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The purpose of this study is to investigate free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using control volume finite element method (CVFEM).

Governing equations formulated in dimensionless stream function, vorticity and temperature variables using the single-phase nanofluid model with Brinkman correlation for the effective dynamic viscosity and Hamilton and Crosser model for the effective thermal conductivity have been solved numerically by CVFEM.

The impacts of control parameters such as the Rayleigh number, Hartmann number, nanoparticles volume fraction, local triangular heater size, shape factor on streamlines and isotherms as well as local and average Nusselt numbers have been examined. The outcomes indicate that the average Nusselt number is an increasing function of the Rayleigh number, shape factor and nanoparticles volume fraction, while it is a decreasing function of the Hartmann number.

A complete study of the free convection of copper-water nanofluid in an upper half of circular horizontal cylinder with a local triangular heater under the effects of uniform magnetic field and cold cylinder shell using CVFEM is addressed.

This paper aims to explore the double diffusive magneto-hydrodynamic (MHD) squeezed flow of (Cu–water) nanofluid between two analogous plates filled with Darcy porous material in existence of chemical reaction and external magnetic field.

The governing nonlinear equations are transformed into ordinary differential equations by means of similarity transforms, and the coupled mass and heat transference equations are resolved analytically with the application of differential transform method (DTM). The effects of different relevant parameters on velocity, temperature and concentration, including the squeeze number, magnetic parameter, Biot number, Darcy number and chemical reaction parameter, are illustrated with figures. In addition, for various parameters, the local skin friction coefficient, local Nusselt number and local Sherwood number are computed and are graphically displayed.

It is observed that the squeeze number has a direct relationship with Sherwood number and an inverse relationship with skin friction as Biot number increases. With enhanced Biot numbers, the temperature value increases during both squeeze and non-squeeze moments, but the temperature values are higher for squeeze moments compared to the other case.

This research has potential applications in various large-scale enterprises that might benefit from increased productivity.

The results are useful to thermal science community.

Unique and valuable insights are provided by studying the impact of chemical reaction on double diffusive MHD squeezing copper–water nanofluid flow between parallel plates filled with porous medium. In addition, this research has potential applications in various large-scale enterprises that might benefit from increased productivity.

According to the previous research, bioconvection has been recognized as an important mechanism in current engineering and environmental systems. For example, researchers exploit this mechanism in modern green bioengineering to develop environmentally friendly fuels, fuel cells and photosynthetic microorganisms. This study aims to analyse how this type of convection affects the flow behaviour and heat transfer performance of mixed convection stagnation point flow in alumina-copper/water hybrid nanofluid. Also, the impact of a modified magnetic field on the boundary layer flow is considered.

By applying appropriate transformations, the multivariable differential equations are transformed into a specific sort of ordinary differential equations. Using the bvp4c procedure, the adjusted mathematical model is revealed. Once sufficient assumptions are provided, multiple solutions are able to be produced.

The skin friction coefficient is declined when the nanoparticle concentration is increased in the opposing flow. In contrast, the inclusion of aligned angles displays an upward trend in heat transfer performance. The presence of several solutions is established, which simply leads to a stability analysis, hence verifies the viability of the initial solution.

The current findings are unique and novel for the investigation of mixed bioconvection flow towards a vertical flat plate in a base fluid with the presence of hybrid nanoparticles.

The purpose of this study is to investigate the impact of the oscillatory movement on heat transfer within a double periodic lid-driven cubic enclosure filled with copper-water nanofluid and to figure out how the oscillations impact the fluid flow and thermal behavior inside the enclosure. The authors asserted that this study will help to improve the heat transfer efficiency and the thermal performance of various technical engineering equipments.

The cubic enclosure is heated differentially; the left side is cold, the right one is warm and the remaining walls are insulated. Based on the movement directions of the upper and bottom lids, two cases for lid-driven walls are examined (Case 1: same movement for both lids; Case 2: opposite movement for the lids). The finite volume approach was implemented to solve the time-dependent three-dimensional momentum and energy equations, adopting the power low as a scheme of resolution. The numerical study was carried out for a range of parameters: volume fraction (0 ≤ φ ≤ 0.06), Richardson number (0.1 ≤ Ri ≤ 10), non-dimensional lid frequency (2π/50 ≤ Ω ≤ 2π/10) and fixed Grashof number 105.

The numerical simulations were executed for two different cases of the direction of the motion of the oscillatory lids. Based on the findings obtained, decreasing the Richardson number with low lids frequency gives the best heat transfer enhancement for both cases. Furthermore, in the same conditions, swapping from Case 2 to Case 1 leads to enhancing the maximum average Nusselt number obtained by 29.74%. At a high Richardson number, using high lids frequency increases the heat transfer rate compared to using low lids frequency (an enhancement of 4.32% for Case 1 and 3.63% for Case 2). The best heat transfer rate was established for Case 1 when the lids move positively, transporting the cold flow to the hot side. In all cases, increasing the concentration of nanoparticles improves the heat transfer.

The current study gives an understanding of the problem of mixed convection in a cubic enclosure with oscillatory walls, which has received little attention. And also, there has been no study published on unsteady mixed convection within a double oscillatory lid-driven cavity.

The purpose of this paper is to theoretically investigate the unsteady separated stagnation-point flow and heat transfer past an impermeable stretching/shrinking sheet in a copper (Cu)-water nanofluid using the mathematical nanofluid model proposed by Tiwari and Das.

A similarity transformation is used to reduce the governing partial differential equations to a set of nonlinear ordinary (similarity) differential equations which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters.

It is found that the solution is unique for stretching case; however, multiple (dual) solutions exist for the shrinking case.

The authors believe that all numerical results are new and original, and have not been published elsewhere.

The purpose of this paper is to focus on the numerical modelling of transient natural convection flow of an incompressible viscous nanofluid past an impulsively started semi-infinite vertical plate with variable surface temperature.

The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. A robust, well-tested, Crank-Nicolson type of implicit finite-difference method, which is unconditionally stable and convergent, is used to solve the governing non-linear set of partial differential equations.

The local and average values of the skin-friction coefficient (viscous drag) and the average Nusselt number (the rate of heat transfer) decreased, while the local Nusselt number increased for all nanofluids, namely, aluminium oxide-water, copper-water, titanium oxide-water and silver-water with an increase in the temperature exponent m. Selecting aluminium oxide as the dispersing nanoparticles leads to the maximum average Nusselt number (the rate of heat transfer), while choosing silver as the dispersing nanoparticles leads to the minimum local Nusselt number compared to the other nanofluids for all values of the temperature exponent m. Also, choosing silver as the dispersing nanoparticles leads to the minimum skin-friction coefficient (viscous drag), while selecting aluminium oxide as the dispersing nanoparticles leads to the maximum skin-friction coefficient (viscous drag) for all values of the temperature exponent m.

The Brinkman model for dynamic viscosity and Maxwell-Garnett model for thermal conductivity are employed. The governing boundary layer equations are written according to The Tiwari-Das nanofluid model. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered.

The present simulations are relevant to nanomaterials thermal flow processing in the chemical engineering and metallurgy industries. This study also provides an important benchmark for further simulations of nanofluid dynamic transport phenomena of relevance to materials processing, with alternative computational algorithms (e.g. finite element methods).

This paper is relatively original and illustrates the influence of variable surface temperature on transient natural convection flow of a viscous incompressible nanofluid and heat transfer from an impulsively started semi-infinite vertical plate.

The purpose of this paper is to study heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet placed in saturated porous medium with internal heat generation or absorption. The authors further introduce a new algorithm for solving heat transfer problems in fluid mechanics. The model used for the nanofluid incorporates the nanoparticle volume fraction parameter and a consideration of the chemical reaction effects among other features.

The partial differential equations for heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet were transformed into a system of nonlinear ordinary differential equations. Exact solutions for the boundary layer equations were obtained in terms of a confluent hypergeometric series. A novel spectral relaxation method (SRM) is used to obtain numerical approximations of the governing differential equations. The exact solutions are used to test the convergence and accuracy of the SRM.

Results were obtained for the fluid properties as well as the skin friction, and the heat and mass transfer rates. The results are compared with limiting cases from previous studies and they show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems.

A new algorithm is used for the first time in this paper. In addition, new exact solutions for the energy and mass transport equations have been obtained in terms of a confluent hypergeometric series.

In this article, we consider the magnetohydrodynamic (MHD) nanofluid flow over a rotating stretchable disk through porous medium. For porous medium, Darcy’s relation is used. It also encompassed the impact of nanoparticles shape on MHD nanofluid flow and heat transfer. The effect of thermal radiation and Joule heating is also being considered.

Three categories of nanoparticles are taken into deliberation, i.e. copper, silver and titanium oxide. The nanofluid is made of pure water and various types of sphere- and lamina-shaped nanoparticles. By using appropriate similarity transformation, the governing partial differential equations are transformed to ordinary one. The coupled ordinary differential equations system is tackled numerically by bvp4c method.

The impact of various pertinent parameters, i.e. solid volume fraction, Hartman number, thermal radiations parameter, Reynolds number, Eckert number, porosity parameter and ratio parameter, on flow and Nusselt number with a fixed value of Prandtl number at 6.2 is discussed in details. The obtained results are presented in the concluding section. The lamina shape of nanoparticles in silver-water performed an excellent role on temperature distribution. The heat transfer rate of lamina shape in copper-water was found to be greater in the system of flow regime.

The authors have discussed the shape effect of nanoparticles on MHD nanofluid flow over a rotating stretchable disk through porous medium using three categories of nanoparticles, such as copper, silver and titanium oxide. To the best of the authors’ knowledge, this is the first study on mass and heat transfer nanofluid flow and no such study is yet published in literature. A detailed mathematical analysis has also to be carried out to prove the regularity of model. The authors believe that the numerical results are original and have not been copied from any other sources.

The purpose of this paper is to study the thermal behavior of radial porous fin surrounded by water-base copper nanoparticles under the influence of radiation.

In order to optimize the response variable, the authors perform sensitivity analysis with the aid of response surface methodology (RSM). Moreover, this study enlightens the applications of artificial neural networks (ANN) for predicting the temperature gradient. The governing modeled equations are firstly non-dimensionalized and then solved with the aid of Runge–Kutta fourth order together with the shooting method in order to guess the initial conditions.

Numerical results are analyzed and presented in the form of tables and graphs. This study reveals that the temperature of the fin is decreasing as the wet porous parameter increases (m₂) and the temperature for 10% concentration of nanoparticles are higher than 5 and 1%. Physical parameters involved in the study are analyzed and processed through RSM. It is come to know that sensitivity of temperature gradient to radiative parameter (Nr) and convective parameter (Nc) is positive and negative to dimensionless ambient temperature (θ_a). Furthermore, after ANN training it can be argued that the established model can efficiently be used to predict the temperature gradient over a radial porous fin for the copper-water nanofluid flow.

To the best of our knowledge, only a few attempts have been made to analyze the thermal behavior of radial porous fin surrounded by copper-based nanofluid under the influence of radiation and convection.

The purpose of this study is to examine the flow and heat transfer performance of titanium oxide/water and copper/water nanofluids with varying nanoparticle morphologies by considering magnetic, Joule heating and viscous dissipation effects. Furthermore, it studies the irreversibility caused by the flow of a hydromagnetic nanofluid past a radiated stretching sheet by considering different shapes of TiO₂ and Cu nanoparticles with water as the base fluid.

In this study, the authors investigated entropy production in an unsteady two-dimensional magneto-hydrodynamic nanofluid regime using water as the base fluid and five unique TiO₂ and Cu nanoparticle morphologies. Using appropriate similarity transformations, the controlling nonlinear system of partial differential equations is transformed into a system of ordinary differential equations. The shooting technique with Runge–Kutta method was then used to solve these equations quantitatively. The findings of this study are depicted graphically, and the skin friction corresponding to various nanoparticle geometries and physical parameter variations is tabulated.

To assess the reliability of the current findings, a tabular representation of the data was compared to that of previously published studies. It is noted that a reduction in thermal energy was detected as a result of the higher levels of Prandtl number (Pr). It is further analysed that the highest heat energy generation of TiO₂ nanoparticles was larger than that of Cu nanoparticles. The most important finding was that the sphere-shaped Cu/H₂O nanofluid had the lowest velocity and greatest temperature. Also, Cu nanoparticles in the shape of platelets generate the most entropy, while TiO₂ nanoparticles in the shape of spheres generate the least.

To the best of the knowledge of the authors, the attempt to investigate the previously unexplored shape effects of TiO₂ and Cu nanoparticles on the heat transfer enhancement and inherent irreversibility caused by hydromagnetic nanofluid flow past a radiated stretching sheet with magnetic, Joule heating and viscous dissipation effects. This study fills this gap in the existing literature and encourages scientists, engineers and businesses to do more research in this area. This model can be used to improve heat transfer in systems that use renewable energy, thermal management in industry and the processing of materials.