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The purpose of this paper is to examine the velocity and temperature profile for a two-dimensional flow of single- and multi-walled nanotubes (CNTs)/H₂O nanofluid over a flat porous plate, under the impact of non-uniform heat sink/source and radiation. The influence of suction/blowing, viscous dissipation and magnetic field is also incorporated.

The solution of the PDEs describing the flow of nanofluid is accomplished using Runge–Kutta–Fehlberg approach with shooting scheme.

Quantities of physical importance such as local Nusselt number and skin friction coefficient for both types of nanotubes are computed and shown in tables. Also, the impact of copious factors like Prandtl number, magnetic field, Eckert number, porosity parameter, radiation parameter, non-linear stretching parameter, injection/suction, heating variable, particle volume fraction and non-uniform heat sink/source parameter on temperature and velocity profile is explained in detail with the aid of graphs.

Till date, no study has been reported that examines the role of radiation and non-uniform heat sink/source on MHD flow of CNTs‒water nanofluid over a porous plate. The numerical outcomes attained for the existing work are original and their originality is authenticated by comparing them with earlier published work. This problem is of importance, as there are many applications of the fluid flowing over a flat porous plate.

The purpose of this paper is to examine numerically the magnetohydrodynamic (MHD) free convection and thermal radiation heat transfer of single walled carbon nanotubes-water nanofluid within T-inverted shaped corrugated cavity comprising porous media including uniform heat source/sink for solar energy power plants applications.

The two-dimensional numerical simulation is performed by drawing on Comsol Multiphysics program, based on the finite element process.

The important results obtained show that increasing numbers of Rayleigh and Darcy and the parameter of radiation enhance the flow of convection heat. Furthermore, by increasing the corrugation height, the convection flow increases, but it decreases with the multiplication of the corrugation height. The use of a flat cavity provides better output than a corrugated cavity.

The role of surface corrugation parameters on the efficiency of free convection and heat transfer of thermal radiation within the porous media containing the T-inverted corrugated cavity including uniform heat source/sink under the impact of Lorentz forces has never been explored. A contrast is also established between a flat cavity and a corrugated one.

The purpose of this paper is to focus on MHD unsteady flow of Carreau fluid over a variable thickness melting surface in the presence of chemical reaction and non-uniform heat sink/source.

The flow governing partial differential equations are transformed into ordinary ones with the help of similarity transformations. The set of ODEs are solved by a shooting technique together with the R.K.–Fehlberg method. Further, the graphs are depicted to scrutinize the velocity, concentration and temperature fields of the Carreau fluid flow. The numerical values of friction factor, heat and mass transfer rates are tabulated.

The results are presented for both Newtonian and non-Newtonian fluid flow cases. The authors conclude that the nature of three typical fields and the physical quantities are alike in both cases. An increase in melting parameter slows down the velocity field and enhances the temperature and concentration fields. But an opposite outcome is noticed with thermal relaxation parameter. Also the elevating values of thermal relaxation parameter/ wall thickness parameter/Prandtl number inflate the mass and heat transfer rates.

This is a new research article in the field of heat and mass transfer in fluid flows. Cattaneo–Christov heat flux model is used. The surface of the flow is assumed to be melting.

This paper aims to develop a mathematical model featuring Brownian motion and thermophoresis. The idea of curved stretching subjected to time-dependent non-Newtonian (Sisko) fluid flow is introduced.

Shooting scheme is implemented to compute nonlinear systems.

Velocity profile of Sisko magnetonanofluid enhances for augmented values of curvature parameter.

To the best of the authors’ knowledge, no such analysis has yet been reported.

This paper aims to address the flow of Sisko nanofluid by an unsteady curved surface. Non-uniform heat source/sink is considered for heat transfer analysis.

Numerical solutions are constructed using bvp4c procedure.

Pressure profile inside boundary region is increased when A and K are enhanced.

No such analysis is yet presented.

The purpose of this paper is to study natural convection heat transfer and fluid flow in a square cavity filled with CuO-water nanofluid.

The entire length of the bottom wall of the cavity is covered by two pairs of heat source-sink, whereas the other walls are insulated. The governing equations of fluid flow are discretized using a finite volume method with a collocated grid arrangement. The coupling between velocity and pressure is solved using the SIMPLEC and the Rhie and Chow interpolation is used to avoid the checker-board solutions for the pressure.

The numerical results are reported for the effect of Rayleigh number, solid volume fraction and both presence and absence of thermophoresis and Brownian motion effects. The numerical results show an improvement in heat transfer rate for the whole range of Rayleigh numbers when Brownian and thermophoresis effects are considered. Furthermore, an increase in the Rayleigh number and nanoparticle volume fraction in both cases – when Brownian and thermophoresis effects are neglected or considered – has an excellent influence on heat transfer of nanofluids.

The area of nanofluids is very original.

The purpose of this paper is to highlight the studies of momentum and transmission of heat on mixed convection boundary layer Darcy‒Forchheimer flow of Casson liquid over a linear extending surface in a porous medium. The belongings of homogeneous‒heterogeneous retorts are also affianced. The mechanism of heat transmission is braced out in the form of Cattaneo‒Christov heat flux. Appropriate restorations are smeared to revolutionize coupled nonlinear partial differential equations conforming to momentum, energy and concentration of homogeneous‒heterogeneous reaction equations into coupled nonlinear ordinary differential equations (ODEs).

Numerical elucidations of the transmogrified ODEs are accomplished via a dexterous and trustworthy scheme, namely optimal homotopy analysis method. The convergence of planned scheme is exposed with the support of error table.

The exploration of mixed convection Darcy‒Forchheimer MHD boundary layer flow of incompressible Casson fluid by the linear stretched surface with Cattaneo‒Christov heat flux model and homogeneous‒heterogeneous reactions is checked in this research. Imitations of the core subsidized flow parameters on velocity, temperature and concentration of homogeneous‒heterogeneous reactions solutions are conscripted. From the recent deliberation, remarkable annotations are as follows: non-dimensional velocities in x_a− and x_b− directions shrink, whereas the non-dimensional temperature upsurges when the Casson fluid parameter ameliorates. Similar impact of Casson fluid parameter, magnetic parameter, mixed convection parameter, inertia parameter, and porosity parameter is observed for both the components of velocity field. An escalation in magnetic parameter shows the opposite attitude of temperature field as compared with velocity profile. Similar bearing of Casson fluid parameter is observed for both temperature and velocity fields. Enhancement in concentration rate is observed for growing values of (N_s) and (Sc), and it reduces for (k₁). Both temperature and concentration of homogeneous‒heterogeneous upturn by mounting the magnetic parameter. Demeanor of magnetic parameter, Casson fluid parameter, heat generation parameter is opposite to that of Prandtl number and thermal relaxation parameter on temperature profile.

In many industrial and engineering applications, the current exploration is utilized for the transport of heat and mass in any system.

As far as novelty of this work is concerned this is an innovative study and such analysis has not been considered so far.

The purpose of this paper is to find the approximate solutions of unsteady squeezing nanofluid flow and heat transfer between two parallel plates in the presence of variable heat source, viscous dissipation and inclined magnetic field using collocation method (CM).

The partial governing equations are reduced to nonlinear ordinary differential equations by using appropriate transformations and then are solved analytically by using the CM.

It is observed that the enhancing values of aligned angle of the magnetic causes a reduction in temperature distribution. It is also seen that the effect of nanoparticle volume fraction is significant on the temperature but negligible on the velocity profile.

To the best of the authors’ knowledge, no research has been carried out considering the combined effects of inclined Lorentz forces and variable heat source on squeezing flow and heat transfer of nanofluid between the infinite parallel plates.

Nanofluid research has piqued the interest of scientists due to its intriguing applications in nanoscience, biomedical and electrical engineering, medication delivery, biotechnology, food processing, chemotherapy and other fields. This paper aims to inspect the behavior of the mixed convection magnetohydrodynamic flow and heat transfer induced by a nonlinear stretching/shrinking sheet in a nanofluid with a convective boundary condition. Tiwari and Das mathematical nanofluid model is incorporated in the analysis.

The mathematical model is initially transformed to a nondimensional form by using dimensionless variables. Then the nondimensional partial differential equations are further transformed to a set of similarity equations by using the similarity technique. These equations are solved numerically by the bvp4c function in MATLAB software.

For a certain range of the stretching/shrinking parameter, two solutions are obtained. The friction factor and the heat transfer rate escalate due to suction parameter with adding nanoparticles volume fraction by almost 27.15% and 0.153% for the upper branch solution, while the friction factor declines by almost 30.10% but the heat transfer rate augments by 0.145% for the lower branch solution. Furthermore, the behavior of the nanoparticle volume fractions on the heat transfer rate behaves differently in the presence of the mixed convection effect. The temperature of fluid augments with increasing Biot number for both solutions.

The present work considers the flow and heat transfer induced by a stretching/shrinking sheet in a nanofluid using the Tiwari–Das nanofluid model with a convective boundary condition, where the effect of the buoyancy force is taken into consideration. It is shown that two solutions are found for a certain range of the shrinking strength, while the solution is unique for the stretching case. This study is important for scientists working in the growing field of nanofluids to become familiar with the flow properties and behaviors of such nanofluids.

The purpose of this paper is to scrutinize the heat and mass transfer attributes of three-dimensional bio convective flow of nanofluid across a slendering surface with slip effects. The analysis is carried out subject to irregular heat sink/source, thermophoresis and Brownian motion of nanoparticles.

At first, proper transmutations are pondered to metamorphose the basic flow equations as ODEs. The solution of these ODEs is procured by the consecutive application of Shooting and Runge-Kutta fourth order numerical procedures.

The usual flow fields along with density of motile microorganisms for sundry physical parameters are divulged via plots and scrutinized. Further, the authors analyzed the impact of same parameters on skin friction, heat and mass transfer coefficients and presented in tables. It is discovered that the variable heat sink/source parameters play a decisive role in nature of the heat and mass transfer rates. The density of motile microorganisms will improve if we add Al-Cu alloy particles in regular fluids instead of Al particles solely. A change in thermophoresis and Brownian motion parameters dominates heat and mass transfer performance.

To the best of the knowledge, no author made an attempt to investigate the flow of nanofluids over a variable thickness surface with bio-convection, Brownian motion and slip effects.