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This paper aims to present the analytical investigation on an unsteady magneto-convective rotation of an electrically conducting non-Newtonian Casson hybrid nanoliquid past a vertical porous plate. The effects of thermal radiation, heat source/sink and hydrodynamic slip phenomenon are also taken into account. Ethylene glycol (EG) is adopted as a base Casson fluid. The Casson fluid model is accounted for to describe the rheological characteristics of non-Newtonian fluid. EG with copper and alumina nanoparticles is envisaged as a non-Newtonian Casson hybrid nanoliquid. The copper-alumina-ethylene glycol hybrid nanoliquid is considered as the regenerative coolant.

The perturbation method is implemented to develop the analytical solution of the modeled equations. Acquired solutions are used to calculate the shear stresses and the rate of heat transfer in terms of amplitudes and phase angles. Numerical results are figured out and tabled to inspect the physical insights of various emerging parameters on the pertinent flow characteristics.

This exploration discloses that the velocity profiles are strongly diminished by the slip parameter. Centrifugal and Coriolis forces caused by the plate rotation are found to significantly change the entire flow regime. The supplementation of nanoparticles is to lessen the amplitude of the heat transfer rate. A comparative study is carried out to understand the improvement of heat transfer characteristics of Casson hybrid nanoliquid and Casson nanoliquid. However, the Casson hybrid nanoliquid exhibits a lower rate of heat transfer than the usual Casson nanoliquid.

This proposed model would be pertinent in oceanography, meteorology, atmospheric science, power engineering, power and propulsion generation, solar energy transformation, thermoelectric and sensing material processing, tumbler in polymer manufacturing, etc. Motivated by such practical implications, the proposed study has been unfolded.

The novelty of this paper is to examine the simultaneous effects of the magnetic field, Coriolis force, suction/injection, slip condition and thermal radiation on non-Newtonian Casson hybrid nanoliquid flow past an oscillating vertical plate subject to periodically heating in a rotating frame of reference. A numerical comparison is also made with the existing published results under some limiting cases and it is found that the results are in good agreement with them. An in-depth review of the literature and the author’s best understanding find that such aspects of the problem have so far remained unexplored.

The purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.

The coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.

Results highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.

The originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

The main purpose of this numerical work is to study free convection of Casson fluid in a square differentially heated cavity taking into account the effects of thermal radiation and viscous dissipation.

The cavity is heated from the left vertical wall and cooled from the right vertical wall while horizontal walls are insulated. The governing partial differential equations invoking Rosseland approximation for thermal radiation with corresponding boundary conditions have been solved by finite difference method of the second-order accuracy using dimensionless variables stream function, vorticity and temperature. The governing parameters are Rayleigh number (Ra = 10⁵), Prandtl number (Pr = 0.1, 0.7, 7.0), Casson parameter (γ = 0.1-5.0), radiation parameter (R_d = 0-10), Eckert number (Ec = 0-1.0).

It is found that an increase in Casson parameter leads to the heat transfer enhancement and fluid flow intensification. While a growth of Eckert number illustrates the heat transfer suppression.

The originality of this work is to analyze for the first-time natural convective fluid flow and heat transfer of a Casson fluid within a differentially heated square cavity under the effects of thermal radiation and viscous dissipation. The results would benefit scientists and engineers to become familiar with the flow behavior of such non-Newtonian fluids, and the way to predict the properties of this flow for possibility of using this specific fluid in various engineering and industrial processes, such as chyme movement in intestine, blood flows, lubrication processes with grease and heavy oils, glass blowing, electronic chips, food stuff, slurries, etc.

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.

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation.

The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables.

Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile.

The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken.

Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

The present investigation aims to deal with the study of unsteady, heat-generating/-absorbing and chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium in the presence of cross-diffusion effects.

A numerical computation for the governing equations has been performed using implicit finite difference method of Crank–Nicolson type.

The influence of various physical parameters on velocity, temperature and concentration distributions is illustrated graphically, and the physical aspects are discussed in detail. Numerical results for average skin-friction, Nusselt number and Sherwood number are tabulated for the pertaining physical parameters. Results indicate that Soret and Dufour effects have notable influence on heat and mass transfer characteristics of the fluid when the temperature and concentration gradients are high. It is also observed that the consideration of heat generation/absorption plays a vital role in predicting the heat transfer characteristics of moving fluids.

Consider a two-dimensional, unsteady, free convective flow of an incompressible Casson fluid over a vertical cone and a flat plate saturated with non-Darcy porous medium. The fluid properties are assumed to be constant except for density variations in the buoyancy force term. The fluid flow is moderate and the permeability of the medium is assumed to be low, so that the Forchheimer flow model is applicable.

The flow of Casson fluids (such as drilling muds, clay coatings and other suspensions, certain oils and greases, polymer melts and many emulsions), in the presence of heat transfer, is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs.

In the heat and mass transfer investigations, the Casson fluid model is found to be accurately applicable in many practical situations in the wings of polymer processing industries and biomechanics, etc.; some prominent examples are silicon suspensions, suspensions of bentonite in water and lithographic varnishes used for printing inks.

The motivation of the present study is to bring out the effects of heat source/sink, Soret and Dufour effects on chemically reacting Casson fluid flow over a vertical cone and flat plate saturated with non-Darcy porous medium. The flow of Casson fluids (such as certain oils and greases, polymer melts and many emulsions) in the presence of heat transfer is an important research area because of its relevance in the optimized processing of chocolate, toffee and other foodstuffs. A numerical computation for the governing equations has been performed using implicit finite difference method of the Crank–Nicolson type.

To amend the efficiency of engineering processes and electronic devices, it is very urgent to assess the irreversibility in the term entropy generation (EG). The efficiency of energy transportation in a system can be improved by minimization of the rate of EG. In this context, the aim of the present study is to estimate irreversible losses of an unsteady magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting non-Newtonian molybdenum disulfide-polyethylene glycol Casson nanofluid past a moving vertical plate with slip condition under the influence of Hall current, thermal radiation, internal heat generation/absorption and first-order chemical reaction. Molybdenum disulfide (MoS₂) nanoparticles are dispersed in the base fluid polyethylene glycol (PEG) to make Casson nanofluid. Casson fluid model is considered to characterize the rheology of the non-Newtonian fluid, whereas Rosseland approximation is adopted to simulate the thermal radiative heat flux in the energy equation.

The closed-form solutions are obtained for the model equations by using the Laplace transform method (LTM). Graphs and tables are prepared to examine the impact of pertinent flow parameters on the pertinent flow characteristics. The energy efficiency of the system via the Bejan number is studied extensively.

Analysis reveals that Hall current has diminishing behavior on entropy production of the thermal system. Strengthening of the magnetic field declines the velocity components and prop-ups the rate of EG. Adding nanoparticles into the base fluid reduces the EG, whereas there are an optimum volume fraction of nanoparticles for which the EG is minimized. Further, the rate of decay of EG is prominent in molybdenum disulfide-polyethylene glycol in comparison to PEG.

The results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of embedded thermophysical parameters. In view of this agenda, this study would be adjuvant in powder technology, polymer dynamics, metallurgical process, manufacturing dynamics of nano-polymers, petroleum industries, chemical industries, magnetic field control of material processing, synthesis of smart polymers, etc.

The novelty of this study is to encompass the analytical solution by using the LTM. Such an exact solution of non-Newtonian fluid flow is rare in the literature. Limited research articles are available in the field of EG analysis during the flow of non-Newtonian nanoliquid subject to a strong magnetic field.

The purpose of this paper is to consider a two-dimensional unsteady Casson magneto-nanfluid flow over an inclined plate embedded in a porous medium. The novelty of the present study is to investigate the effects of Soret–Dufour on unsteady magneto-nanofluid flow.

Appropriate similarity transformations are used to convert the governing non-linear partial differential equations into coupled non-linear dimensionless partial differential equations. The transformed equations are then solved using spectral relaxation method.

The effects of controlling parameters on flow profiles is discussed and depicted with the aid of graphs. Results show that as the non-Newtonian Casson nanofluid parameter increases, the fluid velocity decreases. It is found that the Soret parameter enhance the temperature profile, while Dufour parameter decreases the concentration profile close to the wall.

The novelty of this paper is to consider the combined effects of both Soret and Dufour on unsteady Casson magneto-nanofluid flow. The present model is in an inclined plate embedded in a porous medium which to the best of our knowledge has not been considered in the past. The applied magnetic field gives rise to an opposing force which slows the motion of the fluid. A newly developed spectral method known as spectral relaxation method (SRM) is used in solving the modeled equations. SRM is an iterative method that employ the Gauss–Seidel approach in solving both linear and non-linear differential equations. SRM is found to be effective and accurate.

Microfluidics is one of the interesting areas of the research in thermal and engineering fields due to its wide range of applications in a variety of heat transport problems such as micromixers, micropumps, cooling systems for microelectromechanical systems (MEMS) micro heat exchangers, etc. Lower cost with better thermal performance is the main objective of these devices. Therefore, in this study, the entropy generation in an electrically conducting Casson fluid flow through an inclined microchannel with hydraulic slip and the convective condition hves been numerically investigated. Aspects of viscous dissipation, natural convection, joule heating, magnetic field and uniform heat source/sink are used

Suitable non-dimensional variables are used to reduce the non-linear system of ordinary differential equations, and then this system is solved numerically using Runge-Kutta-Fehlberg fourth fifth order method along with shooting technique. The obtained numerical solutions of the fluid velocity and temperature are used to characterize the entropy generation and Bejan number. Also, the Nusselt number and skin friction coefficient for various values of parameters are examined in detail through graphs. The obtained present results are compared with the existing one which is perfectly found to be in good agreement.

It is established that the production of the entropy can be improved with the aspects of joule heating, viscous dissipation and internal heat source/sink. The entropy generation enhances for increasing values of Casson Parameter (β) and Biot number (Bi). Furthermore, it is interestingly noticed that the enhancement of Reynolds number and uniform heat source/sink shows the dual behaviour of the entropy generation due to significant influence of the viscous forces in the region close to the channel walls. It was observed that increasing behaviour of the heat transfer rate for enhancement values of the Eckert number and heat source/sink ratio parameter and the drag force are retarded with higher estimations of Reynolds number.

Entropy generation analysis on MHD Casson fluid flow through an inclined microchannel with the aspects of convective, Joule heating, viscous dissipation, magnetism, hydraulic slip and internal heat source/sink has been numerically investigated.

The purpose of this study is to provide a numerical investigation of Casson nanofluid along a vertical nonlinear stretching sheet with variable thermal conductivity and viscosity.

The boundary-layer equations are presented in the dimensionless form using proper non-similar transformations. The subsequent non-dimensional nonlinear partial differential equations are solved using the implicit finite difference technique. To linearize the nonlinear terms present in these equations, the quasilinearization technique is used.

The investigation showed graphically the temperature, velocity and nanoparticle volume fraction for particular included physical parameters. It is observed that the velocity profile decreases with an increase in the values of Casson fluid parameter while increases with an increase in the viscosity variation parameter. The temperature profile enhances for large values of velocity variation parameter and thermal conductivity parameter while it reduces for large values of thermal buoyancy parameter. Further, the Nusselt number and skin-friction coefficient are introduced which are helpful in determining the physical aspects of Casson nanofluid flow.

The immediate control of heat transfer in the industrial system is crucial because of increasing energy prices. Recently, nanotechnology is proposed to control the heat transfer phenomenon. Ongoing research in complex nanofluid has been fruitful in various applications such as solar thermal collectors, nuclear reactors, electronic equipment and diesel–electric conductor. A reasonable amount of nanoparticle when added to the base fluid in solar thermal collectors serves to deeper absorption of incident radiation, and hence it upgrades the efficiency of the solar thermal collectors.

The non-similar solution of Casson nanofluid due to a vertical nonlinear stretching sheet with variable viscosity and thermal conductivity is discussed in this work.