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The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH).

The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically.

It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH.

This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids.

Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production.

Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration.

The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

In the present investigation, hydromagnetic boundary layer flow of Walters’-B fluid over a vertical porous surface implanted in a porous material under the action of a strong external applied magnetic field and rotation is presented. In several industrial applications, the external applied magnetic field is strong enough to produce Hall and ion-slip currents. Thus, the influence of Hall and ion-slip currents is also considered in this analysis. The flow through configuration is generated because of time varying motion of the free-stream and buoyancy action.

Regular perturbation scheme is used to obtain the solution of the system of coupled partial differential equations representing the mathematical model of the problem. Numerical computation has been performed to notice the change in flow behavior and the numerical results for velocity field, temperature field, species concentration, skin friction, rate of heat and mass transfer are presented through graphs and tables.

An important fact noticed that the exponential time varying motion of the free-stream induces reverse flow in the direction perpendicular to the main flow. Rising values of the strength of the applied magnetic field give increment in the fluid velocity in the neighbourhood of the vertical surface, this may cause because of the exponential motion of the free-stream. The behaviour of the Darcian drag force is similar as magnetic field on fluid flow.

In literature, very less research works are available on Walters’-B fluid where unsteadiness in the system occurs because of time varying motion of the free-stream. In this paper, the authors have made an attempt to study the action of Hall and ion-slip currents, rotation and external applied magnetic field on hydromagnetic boundary layer flow of Walters’-B fluid over a vertical surface implanted in a porous material.

This research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and electrically conductive fluid over a vertically oscillating flat plate. The study highlights the significance of magnetic fields in influencing thermal and mass transfer, particularly in the context of thermal radiation. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the finite element method (FEM) numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. Key parameters such as skin friction, temperature, concentration, velocity and Sherwood numbers are derived and analyzed. The results demonstrate that viscous dissipation significantly elevates the fluid temperature, while an increase in the radiation parameter is associated with a decrease in internal friction at the plate. These findings provide critical insights into the interplay between thermal radiation and magnetic fields in MHD flows, with potential applications in engineering systems involving heat and mass transfer, such as cooling systems and material processing. This study underscores the importance of understanding these dynamics for optimizing the performance of MHD applications in various industrial settings.

The mainly authorized and energetic FEM to explain the non-linear, dimensionless partial differential equations (11–13) via equation with boundary conditions (14) makes use of Bathe (36), Reddy (37), Connor (38) and Chung (39). Following are the key steps that make up the method: discretize the domain, derivation of element equation, assembly of element equation, imposition of boundary condition and solution of assembly equation.

This study examined the impact of viscid dissipative radiation and the Dufour effect on unsteady one-dimensional MHD natural convective flow of a viscous, incompressible, electrically conducting fluid past an infinite moving vertical flat plate with a chemical reaction. Numerically solving the governing equations using the FEM approach is efficient and precise, aiming to be applied to fluid mechanics and related problems. Along with their effects on temperature, concentration and velocity, the following parameters are included: the mass Grashof number, the Soret number, the Grashof number, the Prandtl number, chemical reaction, the Schmidt number, radiation and the Casson parameter. Both the Grashof numbers of thermal and mass rates (Gr, Gm) make an increment in the velocity region. The velocity decreases with an increase in the magnetic parameter. The velocity increases with an increase in the permeability of the porous medium parameter. The temperature flow rate is higher for both Dufour and Viscid dissipation, while a decrement is noted of both Prandtl number and radiation effects. The decrementing behavior of the concentration region is observed at supreme inputs of chemical reaction coefficient and Schmidt number.

This is an original paper and not submitted anywhere.

The purpose of this paper is to address the combined effects of thermal radiation and chemical reaction on steady MHD mixed convective heat and mass transfer flow past a vertical surface under the influence of Joule and viscous dissipation.

The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique.

With the help of graphs, the effects of the various important parameters entering into the problem on the dimensionless velocity, dimensionless temperature and dimensionless concentration fields within the boundary layer are discussed. The authors noticed that the velocity increases with an increase in the porosity parameter. An increase in the Prandtl number Pr, decreases the velocity and the temperature field. An increase in the radiation parameter, decreases the velocity and the temperature field. Also the effects of the pertinent parameters on the skin-friction coefficient and rates of heat and mass transfer in terms of the Nusselt and Sherwood numbers are presented numerically in tabular form.

To the best of the authors’ knowledge, recent this work has not been finished by any other researchers.

The purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.

The resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.

An interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.

Very little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

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.

In heat transfer problems, if the temperature difference is not sufficiently so small then the linear Boussinesq approximation is not adequate to describe thermal analysis. Also, nonlinear density variation with respect to temperature/concentration has a significant impact on heat and fluid flow characteristics. Because of this reason, the impact of nonlinear density variation in the buoyancy force term cannot be neglected. Therefore in this paper, the unsteady flow and heat transfer of radiating magneto-micropolar fluid by considering nonlinear Boussinesq approximation is investigated analytically.

The flow is fully developed and time-dependent. Heat and mass flux boundary conditions are also accounted in the analysis. The governing equations of transport phenomena are treated analytically using regular perturbation method. To analyze the tendency of the obtained solutions, a parametric study is performed.

It is established that the velocity field is directly proportional to the nonlinear convection parameter and the same trend is observed with the increase of the value of Grashof number. The micro-rotational velocity profile decreases with increase in the nonlinear convection parameter. Further, the temperature profile increases due to the presence of radiative heat aspect.

The effectiveness of nonlinear Boussinesq approximation in the flow of micropolar fluid past a vertical plate in the presence of thermal radiation and magnetic dipole is investigated for the first time.

The purpose of this paper is to consider unsteady free convection flow of a dissipative fluid past an exponentially accelerated infinite vertical porous plate in the presence of Newtonian heating and mass diffusion.

The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A Galerkin finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. It is a powerful, stable technique which provides excellent convergence and versatility in accommodating coupled systems of ordinary and partial differential equations.

It is found that the skin friction coefficient increases with increases in either of the Eckert number, thermal Grashof number, mass Grashof number or time whereas it decreases with increases in either of the suction parameter, Schmidt number or the acceleration parameter for both air and water. The skin friction coefficient is also found to decrease with increases in the values of the Prandtl number. In addition, it is found that the rate of heat transfer increases with an increase in the suction parameter and decreases with an increase in the Eckert number for both air and water. Lastly, it is found that the rate of heat transfer increases with increasing values of the Prandtl number and decreases with increasing time for all values of the Prandtl number.

The present study has considered only Newtonian fluids. Future studies will address non-Newtonian liquids.

A very useful source of information for researchers on the subject of free convective flow over the surface when the rate of heat transfer from the surface is proportional to the local surface temperature.

This paper is relatively original and illustrates the effects of viscous dissipation on free convective flow past an exponentially accelerated infinite vertical porous plate with Newtonian heating and mass diffusion.

This paper aims to explore dual solutions for the flow of a hybrid nanofluid over a permeable melting stretching/shrinking sheet with nanoparticle shape factor, second-order velocity slip conditions and viscous dissipation. The hybrid nanofluid is formulated by dispersing alumina (Al₂O₃) and copper (Cu) nanoparticles into water (H₂O).

The governing partial differential equations (PDEs) are first reduced to a system of ordinary differential equations (ODEs) using a mathematical method of similarity transformation technique. These ODEs are then numerically solved through MATLAB’s bvp4c solver.

Key parameters such as slip parameter, melting parameter, suction parameter, shrinking parameter and Eckert number are examined. The results reveal the existence of two distinct solutions (upper and lower branches) for the transformed ODEs when considering the shrinking parameter. Increasing value of Cu-volume fraction and the second-order velocity slip enhances boundary layer thicknesses, whereas the heat transfer rate diminishes with rising melting and suction parameters. These numerical results are illustrated through various figures and tables. Additionally, a stability analysis is performed and confirms the upper branch is stable and practical, while the lower branch is unstable.

The analysis of hybrid nanofluid flow over a shrinking surface has practical significance with applications in processes such as solar thermal management systems, automotive cooling systems, sedimentation, microelectronic cooling or centrifugal separation of particles. Both steady and unsteady hybrid nanofluid flows are relevant in these contexts.

While the study of hybrid nanofluid flow is well-documented, research focusing on the shrinking flow case with specific parameters in our study is still relatively scarce. This paper contributes to obtaining dual solutions specifically for the shrinking case, which has been less frequently addressed.

The study of novel exponential heat source phenomena across a flowing fluid with a suspension of microparticles and nanoparticles towards a convectively heated plate has been an open question. Therefore, the impact of the exponential heat source in the transport of nano micropolar fluid in the existence of magnetic dipole, Joule heating, viscous heating and convective condition effects has been analytically investigated. Influence of chemical reaction has also been exhibited in this discussion.

The leading equations are constructed via conservation equations of transport, micro-rotation, energy and solute under the non-transient state situation. Suitable stretching transformations are used to transform the system of partial differential equations to ordinary. The transformed ODEs admit numerical solution via Runge–Kutta fourth order method along with shooting technique.

The effects of pertinent physical parameters characterizing the flow phenomena are presented through graphs and discussed. The inclusion of microparticles and nanoparticles greatly affects the flow phenomena. The impact of the exponential heat source (EHS) advances the heat transfer characteristics significantly compared to usual thermal-based heat source (THS). The thermal performance can be improved through the effects of a magnetic dipole, viscous heating, Joule heating and convective condition.

The effectiveness of EHS phenomena in the dynamics of nano micropolar fluid past an elongated plate which is convectively heated with regression analysis is for the first time investigated.