friction caused by changing the nanoparticle volume fraction from φ=0.0 to φ=0.01 for the without aggregation model was about 7.2% for the case of opposing flow area (λ=−1.0) and 7.5% for the case of aiding flow region (λ=1.0). With the aggregation model, the heat transfer rate decreases by approximately 3.6% for cases with opposing flow regions (λ=−1.0) and 3.7% for cases with assisting flow regions (λ=1.0), depending on the nanoparticle volume fraction and ranging from φ=0.0 to φ=0.01, respectively. Recent findings were validated by comparing them to previously published findings for the same setting. There was substantial agreement between the two sets finding.

MHD Mixed Convection Flow of Hybrid Ferrofluid through Stagnation-Point over the Nonlinearly Moving Surface with Convective Boundary Condition, Viscous Dissipation, and Joule Heating Effects

This paper discusses a numerical study performed in analysing the performance regarding the magnetic effect on the mixed convection stagnation-point flow of hybrid ferrofluid, examining the influence of viscous dissipation, convective boundary condition as well as Joule heating across a nonlinearly moving surface. Additionally, the hybrid ferrofluid exhibits an asymmetric flow pattern due to the buoyancy force affecting the flow. Water H2O is employed as the base fluid collectively with the mixtures of nanoparticles containing magnetite Fe3O4 and cobalt ferrite CoFe2O4, forming a hybrid ferrofluid. The partial differential equation’s complexity is reduced by similarity transformation into a system of ordinary differential equations, which are then numerically solved by applying the MATLAB function bvp4c for a specific range of values regarding the governing parameters. Dual solutions were identified under both opposing and assisting flow conditions, and the stability analysis identified that the first solution was stable. Furthermore, it was also revealed that the addition of 1% CoFe2O4 in hybrid ferrofluid led to a higher skin friction coefficient between 3.35% and 7.18% for both assisting and opposing flow regions. Additionally, the growth of magnetic fields results in a reduced heat transfer rate between 8.75% to 10.65%, whilst the presence of the suction parameter expands the range of solutions, which then delays the boundary layer separation. With the Eckert number included, the heat transfer rate continuously declined between 7.27% to 10.24%. However, it increased by about 280.64% until 280.98% as the Biot number increased.

Mixed convective flow of hybrid nanofluid over a heated stretching disk with zero-mass flux using the modified Buongiorno model

In this study, the mixed convective stagnation-point flow of a Al2O3-Cu/H2O hybrid nanofluid towards a stretched disc with a convective boundary and zero mass flux condition is described with mass suction and viscous dissipation effects. The process is accomplished by using thermophoretic and Brownian motion physical phenomena. After performing a similarity transformation on the PDEs in order to convert them into an ODE system, the bvp4c solver is then employed in order to carry out a numerical solution. In the study that was described above, the flow, heat, and mass transfer characteristics were investigated with the assistance of the Buongiorno model and the Devi and Devi model. The following characteristics were brought up as points of contention: ϕ1,ϕ2,λ,S,Nt,Nb,Le,Ec,Bi and B. There is a very good consonance among the existing and antecedent results in undeniable cases, as well as a connection error of approximately 0%. The velocity and temperature profiles upsurge with the increment of the nanoparticle volume fraction and mixed convection parameter, while the velocity increases with the addition of the suction parameters. As a result of this study, we are able to estimate the flow and thermal behavior of Al2O3-Cu/H2O when the physical parameters are embedded.

Three-dimensional mixed convection stagnation-point flow past a vertical surface with second-order slip velocity

Three-dimensional mixed convection stagnation-point flow past a vertical surface with second-order slip velocity

Dual solutions and linear temporal stability analysis of mixed convection flow of non-Newtonian special third grade fluid with thermal radiation

The present study aims to investigate the steady mixed convection stagnation-point flow of a special third grade fluid over a vertical stretching/shrinking sheet with the inclusion of suction and thermal radiation effects. The governing momentum and energy equations are transformed into a system of ordinary differential equations (ODEs) using the Lie scaling group of transformations. The resulting system of highly nonlinear boundary value problems (BVPs) is solved numerically with the help of Matlab solver ‘bvp4c’. Dual similarity solutions are found for the opposing flow case within the range λc≤λ<0, where λ is the buoyancy parameter. Emphasis has been given to conducting a temporal stability analysis to determine the practically reliable solution. The analysis reveals that the primary (upper) solution branch is stable while the other solution branch is unstable. It has been observed that the range of dual solutions and the magnitude of the critical point increase with the increasing value of the suction parameter. The increment of the thermal radiation parameter enhances fluid temperature in the upper solution branch, whereas temperature diminishes far away from the sheet in the lower solution branch.

Effects of higher order chemical reaction and slip conditions on mixed convection hybrid ferrofluid flow in a Darcy porous medium

Many researchers have been captivated by the ability of hybrid ferrofluid to increase heat and mass transmission, leading them to further examine the working fluid. This study is essential for figuring out how Fe3O4-CoFe2O4/H2O hybrid ferrofluid would behave thermally and massively when physical factors like a greater degree of chemical reaction (n) and slip boundary conditions are present through mixed convection stagnation point flow in Fe3O4-CoFe2O4/H2O hybrid ferrofluid toward a permeable vertical flat plate embedded in Darcy porous medium. The complexity of the partial differential equation for heat, flow, as well as mass transfer is reduce through similarity transformation into a system of ordianry differential equation, before being numerically solved using the built-in solver bvp4c in MATLAB for various values of the governing parameters. Dual solutions (first and second solution) are obtained as result produced in regions of opposing and assisting flow. Hybrid ferrofluids with additional CoFe2O4 nanoparticles have a higher heat transfer rate than ferrofluids and base fluid (water). Furthermore, a different order of chemical reaction greatly influences the mass transfer rate. Note that the presence of thermal and concentration slips reduce the heat transfer and mass transfer rate, accordingly, and delay the boundary layer separation.

Dual Solutions of Unsteady Mixed Convection Hybrid Nanofluid Flow Past a Vertical Riga Plate with Radiation Effect

A mathematical model for the unsteady, two-dimensional mixed convection stagnation point flow over a Riga plate is presented in this study. Convective boundary conditions, time-dependent derivatives, mixed convection, radiation effects, and the Grinberg term were all incorporated into the formulation of the governing equations and boundary conditions. By incorporating similarity transformations, ordinary differential (similarity) equations (ODEs) are derived from the partial differential equations (PDEs) of the flow model. The boundary value problem of the fourth-order accuracy code (bvp4c) was implemented in MATLAB (2017b, The MathWorks, Inc., Natick, MA. USA, 2017) to solve the mathematical model numerically. Due to the plate’s shrinking motion, two (dual) solutions are possible (first and second solutions). Based on the stability analysis, it was found that the first solution is stable and physically realizable in practice, while the second solution is not stable and not physically realizable in practice. It was found that the increase in the mixed convection parameter, modified Hartmann number, and unsteadiness parameter improved the hybrid nanofluid’s temperature profile. In addition, increasing the unsteadiness parameter decreased the velocity profile and the skin friction coefficient. Thus, the numerical results suggested that the augmentation of the modified Hartmann number, mixed convection parameter, and unsteadiness parameter can enhance the heat transfer performance in this flow model. This study offers valuable insight into fundamental transport phenomena such as the transmission of momentum, heat, or mass. Hence, it provides valuable information on the gradients of essential factors to control the boundary layer flow pattern.

MHD mixed convective stagnation point flow of nanofluid past a permeable stretching sheet with nanoparticles aggregation and thermal stratification

Using a thermally stratified water-based nanofluid and a permeable stretching sheet as a simulation environment, this research examines the impact of nanoparticle aggregation on MHD mixed convective stagnation point flow. Nanoparticle aggregation is studied using two modified models: the Krieger–Dougherty and the Maxwell–Bruggeman. The present problem's governing equations were transformed into a solvable mathematical model utilizing legitimate similarity transformations, and numerical solutions were then achieved using shooting with Runge–Kutta Fehlberg (RKF) technique in Mathematica. Equilibrium point flow toward permeable stretching surface is important for the extrusion process because it produces required heat and mass transfer patterns and identifies and clarifies fragmented flow phenomena using diagrams. Nanoparticle volume fraction was shown to have an impact on the solutions' existence range, as well. Alumina and copper nanofluids have better heat transfer properties than regular fluids. The skin friction coefficients and Nusselt number, velocity, temperature profiles for many values of the different parameters were obtained. In addition, the solutions were shown in graphs and tables, and they were explained in detail. A comparison of the current study's results with previous results for a specific instance is undertaken to verify the findings, and excellent agreement between them is observed.

Hybrid Nanofluid Radiative Mixed Convection Stagnation Point Flow Past a Vertical Flat Plate with Dufour and Soret Effects

The widespread application of hybrid nanofluid in real applications has been accompanied by a large increase in computational and experimental research. Due to the unique characteristics of hybrid nanofluid, this study aspires to examine the steady two-dimensional mixed convection stagnation point flow of a hybrid nanofluid past a vertical plate with radiation, Dufour, and Soret effects, numerically. The formulations of the specific flow model are presented in this study. The model of fluid flow that is expressed in the form of partial differential equations is simplified into ordinary differential equations via the transformation of similarity, and then solved numerically by using the boundary value problem solver known as bvp4c in MATLAB, which implements the finite difference scheme with the Lobatto IIIa formula. Two possible numerical solutions can be executed, but only the first solution is stable and meaningful from a physical perspective when being evaluated via a stability analysis. According to the findings, it is sufficient to prevent the boundary layer separation by using 2% copper nanoparticles and considering the lesser amount of Dufour and Soret effects. The heat transfer rate was effectively upgraded by minimizing the volume fraction of copper and diminishing the Dufour effect. Stronger mixed convection would lead to maximum skin friction, mass transfer, and heat transfer rates. This important preliminary research will give engineers and scientists the insight to properly control the flow of fluids in optimizing the related complicated systems.

Computational Assessment of Microrotation and Buoyancy Effects on the Stagnation Point Flow of Carreau-Yasuda Hybrid Nanofluid with Chemical Reaction Past a Convectively Heated Riga Plate.

The present framework deliberated the mixed convection stagnation point flow of a micropolar Carreau–Yasuda hybrid nanoliquid through the influence of the Darcy-Forchheimer parameter in porous media toward a convectively heated Riga plate. In this investigation, blood is used as a base liquid and gold (Au) and copper (Cu) are the nanoparticles. The main novelty of the present investigation is to discuss the transmission of heat through the application of thermal radiation, viscous dissipation, and the heat source/sink on the flow of a micropolar Carreau–Yasuda hybrid nanoliquid. Further, the results of the chemical reaction are utilized for the computation of mass transport. Brownian motion and thermophoretic phenomena are discussed in the current investigation. The current problem is evaluated by using the connective and partial slip conditions and is formulated on the basis of the higher-order nonlinear PDEs which are converted into highly nonlinear ODEs by exploiting the similarity replacement. In the methodology section, the homotopic analysis scheme is employed on these resulting ODEs for the analytical solution. In the discussion section, the results of the different flow parameters on the velocity, microrotation, energy, and mass of the hybrid nanofluid are computed against various flow parameters in a graphical form. Some of the main conclusions related to the present investigation are that the velocity profile is lowered but the temperature is augmented for both nanoparticles volume fractions. It is notable that the skin friction coefficient is reduced due to the higher values of the Darcy-Forchheimer parameter. Further, the rising performance of the hybrid nanofluid Nusselt number is determined by the radiation parameter.

Joule heating effect on radiating MHD mixed convection stagnation point flow along vertical stretching sheet embedded in a permeable medium and heat generation/absorption

AbstractThe goal of this study is to investigate magnetohydrodynamics varied convective stagnation point stream with a vertically extended sheet embedded in a permeable material. Warmth generation/absorption, radiation impacts, and viscous dissipation are all considered. Using the process of likeness change, the principal boundary layer equations are written and turned into nonlinear ordinary joined differential equations, and the numerical result is produced using the Runge–Kutta fourth‐order approach via shooting technique. Varied physical limits have different effects, such as velocity fraction restriction, mixed convection restriction, Hartmann numeral, Prandtl numeral, permeability restriction, warm air radiation restriction, hotness generation/absorption restriction, and so on, over velocity and temperature scatterings are introduced graphically and then mathematically. The skin friction constant, in addition to Nusselt numerals, over the sheet is determined, expressed mathematically as well as introduced through tables. Fluid velocity and temperature increase with radiation restriction Ra. Skin friction and Nusselt numeral are increasing functions of Hartmann numeral Ha, and decreasing ones of permeability restriction K.

Unsteady mixed convective stagnation point flow of hybrid nanofluid in porous medium

Unsteady mixed convective stagnation point flow of hybrid nanofluid in porous medium