Unsteady squeezing flow of water‐based nanofluid between two parallel disks with slip effects: Analytical approach

The squeezing flow of an unsteady water‐based nanofluid between two parallel disks has been analyzed in the current study. Thermal and solutal buoyancy along with heat source enhance the flow phenomena of free convective flow through a porous medium. In addition to that velocity slip and temperature slip are also accounted for in the boundary conditions. The similarity transformation is adopted to formulate the governing equations that convert the complex partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). These transformed equations are handled analytically by using the variation parameter method (VPM). For computational purposes, the fixed numeric values of physical parameters are used and their behaviors are shown by means of graphs. The calculated results for the physical quantities of interest are shown in tables. The conformity of the solution is obtained in comparison to an earlier study in a particular case. The major findings are (i) the velocity profile has distinct variations, which are separated by the middle layer of the channel and (ii) enhancement in the heat transfer coefficient is noted due to the interaction of buoyancy parameter.     

Numerical simulation of heat and mass transfers radiative–convective fluid flow on a stretching porous surface with temperature-dependent thermophysical properties

This paper is focused on the analysis of heat and mass transfer radiative–convective fluid flow using quadratic multiple regression and numerical approach. The physical phenomenon is analyzed by utilizing partial differential equations (PDEs). Thermophysical properties, such as viscosity, thermal conductivity, and mass diffusivity, are varied and temperature-dependent. This study is unique because of its applications in magnetohydrodynamic power accelerators, drilling operators, and bioengineering. The governing PDEs are transformed into coupled nonlinear ordinary differential equations (ODEs). The transformed ODEs are solved numerically using the spectral homotopy analysis method. Also, a quadratic multiple regression analysis is performed on quantities of engineering interest to show the significance of the flow parameters. It is observed that the heat and mass transfer process is affected by nonlinear buoyancy impact. The Lorentz force produced by the imposed magnetic field decline the thickness of the hydrodynamic boundary layer. Findings revealed that the nonlinear convective parameter and variable thermophysical properties are greatly affected by the rate of heat and mass transfer. Previously published work was used to validate the present one, which conformed with it. The slope of linear regression through data points is adopted to show the rate of change in skin friction, Nusselt, and Sherwood numbers during the flow phenomenon.     

Magnetohydrodynamic micropolar slip flow due to an exponentially stretching sheet with chemical reaction and nonuniform heat generation

The main focus of the current study is to examine the impact of melting heat transfer and chemical reaction on magnetohydrodynamic micropolar fluid flow over a sheet that is exponentially stretching and immersed in a porous medium. A nonuniform heat source is placed within this flow system. Other impacts like slip phenomena and thermal radiation are also taken into consideration. The governing partial differential equations are converted to a system of ordinary differential equations (ODEs) via similarity transformation and we also get the corresponding necessary boundary conditions. These nonlinear ODEs are resolved with the help of shooting technique and an Runge-Kutta fourth order (RK-4) iterative strategy. Also, we solve this problem using the Bvp4c approach for validating the results of the RK-4 method. Both outcomes are consistent with previously published data. With the help of tables and graphs, we examine the influence of multiple physical parameters on velocity, thermal, microrotation, concentration, Nusselt number, Sherwood number, coefficient of skin friction, and wall couple stress. We see that the temperature distribution and velocity profiles decrease when the melting parameter increases. The temperature profile boosts when the heat source parameter is increased.     

Heat and mass transfer in an unsteady squeezed Casson fluid flow with novel thermophysical properties: Analytical and numerical solution

This study investigates the heat and mass transfer in an unsteady squeezing flow between parallel plates under the influence of novel variable diffusivity. In most of the literature, it is believed that the thermophysical properties of the fluid are unchanged. However, this present study bridges this gap by assuming that viscosity, conductivity, and diffusivity are all temperature-dependent. Physically, an appropriate analysis of thermophysical variables in such a system is required to achieve the best performance for effective heat and mass transfer processes. The equations controlled were first nondimensional and then simplified by a similarity transformation to ordinary nonlinear differential equations. The present study provides a fast convergent method on finite parallel plates, namely, the optimal homotopy analysis method (OHAM) and spectral collocation method (SCM) are used to analyze the fluid flow, heat, and mass transport. The graphical and table understanding is given via an error table and flow behavior of physical parameters. The result reveals that the SCM is more accurate than OHAM. However, the method employed in this paper offers excellent convergence solutions with good accuracy. The solution convergence is also discussed. In this type of problem, squeeze numbers play an important role and the rise in the squeezing parameter increases the fluid temperature.     

Radiative nanofluid flow and heat transfer between parallel disks with penetrable and stretchable walls considering Cattaneo–Christov heat flux model

In this work, we explore the unsteady squeezing flow and heat transfer of nanofluid between two parallel disks in which one of the disks is penetrable and the other is stretchable/shrinkable, in the presence of thermal radiation and heat source impacts, and considering the Cattaneo–Christov heat flux model instead of the more conventional Fourier's law of heat conduction. A similarity transformation is utilized to transmute the governing momentum and energy equations into nonlinear ordinary differential equations with the proper boundary conditions. The achieved nonlinear ordinary differential equations are solved by the Duan–Rach Approach (DRA). This method modifies the standard Adomian Decomposition Method by evaluating the inverse operators at the boundary conditions directly. The impacts of diverse active parameters, such as the suction/injection parameter, the solid volume fraction, the heat source parameter, the thermal relaxation parameter, and the radiation parameter on flow and heat transfer traits are examined. In addition, the value of the Nusselt number is calculated and portrayed through figures.     

Analytical solution of natural convection flow of a nanofluid over a linearly stretching sheet in the presence of magnetic field

In this paper, we examine the convective flow and heat transfer of an incompressible viscous nanofluid past a semi-infinite vertical stretching sheet in the presence of a magnetic field. The governing partial differential equations with the auxiliary conditions are reduced to ordinary differential equations with the appropriate corresponding conditions via scaling transformations. The analytical solutions of the resulting ODEs are obtained, and from which the analytical solutions of the original problem are presented. The influence of pertinent parameters such as the magnetic parameter, the solid volume fraction of nanoparticles and the type of nanofluid on the flow, heat transfer, Nusselt number and skin friction coefficient is discussed. Comparison with published results is presented.     

Exploration of radiative heat on the Jeffery fluid flow in a microchannel for the impact of suction/injection

The purpose of the present paper is to investigate the flow and heat transfer of thermal radiation on the Jeffery fluid flow within a microchannel for the effects of the superhydrophobic surface (SHS) within suction/injection. The governing differential equations of motion and heat transfer are transformed into nonlinear coupled ordinary differential equations (ODEs) using appropriate similarity transformations. The ODEs are solved along with boundary conditions by adopting Runge–Kutta with shooting technique. Symbolic computational software such as MATLAB, the solver bvp4c syntax examines the behavior of the relevant physical parameters. However, some effective emerging parameters on the flow problem reveal that the microchannel walls within the suction/injection parameter increase the temperature, and the SHS is heated. In contrast, without slip, the opposite behavior is rendered. It is clearly shown that the velocity profile diminishes with increasing the Prandtl number. Furthermore, it is noticed that velocity decreases for increasing values of Hartmann number. Comparison with available results for particular cases is an excellent agreement.     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.     

Differential transformed approach of unsteady chemically reactive nanofluid flow over a bidirectional stretched surface in presence of magnetic field

This study investigates the consequences of steady and unsteady nanofluid flow over a bidirectional stretching sheet. Herein, the magnetic field is working in the normal direction. The Brownian motion together with thermophoresis is taken into consideration. Moreover, the chemical reaction within the nanoingredients also occupies a novel corner in this study. The leading equations of the considered model are transferred to nonlinear ordinary differential equations (ODEs) by an appropriate similarity transformation. The differential transformation method is used to solve the set of ODEs. We have used MAPLE‐17 software to solve this with the desired accuracy rate. Results are portrayed with graphs and tables. The corresponding physical consignments such as the Nusselt number, skin friction, and the Sherwood number are exhibited. Excellent improvement in heat and mass transport is observed, which can be visualized through tables. Outcomes reveal that both the temperature and x‐direction velocity are reduced for the stretching parameter. Heat transport escalates for stretching factor, but higher outcomes are marked for the unsteady flow as compared with the steady flow. The mass transfer also increases for the chemical reaction factor, but the rate of increment is higher for the unsteady flow.     

Effects of multislip and distinct heat source on MHD Carreau nanofluid flow past an elongating cylinder using the statistical method

This study focuses on studying the impact of multiple slip effects on the hydromagnetic Carreau nanofluid flow over an elongating cylinder considering a linear heat source and exponential space-based heat source. Suitable transformations are used in converting the highly nonlinear system of partial differential equations governing the flow into a system of ordinary differential equations and hence resolved using the Runge–Kutta method of order four coupled with the shooting method. BVP5C and RKF45 are used to compare the numerical accuracy and an excellent agreement is noted. The parallel effect of parameters on Nusselt number is studied using surface plots and the corresponding effects are scrutinized using multiple linear regression. It is observed that the linear heat source parameter, thermal slip parameter and exponential space-based heat source parameter demote the heat transfer rate. The consequence of different parameters on drag coefficient and mass transfer are quantified using a linear regression slope.     

Influences of Soret and Dufour numbers on mixed convective and chemically reactive Casson fluids flow towards an inclined flat plate

The purpose of this study is to examine the magnetohydrodynamic mixed convection Casson fluid flow over an inclined flat plate along with the heat source/sink. The present flow problem is considered under the assumption of the chemical reaction and thermal radiation impacts along with heat and mass transport. The leading nonlinear partial differential equations of the flow problem were renovated into the nonlinear ordinary differential equations (ODEs) with the assistance of appropriate similarity transformations and then we solved these ODEs with the employment of the bvp4c technique using the computational software MATLAB. The consequences of numerous leading parameters such as thermophoretic parameter, local temperature Grashof number, solutal Grashof number, suction parameter, magnetic field parameter, Prandtl number, chemical reaction parameter, Dufour number, Soret number, angle of inclination, radiation parameter, heat source/sink, and Casson parameter on the fluid velocity, temperature, and concentration profiles are discoursed upon  and presented through different graphs. Some important key findings of the present investigation are that the temperature of the Casson fluid becomes lower for local temperature Grashof number and solutal Grashof number. It is initiated that the Casson fluid parameter increases the velocity of the fluid whereas the opposite effect is noticed in the temperature profile. Higher estimation of Prandtl number and magnetic parameter elevated the Casson fluid concentration. Finally, the skin friction coefficient, Nusselt number, and Sherwood number are calculated and tabulated. It is also examined that the Nusselt number is weakened for both the Dufour number and Soret number but the skin fraction coefficient is greater for both the Dufour number and Soret number.     

Chemically reacting mixed convective Casson fluid flow in the presence of MHD and porous medium through group theoretical analysis

This paper explores the consequences of chemically reacting magnetohydrodynamic mixed convective fluid substances driven by the porous medium, slippery, incompressible, and laminar vertical channel flow. Casson fluid model in a vertical channel is strengthened with mixed convection flow. The effects of the heat source-sink parameter, the suction-injection parameter, slips on the slide wall, and thermal radiation are also considered. A Lie group method is taken into consideration and nonlinear partial differential equations are converted into nonlinear ordinary differential equations (ODEs). The NDSolve command solves these ODEs and shows the action of the related parameters in the velocity, temperature, and concentration figures. The Casson fluid parameter increases the velocity profile but reduces the concentration profile. The parameter of suction-injection enhances the velocity, temperature, and concentration profiles. The variations in skin-friction coefficient in the heat and mass transfer rate are addressed in the diagrams. Moreover, streamlines are plotted for suction-injection parameter.     

Flow and heat transfer inside thin films supported by soft seals in the presence of internal and external pressure pulsations

The effects of both external squeezing and internal pressure pulsations are studied on flow and heat transfer inside non-isothermal and incompressible thin films supported by soft seals. The laminar governing equations are non-dimensionalized and reduced to simpler forms. The upper plate displacement is related to the internal pressure through the elastic behavior of the supporting seals. The following parameters: squeezing number, squeezing frequency, frequency of pulsations, Fixation number (for the seal) and the thermal squeezing parameter are found to be the main controlling parameters. Accordingly, their influences on flow and heat transfer inside disturbed thin films are determined and discussed. It is found that an increase in the Fixation number results in more cooling and a decrease in the average temperature values. Also, it is found that an increase in the squeezing number decreases the turbulence level at the upper plate. Furthermore, fluctuations in the heat transfer and the fluid temperatures can be maximized at relatively lower frequency of internal pressure pulsations.     

Pulsating hydromagnetic flow of Casson fluid in a vertical channel filled with non-Darcian porous medium

This paper analyzes the Joule heating, Dufour number, and Soret number effects on hydromagnetic pulsatile flow of a Casson fluid in a vertical channel filled with a non-Darcian porous medium. The governing partial differential equations (PDEs) of the Casson fluid flow are transformed to ordinary differential equations (ODEs) using perturbation technique and solved by employing shooting method with Runge–Kutta (R–K) fourth-order technique using MATHEMATICA function NDSolve. The influence of Forchheimer number, Casson fluid parameter, Dufour number, radiation parameter, and Soret number on flow variables has been studied and the numerical results obtained are presented. The results reveal that the velocity rises with the rise of Darcy number, whereas it decreases for a given rise in the Forchheimer number. Furthermore, the temperature distribution enhances by increasing the Dufour number.     

Interaction of Cu and Ag nanoparticles on MHD water‐based nanofluids past a stretching sheet

The study explores the MHD flow of water‐based nanofluids past a stretching sheet that melts at a constant rate. Cu and Ag nanoparticles are considered to merge into the base fluid to discuss the flow, heat and mass transfer characteristics. Suitable transformation is employed to transform the governing partial differential equations to a system of nonlinear coupled ordinary differential equations (ODEs). A semi‐analytical technique, that is, in particular, the Adomian decomposition method is implemented to tackle this system of ODEs. The influences of characterizing parameters for the flow phenomena are determined via graphs and displayed. Furthermore, the computed values of the quantities of engineering interest are exhibited through tables and discussed. The main findings of the results are laid down as follows: the Cu‐water nanofluid momentum is more pronounced than that of Ag‐water due to the heavier density of the Ag nanoparticles and an increasing melting parameter is favorable to decrease the fluid temperature, which is useful for the cooling of the substances at the final stage of production in industries.     

Stefan Blowing and Slip Effects on Unsteady Nanofluid Transport Past a Shrinking Sheet: Multiple Solutions

The aim of a present article is to investigate the laminar unsteady two‐dimensional boundary layer flow of a nanofluid with Stefan blowing and slip effect. First, governing boundary layer equations are converted in the ordinary form of the differential equations (ODEs) from partial differential equations using appropriate coordinate transformations. The obtained ODEs are then solved by applying a shooting method with the Runge‐Kutta fourth order method by implementation of the Maple software. The influences of different controlling dimensionless parameters over the dimensionless velocity, temperature, concentration, friction factor, local heat as well as mass transfer have been discussed and represented by plots. It is found that there exist dual solutions for the different applied nanofluid parameters along with the blowing parameter. The results reveal that by increasing the values of the Brownian motion (Nb), thermophoresis (Nt) and blowing parameters (fw), the skin friction increases (decreases) in the first (second) solution.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

Optimal Homotopy Asymptotic Solutions for Nonlinear Ordinary Differential Equations Arising in Flow and Heat Transfer due to Nonlinear Stretching Sheet

Optimal homotopy asymptotic method (OHAM) is used to obtain solutions for nonlinear ordinary differential equations (ODEs) arising in fluid flow and heat transfer at a nonlinear stretching sheet. The solutions for skin friction and temperature gradient for some special cases are tabulated and compared with the available numerical results in the literature. Moreover, OHAM is found to be very easy to use and the technique could be used for solving coupled nonlinear systems of ordinary differential equations arising in science and engineering.     

Entropy generation analysis of natural convective chemically reacting squeezing flow of Casson fluid between parallel disks with Hall and Ion slip currents

This paper concerns the second law analysis of free convective squeezing flow of a chemically reacting Casson fluid confined between two parallel disks with Hall and Ion slip effects. The upper one is impermeable and the lower disk is porous. The linear momentum, energy balance and mass partial differential equations converted as system of ODEs by similarity transformations and tackled with shooting method via fourth order Runge‐Kutta scheme. The impact of various dimensionless geometric and fluid parameters on the velocity fields, temperature and concentration fields, entropy generation and Bejan numbers are studied and presented in the form of pictorially. The present results are correlated with already published outcomes for viscous case and found to be good agreement. The Bejan number of the fluid enhances with Ion slip parameter, whereas the concentration profile of the fluid is decreases with increasing of the Casson fluid parameter. The entropy generation of the fluid is enhanced with Eckert number whereas the Bejan number is decreased with suction/blowing parameter