Spectral Quasi-linearization Method Research Articles

Entropy generation and activation energy on nonlinearly thermo-radiative and magnetohydrodynamic heat transfer of Jeffrey nanofluid with non-uniform heat source/sink using SQLM

ABSTRACT Entropy generation and activation energy analysis on MHD heat and mass transfer of Jeffrey nanofluid under the impact of nonlinear thermal radiation and heat source/sink (non-uniform) over a linearly stretching sheet has been investigated numerically using Spectral Quasilinearization Method (SQLM). The Brownian motion with thermophoretic effects has been utilized. The basic equations concerned with the problem are solved numerically. The impacts of different governing physical parameters are analyzed on the velocity, temperature, and concentration fields, along with entropy generation, and Bejan number profiles are analyzed graphically. It is found that the concentration profiles have a mixed tendency with magnetic parameters. In addition, the temperature profiles increase in the presence of Brownian motion with thermophoresis effects, whereas the composite behavior is noticed on the entropy generation profiles. It is also found that both the temperature and concentration profiles diminish for various values of Deborah number while the velocity profile increases. Also, it is noticed that both the temperature profiles increase for enhanced values of the space-dependent and time-dependent parameters. Due to activation energy, the Bejan number profiles decrease, whereas the entropy generation profiles increase far away from the expandable sheet but decrease closer to the sheet.

Thermohydrodynamics of Bödewadt hybrid-nanofluid flow in a horizontal magnetic field

Since disks, rotating or stationary, are integral in many thermal systems, such as rotating heat exchangers, thermoelectric coolers, solar energy systems, and geothermal plants, this study scrutinizes the thermohydrodynamics of rotating hybrid nanofluid flow over a stretchable disk at rest. Further, the shape of the nanoparticles and the choice of base fluid substantially impact the enhancement of the heat transfer rate in various such thermal systems. Therefore, the present investigation considers engineered colloids made of four distinct (sphere, cylinder, column, lamina) titania and copper nanoparticle shapes in two different base fluids: water and engine-oil. The problem is formulated mathematically in an externally applied horizontal magnetic field and incorporating a non-Fourier heat flux model in the presence of solar radiation. Analogous to the case of the conventional vertical magnetic field, a similarity solution is also possible when magnetic forces act horizontally, both towards and opposite to the direction of rotation. Thus, the governing partial differential equations (PDEs) are first reduced to a set of highly non-linear and coupled ordinary differential equations (ODEs) via similarity transformations. These resulting set of ODEs are then solved numerically using a rapid and efficient spectral quasilinearization method (SQLM). Obtained results show that lamina-shaped TiO2−Cu/ engine-oil hybrid-nanofluid is a better choice than the other shapes of nanoparticle suspension in water. The horizontally applied magnetic field exhibits a stronger influence on the flow and heat transfer characteristics when compared to a vertical magnetic field. Additionally increasing the thermal relaxation parameter αt from 0.1 to 0.35, the Nusselt number boost by 24.44%, 23.41%, 22.54%, and 17.93% for sphere, cylinder, column, and lamina nanoparticles of TiO2−Cu/water hybrid nanofluid. In the case of TiO2−Cu/engine-oil hybrid-nanofluid augmenting αt from 0.1 to 0.35, the Nusselt number rise by 23.95%, 22.83%, 21.82%, and 15.89% for sphere, cylinder, column, and lamina nanoparticles. Based on their increasing NS and Be values, the various shapes follow the sequence: lamina ¡ column ¡ cylinder ¡ sphere. Furthermore, entropy generation can be optimized through the augmentation of solar radiation factors QSR, δ, along with the reduction of the magnetic interaction parameter M, and by a proper selection of nanoparticle’s shape. Interestingly, dual solutions are observed for the case of a shrinking disk, i.e., for S<0, and a linear temporal stability analysis reveals that only one of these two branches, namely the first solution branch, is stable and the second branch unstable.

Influence of magnetic field-dependent viscosity on Casson-based nanofluid boundary layers: A comprehensive analysis using Lie group and spectral quasi-linearization method

This study examines the effects of magnetic-field-dependent (MFD) viscosity on the boundary layer flow of a non-Newtonian sodium alginate-based Fe3O4 nanofluid over an impermeable stretching surface. The non-Newtonian Casson and homogeneous nanofluid models are utilized to derive the governing flow and heat transfer equations. Applying Lie group transformations to dimensional partial differential equations yields nondimensional ordinary differential equations, which are then numerically solved using the spectral quasi-linearization technique. The analysis primarily focuses on the impacts of the MFD viscosity parameter, nanoparticle volume fraction of Fe3O4, and magnetic parameters on the flow and heat transfer characteristics. The local skin friction and heat transfer rate behaviors influenced by viscosity changes due to the magnetic field are discussed. It is found that MFD viscosity significantly impacts flow and thermal energies, enhancing skin friction coefficients and reducing Nusselt numbers in the boundary layer region.

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.

Effect of Hall current, Soret number, and inclined magnetic field on entropy generation of mixed convection Jeffrey fluid flow through sloping channel under Navier‐slip condition

AbstractIn this research article, the irreversibility of Jeffery fluid in mixed convective flow with inclined channel under the influence of Navier‐slip condition is analyzed. The effects of Hall current, Soret number, and an inclined magnetic field are taken into account. The spectral quasi‐linearization method (SQLM) is used to solve the governing equations after transforming them into a dimensionless form. The impacts of various parameters on velocity, temperature, and concentration are examined graphically. With the use of tabular data, variations in skin friction, the Nusselt number, and the Sherwood number are also discussed. Our findings indicate that entropy production increases with higher values of the magnetic parameter, Hall current, and inclination angle. Conversely, we have observed an opposing trend with an increased value of slip condition at the left plate and the Jeffrey fluid parameter.

The Impact of Thermal Radiation on Mixed Convective Unsteady Nanofluid Flow in a Revolving Vertical Cone

This study investigates the effects of an unsteady mixed convection nanofluid flow in a rotating vertical cone submerged in spinning nanofluid. Our analysis considered the impacts of heat flux, chemical reactions, and thermal radiation, with the thermal and concentration Biot numbers serving as constraints at the boundary. The governing unsteady and coupled partial differential equations were solved through appropriate similarity transformations, addressing the nonlinear terms inherent in these equations. The spectral quasi-linearisation method (SQLM) was employed to solve the higher-order nonlinear differential equations. This study elucidates and assesses the impact of diverse physical constraints and parameters through the use of graphical representations. Notably, the temperature distribution of the liquefied substance was intensified as the thermal and solutal Biot numbers increased.

Irreversibility mixed convection Jeffrey fluid flow analysis in a vertical channel with an inclined magnetic field and Soret effects under slip conditions

Jeffrey fluid flow is found to have extensive applications in many fields of engineering. There are numerous applications of Jeffrey fluid in polymer industries and industrial fluids such as paints, paper, toothpaste, ketchup, etc. The present work explains the irreversibility of Jeffrey fluid in mixed convection Navier–slip flow through a vertical channel having an inclined magnetic field. The model equations of linear momentum, energy, and concentration are formulated and numerically solved using the spectral quasi-linearization method. The outcomes are depicted graphically and quantitatively discussed for active parameters that appeared in mathematical formulations. Moreover, flow and cross-flow velocity increase with an enhancement in Soret number and magnetic parameter, whereas heat transfer rate decreases with these parameters. Temperature, cross-flow velocity, and heat transfer decrease as the inclination angle increases. Flow velocity, concentration, and mass transfer rise as the inclination angle rises. The results demonstrate that as the magnetic parameter, hall parameter, angle of inclination, and slip condition at the right plate increase, the entropy generation number also increases. Conversely, it decreases as the slip condition at the left plate and Jeffrey fluid parameter increase.

Computational investigation for silica-molybdenum disulfide/water-based hybrid nanofluid over an exponential stretching sheet with spectral quasi-linearization method

The current research is focused on analyzing gyrotactic microorganisms within a hybridized nanofluid (NF) model by considering magnetohydrodynamics, electroosmosis, and radiation effects. Demarcated flow is mathematically modeled to yield coupled nonlinear partial differential equations, which are consequently transmuted into ordinary differential equations (ODEs) by adopting similarity transformations. The spectral quasilinearization method is used to generate the solutions of the transformed ODEs via MATLAB. The influence of various flow parameters on both mono NF and hybrid NF phases for velocity, thermal, concentration, and density of motile microorganism is depicted using graphs. The convergence and residual errors are demonstrated in tables for various influenced parameters on hybrid NF. Additionally, interested physical quantities like shear stress and rate of thermal diffusion at the wall have been tabulated by varying the controlling parameters. It is concluded from the current analysis that the higher velocities and temperatures are observed in hybrid NF model as compared with the mono NF model. Biot number and Hartmann number enhance the temperature profile. The velocity is an enhancing function of mixed convection parameter and bioconvection Rayleigh constant. NF flow over a stretching sheet finds applications in enhancing heat transfer for efficient cooling systems, such as electronics and solar collectors, as well as improving drug delivery in biomedicine, nanoparticle synthesis, and chemical processes.

Prediction model based on artificial neural network and bivariate spectral quasi-linearization method for compressible turbulent boundary-layer flow over a smooth flat surface

The compressible two-dimensional turbulent flow solutions at an arbitrary point in time and space by incorporating the mass, momentum, and energy conservation equations over a smooth flat surface and parallel free stream with unfavorable pressure gradient are studied. The Falkner–Skan transformation is applied to the turbulent boundary-layer equations and related boundary conditions, and the resulting nonlinear coupled system of partial differential equations is solved by the bivariate spectral quasi-linearization method. Moreover, to predict the thermal distribution of the flow, an artificial neural network model has been developed with the Nusselt number as target values. Several plots have been depicted, it is evaluated that the mean squared error value is 6.41 × 10−7, the overall coefficient of determination (R) is 0.997 52, and the average error rate is 0.68% for the said model, indicating the attainment of high accuracy for estimation.

Effect of viscous dissipation due to magnetohydrodynamic flow in an inclined channel

Graphene oxide nanoparticles with higher thermal conductivity aid in enhancing the flow and heat transport in magnetohydrodynamic (MHD) devices such as MHD pumps. Modelling such devices with promising applications inherently necessitates the entropy studies to ensure efficient models. In conventional fluids, Lorentz force controls the fluid velocity in the presence of magnetic field. Whereas, the use of graphene oxide hypothesized the enhancement of flow, despite the impacts of Lorentz force, due to high thermal conductivity. This paper is an investigation to computationally study the hypothesis and to analyse the entropy generation in magnetohydrodynamic flow of graphene oxide (GO) in an inclined channel. Buongiorno nanofluid model is used including the impacts of nanoparticle attributes namely thermophoretic and Brownian diffusion along with viscous dissipation effects. Spectral quasilinearization method with Chebyshev's polynomials is adapted to solve the differential equations under convective conditions. On studying the effects of implanted parameters, it is concluded that the flow velocity enhancement by Hartmann number is remarked and is proved to be achieved from the thermal conductivity of graphene oxide particles. A quantitative analysis is made with the previously published results for special cases. Furthermore, investigations conclude that the entropy is contributed primarily from the heat transfer.

Investigation of thermodynamics characteristics of ternary hybrid nanofluid flow over a stretching sheet

This paper considers two-dimensional electrically conducting and incompressible ternary hybrid nanofluid flow on a stretching sheet with the convective boundary condition and heat source effect. Relevant similarity formulas are effectuated in converting the governing equations into a system of ordinary differential equations (ODEs) and are further treated numerically using the spectral quasilinearization method (SQLM), with error analysis. The prominent dimensionless parameters controlling the flow, and heat transfer characteristics are discussed. The results of this study show that Eckert number, heat source parameter, and magnetic effect boost the temperature profile. This work expected significant information for the future applications of innovative heat transfer devices, as well as a valuable reference for researchers to study flow behavior under various assumptions.

Analysis of activation energy and microbial activity on couple stress nanofluid with heat generation

This investigation includes the performance of the Couple Stress Nanofluid with microbial activity, activation energy incorporation of thermal conductivity, heat generation, variable viscosity and other parameters. We used some suitable similarity transformations to convert the governing partial differential equations and the initial boundary conditions of our model into the coupled structure of ordinary differential equations and final boundary conditions. Furthermore, the Spectral Quasi Linearization Method (SQLM) was used to numerically solve these ordinary differential equations with boundary conditions, generating the reassuring impacts of various parameters taken in our model. The graphical representation for the flow, temperature, solute and microbial distribution was analyzed with activation energy, heat generation and other interesting parameters. The impact of variable viscosity and thermal conductivity with the Prandtl number for the local skin friction, Nusselt, Sherwood, and the microbial density numbers was included and reflects the favorable results. The comparison table is also included to validate our model. The rising values of the activation energy parameter enhances the solute and microbe profiles, while rising of bio-convection Rayleigh number and Reynolds numbers discriminates the heat profiles, but enhances the solute profile. The microbial profile of the model falls for the rising values of the microbe reaction parameter.

Analysis of Entropy Generation on MHD Radiative Viscous-Ohmic Dissipative Heat Transfer Over a Stretching Sheet in a Chemically Reactive Jeffrey Nanofluid with Non-Uniform Heat Source/Sink Based on SQLM

We have examined the effect of entropy generation and nonlinear thermal radiation on magnetohydrodynamic (MHD) in Jeffrey nanofluid over a permeable stretching sheet with viscous-Ohmic dissipation and non-uniform heat source/sink. Brownian motion and thermophoresis effects have also been taken into account. The basic governing equations of the boundary layer flow are then solved numerically by the Spectral Quasilinearization method (SQLM). Various controlling physical parameters effects on velocity, temperature, concentration, entropy generation and Bejan number profiles are presented graphically. Results show that increasing the magnetic parameter, Brownian motion parameter, and thermophoresis parameter enhance the temperature profiles. Furthermore, the entropy generation profiles increase with space-dependent and temperature-dependent parameters, wall mass flux parameter, and chemical reaction parameter near to the sheet. In contrast, reverse trends are observed away from the sheet. Novelty of entropy generation is also provided to reflect the effects of several relevant physical parameters on the entropy generation rate and Bejan number.

Numerical Analysis of Magnetohydrodynamic and Dissipated Hybrid Casson Nanofluid Flow Over an Unsteady Stretchable Rotating Disk with Cattaneo-Christov Heat Flux Model

The study scrutinized MHD and dissipated (SWCNTs-Fe3O4)/C2H6O2 hybrid Casson nanofluids flow over an unsteady stretchable rotating disk with a Cattaneo-Christov heat flux model. By means of proper similarity conversion, the boundary layer flow governing PDEs was changed into systems of dimensionless coupled nonlinear ordinary differential equations. Subsequently, the consequent nonlinear momentum and energy equations with their boundary conditions were worked out numerically employing the spectral quasilinearization method (SQLM). The convergence, stability, and accuracy of the SQLM were established as a computationally efficient method to solve a coupled system of boundary layer problems. It is specified that 5% of SWCNTs, 20% of Fe3O4, and 75% of C2H6O2 being taken for the preparation of (SWCNTs−Fe3O4)/C2H6O2 hybrid nanofluid with shape factor n1 = n2 = 3, and the values of the parameters used are fixed to M = 5, S = 0.5, β = 5, κ = 0.5, Ec = 2, Λ = 2, Pr = 7.3, α = 0.5, δ = 0. The effects of more perceptible parameters on velocity and thermal flow fields were considered and scrutinized carefully via graphs and tables. The results disclose that the momentum and thermal boundary layer thickness markedly declined with more value of the unsteady parameter. The local heat transfer rate improves nearly by 14% as 0.2 volume of Fe3O4 nanoparticles dispersed in 0.05 volume of SWCNTs and 0.75 volume of C2H6O2 nanofluid, hence, in realistic uses adding more values of nanoparticles in the hybrid nanofluids is useful to progress the heating process. The study is novel since to the best of the author’s knowledge, no paper has been published so far on the unsteady flow of (SWNT-Fe3O4)-Ethylene glycol hybrid Casson nanofluid with the effects of the Cattaneo-Christov heat flux model. As well, the model used for the thermophysical properties of the hybrid nanofluid is a new approach. Generally, hybrid nanofluids of (SWCNTs-Fe3O4)/C2H6O2 show better flow distributions with good stability of thermal properties than their mono counterparts.

Spectral simulation of hydromagnetic flow with dissipative and radiative heat transfer over an inclined rotating disk within a non‐Darcy porous medium

AbstractThe goal of the research presented in this paper is to examine how a magnetic field affects the unsteady flow of an incompressible nanofluid over a spinning disc that is inclined and stretched while the flow is embedded in a non‐Darcy porous medium. Furthermore, the heat transmission mechanism takes into account Joule heating and viscous dissipation. By imposing thermal radiation to enhance the heat transmission system under the effects of convection, the current article becomes more realistic. A set of nonlinear partial differential equations and associated boundary conditions defines the mathematical problem. Using an appropriate similarity transformation, the mathematical model is converted into a set of nonlinear ordinary differential equations with boundary conditions, which are then solved numerically by the Spectral Quasi Linearization Method (SQLM). Graphs and tables for various flow parameters illustrate the complete results for the exploration of dimensionless velocity and temperature. Regression analysis is used to statistically estimate the local Nusselt number and the skin friction coefficients. From the numerical results, it is found that when the magnetic parameter is increased, the flow velocity in the radial and tangential directions decreases due to the Lorentz force. With the variation of the Forchheimer number, the fluid flow in both directions decreases with increasing inertia coefficient. By increasing the magnetic parameter and Eckart number, the temperature of the fluid increases. The performed quadratic regression analysis reveals that the permeability of the medium and the generated Lorentz force are significant for the skin friction coefficient in the radial direction, whereas the stretching parameter and Forchheimer number are significant for the skin friction coefficient in the tangential direction. Thermal radiation and convective heating are found to significantly affect the heat transfer coefficient.

Entropy optimization in mixed convective boundary layer flow of CNTs Casson nanoliquid through a vertical cylinder moving with nonlinear velocity

This article inspects entropy generation and mixed convection boundary layer flow of carbon nanotubes (CNTs) Casson nanoliquid via semi-infinite vertical cylinder which moves with nonlinear velocity in Darcy-Forchheimer porous medium. Appropriate similarity variables have been employed to convert the original partial differential equations into ordinary differential equations that have been solved using overlapping grid spectral quasilinearisation method (SQLM). Comparison of accuracy, convergence and stability between the two methods is made. Rate of entropy generated, flow fields and engineering quantities are discussed for different embedding parameters. It is revealed that single-wall CNTs are more efficacious to improve heat transport features than multi-wall CNTs. The fluid flow and thermal dispersion processes improve with consideration of curved surface, CNTs, non-Newtonian fluid and injection of the fluid. The curvature surface and suction of the fluid contribute towards growth of skin friction factor and rate of thermal transference. Entropy generated expands by accounting for viscous nature of the fluid, strong nonlinearity, suction, non-Newtonian fluid, convective boundary condition and CNTs. The study finds applications in various processes, which are massively impacted by heat transport enhancement and high porosity. Boundary layer flow and heat transfer analysis through cylinders are relevant to various metallurgical and engineering solicitations.

Entropy Generation in a Magnetohydrodynamic Hybrid Nanofluid Flow over a Nonlinear Permeable Surface with Velocity Slip Effect

The current study is designed to model the hydrothermal feature of a hybrid nano liquid slip flows over a permeable expanding/contracting surface with entropy generation. The model incorporates Cu-Al2O3 nanoparticles with water as the host liquid to simulate the flow. Additional impacts incorporated into the novelty of the model are viscous dissipation and Joule heating. The model is transformed appropriately to its dimensionless form using similarity quantities and the solution is numerically obtained using the spectral quasi-linearization method (SQLM). The impact of pertinent factors on the flow characteristics is communicated through graphs for the hybrid nano-suspension to discuss the hydrothermal variations. The friction factor and the rate of heat transport are also discussed with sensible judgment through tables. To ensure the code validity, a comparison with earlier studies is conducted and excellent consensus is accomplished. The result explored that diminution in the irreversibility ratio is witnessed for rising magnetic field strength along the free stream, distance away from the permeable surface as the heat dissipation to the surrounding decelerates. Also, the augmented nonlinearity parameter intensified the heat transfer rate for about 2.79% of the hybrid nano-suspension.

Numerical and statistical analysis of hydromagnetic couple-stress hybrid nanofluid flow in a channel induced due to stretching of a wall

In this research paper, the authors wish to examine the effects of couple stress on hybrid nanofluid considering magnetohydrodynamic three-dimensional transient flow between two parallel plates. Stretching of the lower plate causes fluid flow in the channel. The fluid flow model is shown in mathematical form using a set of coupled nonlinear partial differential equations, which are then translated into coupled nonlinear ordinary differential equations using the proper transformation. The authors used the spectral quasi linearization method (SQLM), an effective numerical technique, to solve the updated equations and study the effects of various flow parameters on fluid temperature and velocity. The Nusselt number and skin friction coefficients were also investigated from an engineering standpoint. The generated solutions are verified using the residual analysis. Statistical analysis is performed on the skin-friction coefficients and the Nusselt number using quadratic regression models.

Magnetohydrodynamics Williamson Nanofluid Flow over an Exponentially Stretching Surface with a Chemical Reaction and Thermal Radiation

Presented in this current study is the numerical analysis of magnetohydrodynamics Williamson nanofluid flow over an exponentially stretching surface. The most important aspect of the investigation is that the effects of the magnetic field, chemical reaction and thermal radiation in the fluid flow are taken into account. The partial differential equations governing the present Williamson nanofluid flow problem were observed to be highly nonlinear and coupled. Suitable similarity transformations were used to transmute the coupled system of nonlinear partial differential equations governing the fluid flow into a linear system. The linear system was solved numerically using the spectral quasi-linearization method. The MATLAB bvp4c numerical technique and a comparison with existing results for the skin friction coefficient were used to confirm the appropriateness of the method in solving the current problem. The influence of some pertinent physical parameters on the fluid’s velocity, temperature and concentration profiles were displayed graphically. The effects of all the physical parameters on the skin friction coefficient, Nusselt number and Sherwood number were portrayed in a tabular form. It was noted that enhancing the thermal radiation parameter reduces the fluid’s temperature, Nusselt number and the skin friction coefficient, while the Sherwood number is improved.

Flow Analysis of Mixed Convective Nanofluid Flow in Presence of Magnetic Field with Thermal Radiation and Heat Source/Sink

This study discussed the mixed convection with thermal radiation on nanofluid flow with magnetic field and mass transfer with heat source over an inclined stretching cylinder in the presence of thermal conductivity. The governing equations in cylindrical form are transformed into the system of ODE and solved mathematically by spectral quasilinearization method (SQLM). The governing parameters velocity, temperature and concentration profile are derived using this new approach. Here it is mention that due to Hartman number (Ha) and relaxation to retardation time ratio (λ1), the velocity decreases but temperature enhanced in the boundary layer but in opposite effect on higher value of curvature parameter (γ) and thermal bouncy (λT) parameter. Here also observed convergence and accuracy in velocity and temperature profile. The SQLM is used to find out the solution of convergent series and various effect are shown graphically.