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The purpose of this study is to investigate the Dynamics of micropolar – water B Fluids flow simultaneously under the influence of thermal radiation and Soret–Dufour Mechanisms.

The thermal radiation contribution, the chemical change and heat generation take fluidity into account. The flow equations are used to produce a series of dimensionless equations with appropriate nondimensional quantities. By using the spectral homotopy analysis method (SHAM), simplified dimensionless equations have been quantitatively solved. With Chebyshev pseudospectral technique, SHAM integrates the approach of the well-known method of homotopical analysis to the set of altered equations. In terms of velocity, concentration and temperature profiles, the impacts of Prandtl number, chemical reaction and thermal radiation are studied. All findings are visually shown and all physical values are calculated and tabulated.

The results indicate that an increase in the variable viscosity leads to speed and temperature increases. Based on the transport nature of micropolar Walters B fluids, the thermal conductivity has great impact on the Prandtl number and decrease the velocity and temperature. The current research was very well supported by prior literature works. The results in this paper are anticipated to be helpful for biotechnology, food processing and boiling. It is used primarily in refrigerating systems, tensile heating to large-scale heating and oil pipeline reduction.

All results are presented graphically and all physical quantities are computed and tabulated.

The purpose of this study is to explore numerical scrutinization of micropolar and Walters-B non-Newtonian fluids motion under the influence of thermal radiation and chemical reaction.

The two fluids micropolar and Walters-B liquid are considered to start flowing from the slot to the stretching sheet. A magnetic field of constant strength is imposed on their flow transversely. The problems on heat and mass transport are set up with thermal, chemical reaction, heat generation, etc. to form partial differential equations. These equations were simplified into a dimensionless form and solved using spectral homotopy analysis method (SHAM). SHAM uses the basic concept of both Chebyshev pseudospectral method and homotopy analysis method to obtain numerical computations of the problem.

The outcomes for encountered flow parameters for temperature, velocity and concentration are presented with the aid of figures. It is observed that both the velocity and angular velocity of micropolar and Walters-B and thermal boundary layers increase with increase in the thermal radiation parameter. The decrease in velocity and decrease in angular velocity occurred are a result of increase in chemical reaction. It is hoped that the present study will enhance the understanding of boundary layer flow of micropolar and Walters-B non-Newtonian fluid under the influences of thermal radiation, thermal conductivity and chemical reaction as applied in various engineering processes.

All results are presented graphically and all physical quantities are computed and tabulated.

The purpose of this study is to investigate the effects of entropy generation of some embedded thermophysical properties on heat and mass transfer of pulsatile flow of non-Newtonian nanofluid flows between two porous parallel plates in the presence of Lorentz force are taken into account in this research.

The governing partial differential equations (PDEs) were nondimensionalized using suitable nondimensional quantities to transform the PDEs into a system of coupled nonlinear PDEs. The resulting equations are solved using the spectral relaxation method due to the effectiveness and accuracy of the method. The obtained velocity and temperature profiles are used to compute the entropy generation rate and Bejan number. The influence of various flow parameters on the velocity, temperature, entropy generation rate and Bejan number are discussed graphically.

The results indicate that the energy losses can be minimized in the system by choosing appropriate values for pertinent parameters; when thermal conductivity is increasing, this leads to the depreciation of entropy generation, and while this increment in thermal conductivity appreciates the Bejan number, the Eckert number on entropy generation and Bejan number, the graph shows that each time of increase in Eckert will lead to rising of entropy generation while this increase shows a reduction in Bejan number. To shed more light, these results were further demonstrated graphically. The current research was very well supported by prior literature works.

All results are presented graphically, and the results in this article are anticipated to be helpful in the area of engineering.

The purpose of this paper is to consider the simultaneous flow of Casson Williamson non Newtonian fluids in a vertical porous medium under the influence of variable thermos-physical parameters.

The model equations are a set of partial differential equations (PDEs). These PDEs were transformed into a non-dimensionless form using suitable non-dimensional quantities. The transformed equations were solved numerically using an iterative method called spectral relaxation techniques. The spectral relaxation technique is an iterative method that uses the Gauss-Seidel approach in discretizing and linearizing the set of equations.

It was found out in the study that a considerable number of variable viscosity parameter leads to decrease in the velocity and temperature profiles. Increase in the variable thermal conductivity parameter degenerates the velocity as well as temperature profiles. Hence, the variable thermo-physical parameters greatly influence the non-Newtonian fluids flow.

This study considered the simultaneous flow of Casson-Williamson non-Newtonian fluids by considering the fluid thermal properties to vary within the fluid layers. To the best of the author’s knowledge, such study has not been considered in literature.

This paper aims to explore the numerical simulation of MHD flow of Williamson hybrid nanofluid over a porous stretched sheet. Cattaneo–Christov thermal and specie fluxes were used in the model. Partial differential equations are exploit to model the underlying physics of the situation (PDEs).

Using an acceptable similarity functions, these equations were changed into total differential equations (ODEs). The spectral relaxation method (SRM) was used to solve the linked and nonlinear altered ODEs. The Gauss–Seidel procedure is used to figure out how to use Chebyshev pseudospectral techniques in SRM. This is an iterative process.

Increasing the heat relaxation flow increases temperature distributions; increasing the mass relaxation flux increases concentration distributions. A higher value of thermal radiation heat generation and Eckert number was noticed to improve temperature and velocity distributions. Due to the imposed electromagnetic force, a higher magnetic field is detected to cause an elevation in the velocity distribution. Also, a higher thermal radiation is observed to upsurge the velocity in company with temperature distributions.

This research benefits from biomedical engineering, biological sciences, astrophysics and geophysics. The rheological applications of Williamson fluid finds usefulness in biological sciences. The nanoparticles as considered in this study finds applications in the field of biomedical engineering. Also, the application of the imposed electromagnetic field and magnetic field strength is very useful in the area of astrophysics. A good agreement may be found in the literature on this study’s findings.

This paper aims to examine the Dufour and Soret combined effects on the study of two-dimensional squeezed flow of copper water nanofluid between parallel plates along with applied (external) magnetic field. Impact of higher order chemical reaction is also considered.

The nonlinear partial differential equations (PDEs) are changed into system of ordinary differential equations (ODEs) by employing suitable similarity transformations. These transformed ODEs are then solved by means of a semianalytical method called differential transform method (DTM). Effects of several changing physical parameters on fluid flow, temperature and concentration have been deliberated through graphs.

It is observed that Dufour and Soret numbers are directly related to temperature profile and a reverse trend was observed in the concentration profile. Temperature enhancement is perceived for the enhanced Dufour number. Enhancement in Dufour number shows a direct association with Sh and Nu for all values of squeezing parameter.

The combined Dufour and Soret effects are used in separation of isotopes in mixture of gases, oil reservoirs and binary alloys solidification. The squeeze nanoliquid flow can be used in the field of composite material joining, rheological testing and welding engineering.

This study is mainly useful for geosciences and chemical engineering.

The uniqueness in this research is the study of the impact of cross diffusion on chemically reacting squeezed nanoliquid flow with the chemical reaction order more than one in the presence of applied magnetic force using a semianalytical procedure, named DTM.

This chapter defines a learning culture and discusses the relationship between knowledge and learning. The authors explain why learning is essential to bringing knowledge to life and incentivizing knowledge flows and use. The chapter addresses the interplay between knowledge and learning cultures. A key point in the chapter is the value of mistakes as learning opportunities. The authors explain how mistakes are viewed in the industrial economy and how this perspective impedes critical organizational learning. Specifically, we define mistakes, explain the double cognitive bias of mistakes, explain the tendency and impact of hiding mistakes, the side effects of double mistake bias, learn to learn from mistakes, and take on the challenge of reconciling mistake acceptance and avoidance. Finally, the chapter addresses the importance of cultivating a learning climate to realize your learning culture.

This paper aims to analyze heat and mass transfer of magnetohydrodynamic (MHD) non-Newtonian fluids flow past an inclined thermally stratified porous plate using a numerical approach.

The flow equations are set up with the non-linear free convective term, thermal radiation, nanofluids and Soret–Dufour effects. Thus, the non-linear partial differential equations of the flow analysis were simplified by using similarity transformation to obtain non-linear coupled equations. The set of simplified equations are solved by using the spectral homotopy analysis method (SHAM) and the spectral relaxation method (SRM). SHAM uses the approach of Chebyshev pseudospectral alongside the homotopy analysis. The SRM uses the concept of Gauss-Seidel techniques to the linear system of equations.

Findings revealed that a large value of the non-linear convective parameters for both temperature and concentration increases the velocity profile. A large value of the Williamson term is detected to elevate the velocity plot, whereas the Casson parameter degenerates the velocity profile. The thermal radiation was found to elevate both velocity and temperature as its value increases. The imposed magnetic field was found to slow down the fluid velocity by originating the Lorentz force.

The novelty of this paper is to explore the heat and mass transfer effects on MHD non-Newtonian fluids flow through an inclined thermally-stratified porous medium. The model is formulated in an inclined plate and embedded in a thermally-stratified porous medium which to the best of the knowledge has not been explored before in literature. Two elegance spectral numerical techniques have been used in solving the modeled equations. Both SRM and SHAM were found to be accurate.

The study aims to explore how Soret and Dufour diffusions, thermal radiation, joule heating and magnetohydrodynamics (MHD) affect the flow of hybrid nanofluid (Al₂O₃-SiO₂/water) over a porous medium using a mobile slender needle.

To streamline the analysis, the authors apply appropriate transformations to change the governing model of partial differential equations into a group of ordinary differential equations. Following this, the authors analyze the transformed equations using the homotopy analysis method within Mathematica software, leading to the derivation of analytical solutions. This study investigates how changing values for porous medium, MHD, Soret and Dufour numbers and thermal radiation influence concentration, temperature and velocity profiles. In addition, the research assesses the effects on local Sherwood number, skin friction and Nusselt number.

In this investigation, the authors explore the movement of a needle away from its origin (ε>0). As the magnetic and porous medium parameters increase, there is a correspondence decrease in the velocity profile. Simultaneously, an increase in the Dufour number and thermal radiation parameter yields to a higher temperature profile, whereas arise in the Soret number results in an enhanced concentration profile. Furthermore, growth in the magnetic field parameter is correlated with a reduction in skin friction, Nusselt and Sherwood numbers. In addition, an examination of the data reveals that an escalation in the thermal radiation parameter is associated with an elevation in the Nusselt number. Moreover, an elevation in the Dufour number results in an augmentation in the Nusselt number.

These results have practical applications across diverse fields, including heat transfer enhancement, energy conversion systems, advanced manufacturing and material processing.

This study is distinctive in its investigation of the flow of hybrid nanofluid (Al₂O₃-SiO₂/water) over a slender, moving needle. The analysis includes joule heating, MHD, porous medium, thermal radiation and considering the effects of Soret and Dufour.

The purpose of this study is to explore the impact of Joule heating, slip conditions, Dufour and Soret effects on three-dimensional magneto-convection of nanoliquid over a rotating surface in the existence of thermal radiation, viscous dissipation and internal heat generation/absorption.

The considered physical system is modelled by a set of partial differential equations (PDEs) with conditions at surface. Then, the nonlinear PDEs are altered into a system of ordinary differential equations and they are solved numerically by the Runge−Kutta−Fehlberg method. Plotting the collected velocity, temperature and solute concentration characteristics allows one to see how relevant parameters affect the results. Calculations are made for skin friction and the rate of heat and mass transfer.

The outcomes are portrayed in the form of tables and graphs with a wide range of parameter involved in the study. It is observed that the local thermal energy transfer rate enriches on increasing the value of both thermal and solute slips. The solutal slip parameter suppresses the solute transport rate and thermal slip supports the solute transport.

Combining the Dufour and Soret effects is used in oil reservoirs, binary alloy solidification and isotope separation in mixtures of gases. Heat exchangers, nuclear reactors and thermal engineering can all benefit from the usage of nanofluid with Joule heating.

This study is mainly useful for thermal sciences and chemical engineering.

The investigation of the effects of slip circumstances and Joule heating on magnetohydrodynamic rotating nanoliquid stream with thermal radiation and cross-diffusion makes this work unique. The discoveries produced are valuable and distinctive, and they have applications in many areas of thermal science and technology.