Nonlinear Convection Parameter Research Articles

Lie group analysis and SQLM of entropy generation of MHD nonlinear radiative micropolar nanofluid flow with thermophoresis and Brownian motion

This study investigates the entropy generation in hydromagnetic mixed convection of a micropolar fluid flowing over a stretchable sheet, taking into account various influential factors such as nonlinear thermal radiation, Ohmic dissipation, uniform heat source/sink effects, chemical reaction, thermophoresis, and Brownian motion. The Spectral Quasilinearization Method (SQLM) is employed, which transforms nonlinear equations into a series of linearized ones, streamlining the solving process. Additionally, Lie group analysis is utilized to identify symmetries and derive similarity transformations crucial for converting partial differential equations into coupled ordinary differential equations, which are then solved numerically. A comprehensive sensitivity analysis is conducted on critical parameters, including the Darcy parameter, Biot number, Brinkman number, nonlinear convection parameter, and chemical reaction parameter. This analysis explores the impacts of these parameters on various flow profiles, such as velocity, temperature, microrotation, concentration, and entropy generation, enriching the depth and practical relevance of the findings. The results reveal that increasing the Brinkman and Reynolds numbers enhances entropy generation profiles while increasing the coupling parameter reduces them. The focus on entropy generation analysis provides valuable insights into energy utilization and system efficiency, particularly in micropolar fluid dynamics. Furthermore, the study underscores the practical implications of its findings by highlighting their relevance in evaluating the effectiveness of industrial processes, especially those related to energy conversion and heat transfer phenomena.

Overlapping Grid-Based Spectral Collocation Technique for Bioconvective Flow of MHD Williamson Nanofluid over a Radiative Circular Cylindrical Body with Activation Energy

The amalgamation of motile microbes in nanofluid (NF) is important in upsurging the thermal conductivity of various systems, including micro-fluid devices, chip-shaped micro-devices, and enzyme biosensors. The current scrutiny focuses on the bioconvective flow of magneto-Williamson NFs containing motile microbes through a horizontal circular cylinder placed in a porous medium with nonlinear mixed convection and thermal radiation, heat sink/source, variable fluid properties, activation energy with chemical and microbial reactions, and Brownian motion for both nanoparticles and microbes. The flow analysis has also been considered subject to velocity slips, suction/injection, and heat convective and zero mass flux constraints at the boundary. The governing equations have been converted to a non-dimensional form using similarity variables, and the overlapping grid-based spectral collocation technique has been executed to procure solutions numerically. The graphical interpretation of various pertinent variables in the flow profiles and physical quantities of engineering attentiveness is provided and discussed. The results reveal that NF flow is accelerated by nonlinear thermal convection, velocity slip, magnetic fields, and variable viscosity parameters but decelerated by the Williamson fluid and suction parameters. The inclusion of nonlinear thermal radiation and variable thermal conductivity helps to enhance the fluid temperature and heat transfer rate. The concentration of both nanoparticles and motile microbes is promoted by the incorporation of activation energy in the flow system. The contribution of microbial Brownian motion along with microbial reactions on flow quantities justifies the importance of these features in the dynamics of motile microbes.

Combined Effect of Non-Linear Mixed Convection, and Non-Uniform Heat Source/Sink on Casson Ternary Hybrid Nanofluid Flow Across a Stretched Rotatory Disk

This present study emphasizes the importance of a specific type of fluid called a Casson ternary hybrid nanofluid. Our research explores a novel approach using the combination of several complex phenomena, including magnetohydrodynamic radiative flow, non-linear mixed convection, a non-uniform heat source or sink, a chemical reaction described by the Arrhenius model, and multiple slip effects. The researchers transformed the system of governing equations into a set of first-order ordinary differential equations using appropriate mathematical transformations and then solved them numerically using the bvp4c solver. The study investigated the behavior of velocity profiles, thermal dispersion, concentration dispersion, and heat and mass transfer for different values of the parameters involved. Our results indicated that the rising values of the heat transmission rate escalated by 2.98% for Casson ternary hybrid nanofluid when compared to ternary hybrid nanofluid. Further, ternary hybrid nanofluid had a 7.49% and 6.89% higher heat transmission rate compared to the hybrid nanofluid and conventional nanofluid, respectively. Besides, the heat transmission rate is enhanced by 17.5% and 3.11% respectively under the existence of the mixed convective and non-linear thermal convection parameters. Also, the presence of chemical reaction parameter shows a positive impact on the rate of mass transmission

Nonlinear Convection Flow of a Micropolar Nanofluid Past a Stretching Sphere with Convective Heat Transfer

An incompressible, steady combined nonlinear convective transport system on a micropolar nanofluid through a stretching sphere with convective heat transfer was investigated. The conservation equations corresponding to momentum, microrotation, thermal energy, and concentration particles have been formulated with suitable boundary constraints. By using the required non-dimensional variables, the conservation equations have been turned into a set of high-order standard differential equations. Then, an implicit finite difference method, also known as the Keller-Box Method (KBM), was used to numerically solve the flow problem. The obtained outcomes are displayed through graphs and tables to explain the impact of various governing variables over velocity, temperature, concentration, number of skin friction, wall coupled stress, Nusselt number, and Sherwood number. The findings demonstrate that increasing the convective heat parameter Bi enhances the factor of skin friction, local Nusselt number, Sherwood number, velocity field, and temperature profile while lowering the wall-coupled stress. It is observed that for high values of the material parameter β, the fluid velocity and the spin of the micro-elements both increase, which causes the dynamic viscosity and microrotation velocity to decrease. In addition, as the rates of magnetic constant Ma, thermophoresis Nt and Brownian movement Nb rise, the thermal distribution and its thickness of boundary layer increase. However, it decline along the enlarging quantities of nonlinear convection parameter λ, Prandtl number Pr, material parameter β, and solutal Grashof number Gm, which agrees to increase fluid density. When the range of thermophoresis Nt surges, it causes an increment in the nanoparticle species, but the opposite behavior have seen in the case of Brownian number Nb, and Lewis number Le. The comparison made with the related published paper achieves a significant agreement. The numerical result is generated through the implementation of the computational software MATLAB R2023a.

Soret and dufour effects on unsteady non-linear mixed convection flow past a stretching sheet influenced by non-linear thermal radiation

This article presents a novel mathematical model to analyze the behavior of a time-dependent, incompressible, non-linear (quadratic) mixed convection flow across a stretching surface heated by convection. The model takes into account the influence of non-linear thermal radiation, along with the Soret and Dufour effects. The equations governing the flow characteristics in the boundary layer approximation are derived and transformed into ordinary differential equations (ODEs) using similarity variables. The second-order ODEs are transformed into an initial value problem, which is then numerically solved using the bvp4c solver in MATLAB. The novel findings of the study have been presented using graphs and tables. The intensification of non-linear convection parameters has been shown to lead to the development of velocity near the sheet while simultaneously reducing velocity toward the free stream. The non-linear convection parameters reduce the temperature distribution, while the temperature ratio and the non-linear thermal radiation parameters enhance it. The non-linear convection parameters ( 0.5 ≤ α 1 , α 2 ≤ 2.0 ) , temperature ratio ( 1.2 ≤ θ w ≤ 1.5 ) , and non-linear thermal radiation ( 1.0 ≤ Rd ≤ 1.5 ) , parameters are influential factors in decreasing the surface drag force (by about 15.4%, 28.5%, 4.4%, and 4.3%) and increasing the cooling rate (by about 0.4%, 0.5%, 19.5%, and 23%), respectively. The Biot ( 0.5 ≤ Bi ≤ 1.0 ) number is also found to significantly contribute toward enhancing the cooling rate of the system by about 51.6%.

Analysis of heat and mass transfer of a non-linear convective heat generating fluid flow in a porous medium with variable viscosity

The present study addresses the significance of analyzing the heat and mass transfer characteristics of a non-linear convective fluid flow featuring variable viscosity within a porous medium. Our focus lies on understanding the impact of varying viscosity on the hydromagnetic coupling stress, particularly in the presence of internal heat generation. The fluid is confined within a porous medium, and convection cooling takes place at both wall of the fluid. A key assumption in our investigation is the nonlinearity nature of the buoyancy force, specifically when there is a substantial difference in temperature and concentration within the fluid and its surroundings, the buoyancy force becomes quadratic. The exploration of couple stress fluids, alongside considerations of temperature-dependent internal heat generation and mass transfer, contributes to advancing our understanding of thermal system performance. By accounting for nonlinearity in density, temperature, and concentration, the research aims to provide more accurate results than previous linear models, crucial for optimizing energy consumption in practical applications such as nuclear reactors and heat exchangers. Dealing with this type of problem often pose significant challenges, as they often lack analytical solutions, necessitating the use of more advanced numerical methods or approximation techniques. We employ Spectral Quasilinearisation Method (SQLM) to solve the coupled non-linear boundary value problems (PDE) arising from the model, momentum equation, energy equation, concentration equation, and entropy generation. The obtained results are then validated using the Runge–Kutta method and a good agreement is achieved. The findings for the dimensionless velocity, temperature, mass concentration and entropy generation are presented in graphics and in table manner, and effects of controlling parameters are extensively explained. The results highlight that an increase in variable viscosity leads to an enhancement in the velocity profile, while simultaneously reducing the temperature in the system. Furthermore, increments in the non-linear convection parameter and coupling stress parameter result in an appreciation of the velocity profile, temperature profile, and entropy generation rate.

Computational analysis of magnetized Casson liquid stretching flow adjacent to a porous medium with Joule heating, stratification, multiple slip and chemical reaction aspects

This article aims to investigate the characteristics of thermo-solutal magnetohydrodynamic (MHD) non-Newtonian smart coating boundary layer flow of a stretching substrate adjacent to a porous medium, considering the influence of chemical reactions and thermal radiation subject to a transverse static magnetic field. A non-Darcy drag force model is deployed to capture both Darcy bulk drag and inertial Forchheimer (quadratic) drag effects. A diffusion flux model is deployed for radiative heat transfer. The Casson viscoplastic model has been utilized to simulate rheological characteristics. Due to polymeric slip effects, three slip phenomena are included at the wall (hydrodynamic, thermal and concentration) in the formulation. Furthermore, viscous dissipation and Ohmic heating (Joule dissipation) are also included. Robust scaling similarity variables are deployed to transform the governing partial differential equations into ordinary differential equations. Subsequently, the emerging dimensionless coupled nonlinear boundary value problem is solved utilizing the Bvp4c method in MATLAB version 2022. This numerical approach allows for a logical parametric examination of all key control parameters on the transport phenomena, enabling a comprehensive understanding of the system behavior. Validation with previous studies is included. Detailed graphical and tabular computations are included for velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number, for the influence of Darcian parameter, Forchheimer inertial parameter, mixed convection, velocity (momentum) slip, magnetic number, Casson parameter, nonlinear thermal convection parameter, nonlinear concentration convection parameter, radiation parameter, thermal stratification parameter, Prandtl number, heat source/sink parameter, Eckert number, thermal slip parameter, Schmidt number, chemical reaction, solutal stratification parameter and solutal slip parameter. Detailed interpretation of the physics associated with these multiple effects is included. The simulations provide further insight into the transport characteristics of electromagnetic viscoplastic coating material manufacturing.

Numerical approach for the modified heat transport process under improved Darcian and nonlinear mixed convective effects

Analysis regarding heat transport subjected to non-Darcian media has increased in science and technological utilization. Typical applications comprise grain storage, nuclear waste discarding, production of crude oil, pollution in groundwater, porous insulation, and several others. This motivates us to demonstrate the heat transport phenomenon in the viscous fluid's flow deformed by a linearly stretchable surface submerged in Darcy-Forchheimer porous medium. Properties of heat transfer are elaborated with nonlinear mixed convection and Cattaneo-Christov heat model. Slip phenomenon is implemented at the wall surface. The governing equations are achieved in dimensionless form through appropriate transformations. Numerical solutions are constructed through shooting scheme along with 4–5 order Runge-Kutta Fehlberg technique. Graphical behaviors of velocity field and liquid temperature are constructed through various physical parameters. Results witnessed that decrement occurs in velocity field for dominant behavior of velocity slip parameter while it enhances for dominant nonlinear mixed convection parameter.

Significance of heat transfer rate in water-based nanoparticles with magnetic and shape factors effects: Tiwari and Das model

Nanofluids are implementable in a variety of applications, such as heat exchangers, the healthcare sector, the cooling of various devices, hybrid-powered machines, microelectronics, power plants, chemical processes, astronomical technology, cancer treatment, etc. Nanofluids also have enhanced heat transmission and thermal efficiency. The heat radiation of nanoparticles and the natural-convective flow of electrically conducting nanofluids over the rotating disk using Darcy Forchheimer’s porous media, thermal radiation is investigated in this paper. The nanoparticles titanium dioxide and single-walled carbon nanotubes are taken into account with base fluid water. The main goal of this investigation is to enhance heat transfer in nanofluids. The mathematical solution for the model has been obtained through the utilization of cylindrical coordinates. The flow model, which forms the basis of the investigation, is constructed around partial differential equations (PDEs). To address the inherent nonlinearity of these PDEs, physical similarities are employed to transform them into ordinary differential equations (ODEs). Subsequently, the fourth-order Runge–Kutta technique is employed via Matlab to solve these ODEs. The graphical examination of the velocities and temperature with various parameters is an exquisite display of scientific artistry. The magnetic field component is anticipated to exhibit an inverse correlation with velocities, while the temperature profile is expected to surge with the rise of the nonlinear mixed convection parameter. Additionally, the skin friction and Nusselt number are meticulously computed and presented in a tabular format, adding a touch of elegance to the already breathtaking analysis. By boosting the radiation parameter, the Nusselt value declined. Moreover, it is observed that the nanofluids having a laminar nanoparticle shape have a greater heat transfer rate.

Numerical Analysis of unsteady Non-linear mixed convection flow of Reiner-Philippoff nanofluid along Falkner-Skan wedge with new mass flux condition

The main goal of this research focuses on the theoretical examination of the melting and nonlinear mixed convection mechanisms in unsteady Falkner-Skan wedge flow of Reiner-Philippoff nanofluid with nonlinear thermally radiative, nanoparticle mass flux condition, uniform heat source/sink, chemically reactive, and Arrhenius activation energy effects are considered. The nanoparticle concept includes thermophoretic and Brownian motion. Arrhenius activation energy idea is adopted in the concentricity equation. Appropriate transformations are employed to obtain non-linear ordinary differential equations. The outcoming non-linear (ODEs) are then computationally implemented through R-K 4th order approach based on shooting method. We investigate and discuss the impacts of various physical parameters on thermal, velocity, solutal, skin friction, heat transport, and streamlines field. A comparative examination is presented between the present findings and available date and displayed to be in excellent agreement. Velocity field diminished against escalating valuations of concentration buoyancy and wedge angle parameters, respectively. Concentricity field has opposite trend for augmenting thermophoretic and non-linear solutal convection parameters, respectively.

Numerical study of unsteady nonlinear convective flow of a nanofluid over a vertical plate with variable fluid properties

This study examines heat transfer in a two-dimensional flow of nano liquid ( Cu − H 2 O ) over a linearly elongated sheet under magnetic field with temperature-dependent thermophysical properties. A numerical investigation using the Homotopy perturbation technique is carried out to analyse the heat transfer in the flow by considering the quadratic form of Boussinesq approximation, and thermal radiation. The importance of the parameters affecting the momentum and thermal characteristics of the flow is analysed through 2D plots, streamlines, and surface plots. Further, a regression model for the Nusselt number and friction factor is constructed to check the statistical significance of the parameters involved in the model. The findings indicate a smooth transition from the initial unsteady state to the final steady state. Moreover, the quadratic or non-linear convection parameter, heat source/sink parameter, improves the rate of heat transfer and magnetic parameter, and the angle of inclination diminishes the friction factor.

Insight into the relationship between non-linear mixed convection and thermal radiation: The case of Newtonian fluid flow due to non-linear stretching

The current research focuses the light on the characterization of buoyancy-driven non-linear mixed convection and non-linear radiation in a Newtonian flow over a non-linearly stretching vertical sheet, and this type of flow has useful applications in many industrial processes, such as the paper and pulp industry, polymer industry, electronic device cooling, solar collectors, gas turbine plants, and nuclear power. Using appropriate transformations, governing PDEs for non-linear mixed convection are reduced to higher-order non-linear ODEs and those are numerically solved. Along with tabular presentations of computed results, the graphical representations are generated to elucidate the effects of involved parameters on convection transport properties and their inter-relations. It demonstrates that flow velocity increases near the surface and decreases away from the surface as the non-linear convection parameter increases. Furthermore, increments in the thermal buoyancy, temperature ratio and non-linear radiation parameters result in the boost of velocity. The temperature decreases as linear and non-linear buoyancy-related parameters (non-linear convection and thermal buoyancy parameters) are of higher levels. In contrast, the temperature rises with two non-linear thermal radiation-related parameters (thermal ratio and non-linear radiation parameters). For greater values of the non-linear stretching related parameter, a lower velocity and a higher temperature are witnessed. The non-linear convection, thermal buoyancy, thermal ratio and non-linear radiation parameters contribute toward the reduction of the magnitude of surface-drag force and growth of the surface cooling rate. But, with the non-linearity in surface stretching there are significant percentage hikes of surface-drag force magnitude and surface cooling rate.

Analysis of periodic magnetohydrodynamics effects on triple diffusive nonlinear mixed convective flow of Eyring–Powell nanoliquid

AbstractThe article spotlights aspects of the triply diffusive mixed convective flow of Eyring–Powell nanoliquid over a vertical plate. A periodic magnetic field with nonlinear convection is exhibited. The governing partial differential equations (PDEs) with boundary restrictions are the case paradigm transformed into a non‐dimensional system by feasible non‐similar transformations. The quasilinearization technique combined with an implicit finite difference scheme is used for numerical simulation, resulting in a block‐tridiagonal matrix form. Furthermore, a system of algebraic linear equations has been solved through Varga's algorithm. The numerical outcomes are correlated with various physical parameters graphically. The variations in the nonlinear mixed convection parameter and Powell–Eyring liquid parameter raise the skin friction coefficient more than a Newtonian fluid. In a periodic magnetic field, the fluid temperature rises and drops in the corresponding energy transfer rate. Also, wavy variations have been observed because of oscillatory magnetic fields. The current study can find its potential applications in medical, engineering and industrial developments, including polymer sheet manufacture, medicine cover coating, fibre production, crystal growth, heat exchangers and metal extrusion.

THERMAL CHARACTERISTICS OF NONLINEAR CONVECTION AND RADIATION FOR THE FLOW OF TRI-HYBRID NANOFLUIDS OVER STRETCHABLE SURFACE WITH ENERGY SOURCE

In this paper, an innovative form of nanofluids is identified as tri-hybrid nanofluid, which is synthesized by dispersing three or more varieties of nanomaterials in the considered base fluid. So, in this study, we comparatively examined SiO2/H2O nanofluid, TiO2+Al2O3/H2O hybrid nanofluid and SiO[Formula: see text]TiO2+Al2O3/H2O ternary hybrid nanofluid. Stretching of the flat surface enables us to develop the nanofluids flow. Additional considerations include the impacts of MHD, viscid dissipation, nonlinear thermal convection and radiation, joule heating and the presence of a heat source. For transforming PDEs (continuity, motion, heat equation and boundary constraints) into ODEs, an appropriate transformation procedure is used. HAM technique is used to solve these nonlinear coupled ODEs. Graphs are used to evaluate and examine the effect of numerous describing variables on nano, hybrid and tri-hybrid nanofluids speed and heat distribution. Furthermore, the computed values of engineering-relevant parameters ([Formula: see text] and Nu) are tabulated and analyzed. The velocity of nanofluids acquires enhancing tendency for nonlinear thermal and mix convection parameter, but reverse upshot is assured due to nanoparticle volume fraction, Weissenberg number and magnetic parameters. Thermal field gets intensified in nature for magnetic and Eckert number, heat generation, thermal radiation and nanoparticles volume fractions. The ternary hybrid nanofluid has the most efficient behavior according to the comparative examination of ternary, hybrid and nanofluids.

Radiative couple stress Casson hybrid nanofluid flow over an inclined stretching surface due to nonlinear convection and slip boundaries

The study of fluid dynamics due to the stretching surface is one of the most eminent topics due to its potential industrial applications viz. drawing wire and plastic films, metal and polymer extrusion, fiber and glass production. In the present article, the author is going to study the effects of hybrid nanofluids flow on an inclined plate including CuO (Copper Oxide), and Cu (Copper). The Casson fluid with a couple-stress term has been used in the flow analysis. The surface of the plate is considered slippery. The convection has been taken nonlinear with thermal radiation. The governing equation of the flow of hybrid nanofluids with energy equation has been transformed into highly nonlinear ODEs through similarity transformation. The proposed model has been solved through a numerical RK-4 method. Significant variables of the physical process such as solar radiation, nonlinear convection parameters, heat transfer rates, and their effect on the solar power plant have been noticed.

Modeling and analytical analysis of dual diffusive Williamson nanoliquid considering generalized heat-mass concepts

The primary objective of this investigation is to explore the Cattaneo–Christov flux models impact on Williamson nanofluid over a stretching surface. Buongiorno’s model featuring diffusions (Brownian and thermophoretic) is opted for nonlinear analysis. Buoyancy-driven nonlinear convection flow in stagnation region is modeled. Surface is permeable and transpiration effects are considered. Energy expression captures heat source/sink aspects. The nondimensional differential systems are tackled analytically via homotopy analysis method (HAM). The profiles of dimensionless temperature, concentration and skin friction are examined graphically for the attributes of multiple physical parameters. It is revealed that the heat transfer elevates with the increment of thermophoresis, heat source and Brownian motion parameters while it dwindles with the improvement of thermal relaxation parameter. The mass transfer strengthens with the enlargement of thermophoresis parameter while diminishing with the enhancement of solutal relaxation and Brownian motion parameters. The skin friction is elevated for higher values of material variable against nonlinear mixed convection parameter.

The unsteady nonlinear convective flow of a nanofluid due to impulsive motion: Triple diffusion and magnetic effects

• The unsteady nonlinear convection due to impulsive motion is investigated. • Governing equations have been transformed using Mangler's transformations. • Quasi-linearization technique is utilized for solution of the problem. • The surface drag coefficient increases with magnetic parameter. • Heat transport rate rises only when the Eckert number is positive. By a semi-similar approach, the paper aims to study the unsteady nonlinear convection due to impulsive motion with triple diffusion and magnetic effects. Since the mainstream has been set into impulsive motion, the fluid motion is unsteady. Simultaneously, the temperature of the surface is abruptly changed from its ambient fluid temperature. The influence of chemical reactions and convective boundary constraints are also considered in this investigation. The nonlinear coupled partial differential equations (PDEs) with appropriate boundary conditions that govern the given problem are transformed into dimensionless equations by using Mangler's transformations. For mathematical computations, the technique of Quasi-linearization and second order implicit finite difference method are utilized, and so obtained results are semi-similar solutions that are discussed with the aid of graphs. The results reveal that for the case of aiding buoyancy, the surface drag coefficient increases about 5% when the nonlinear convection parameter increases from 0 to 3 and about 61% when the magnetic parameter increases from 0 to 0.5. The heat transfer rate enhances about 65% for variation of the magnetic parameter from 0 to 0.3 for a positive Eckert number. The mass transfer rate is pronounced more for linear chemical reaction than the nonlinear chemical reaction for the constructive chemical reaction parameter. It is found at about 7% for Schmidt number 240. The current findings are compared to previously reported literature and are found to be in good agreement.

Spectral relaxation computation of Maxwell fluid flow from a stretching surface with quadratic convection and non-Fourier heat flux using Lie symmetry transformations

A mathematical model for nonlinear quadratic convection with non-Fourier heat flux in coating boundary layer flow of a Maxwell viscoelastic fluid is presented. Nonlinear quadratic thermal radiation and heat source/ sink effects are also considered. The transformations of Lie symmetry are employed. The resultant nonlinear differential equations with defined boundary conditions are numerically solved using the spectral relaxation technique (SRM), a robust computational methodology. Graphical visualization of the velocity and temperature profiles is included for a range of different emerging parameters. For skin friction and the Nusselt number, numerical data are also provided. There is a very strong correlation between the outcomes of this study and those published in the literature. Higher values of the nonlinear thermal radiation, mixed convection, thermal conductivity, nonlinear convection and heat source/ generation parameters increase temperature as well as the thickness of the thermal boundary layer. However, a higher Prandtl number, thermal relaxation parameter and heat sink/ absorption parameter all reduce temperature. Deborah number causes velocity to be raised (and momentum boundary layer thickness to be lowered), whereas raising nonlinear mixed convection parameter causes velocity to be decreased (and momentum boundary layer thickness to be increased), and a velocity overshoot is calculated. The models are applicable to simulations of high-temperature polymeric coatings in material processing.

The modified finite element method for heat and mass transfer of unsteady reacting flow with mixed convection

This study reveals the extension of a mathematical model of heat and mass transfer of fluid flow over a sheet by incorporating the effect of non-linear mixed convection. The governing equations of flow phenomena are expressed as partial differential equations (PDEs). Similarity transformations are employed to get a dimensionless set of boundary value problems. Most of the existing relevant literature employed some solver to solve a set of differential equations, but this study implements the finite element method to tackle the boundary value problems. The employed finite element method is based on the Galerkin approach. For verifications of the obtained results, a set of linear and non-linear boundary value problems is also solved with Matlab solverbvp4c. The results are displayed in graphs by varying Grashof number, modified (solutal) Grashof number, non-linear convection parameters in heat and mass transfer, radiation parameter, Prandtl number, Schmidt number, and reaction rate parameter. Also, numerical values for the friction at the wall and local Nusselt and Sherwood numbers are given in tables. The problem in PDEs form is also solved with software that implements the finite element method to solve problems. The simulations are also provided, which is the outcome of the software. It is shown that the velocity profile escalates by growing values of thermal and solutal Grashof numbers. Problem-solving techniques from this study may be used in future research to address other unsolved heat transfer fluid physics issues.

Electroosmosis-Optimized Thermal Model for Peristaltic Transportation of Thermally Radiative Magnetized Liquid with Nonlinear Convection.

The present study addresses the heat transfer efficiency and entropy production of electrically conducting kerosene-based liquid led by the combined impact of electroosmosis and peristalsis mechanisms. Effects of nonlinear mixed convection heat transfer, temperature-dependent viscosity, radiative heat flux, electric and magnetic fields, porous medium, heat sink/source, viscous dissipation, and Joule heating are presented. The Debye–Huckel linearization approximation is employed in the electrohydrodynamic problem. Mathematical modeling is conducted within the limitations of δ << 1 and Re → 0. Coupled differential equations after implementing a lubrication approach are numerically solved. The essential characteristics of the production of entropy, the factors influencing it, and the characteristics of heat and fluid in relation to various physical parameters are graphically evaluated by assigning them a growing list of numeric values. This analysis reveals that heat transfer enhances by enhancing nonlinear convection and Joule heating parameters. The irreversibility analysis ensures that the minimization of entropy generation is observed when the parameters of viscosity and radiation are held under control. Fluid velocity can be regulated by adjusting the Helmholtz–Smoluchowski velocity and magnetic field strength.