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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.

This paper aims to explore the numerical study of the steady two-dimensional MHD hybrid Cu-Fe₃O₄/EG nanofluid flows over an inclined porous plate with an inclined magnetic effect. Iron oxide (Fe₃O₄) and copper (Cu) are hybrid nanoparticles, with ethylene glycol as the base fluid. The effects of several physical characteristics, such as the inclination angle, magnetic parameter, thermal radiation, viscous propagation, heat absorption and convective heat transfer, are revealed by this exploration.

Temperature and velocity descriptions, along with the skin friction coefficient and Nusselt number, are studied to see how they change depending on the parameters. Using compatible similarity transformations, the controlling equations, including those describing the momentum and energy descriptions, are turned into a set of non-linear ordinary differential equations. The streamlined mathematical model is then solved numerically by using the shooting approach and the Runge–Kutta method up to the fourth order. The numerical findings of skin friction and Nusselt number are compared and discussed with prior published data by Nur Syahirah Wahid.

The graphical representation of the velocity and temperature profiles within the frontier is exhibited and discussed. The various output values related to skin friction and the Nusselt number are shown in the table.

The new results are compared to past research and discovered to agree significantly with those authors’ published works.

The purpose of this study is to examine how fluid flow and heat transfer are affected by the influence of hybrid nanofluids flowing across a stagnation zone of a stretching curved surface. Stagnation point flow has garnered considerable attention over the past few decades. This is because many technical applications, such as the cooling of nuclear reactors and rotating equipment divisions, rely on stagnation-point flow.

A thorough analysis is conducted of the impacts of several regulating parameters on fluid flow and thermal performance, including the radiation parameter, heat source parameter, mixed convection parameter, porosity parameter curvature and nanoparticle concentration. The laws governing the field of flow equations are transformed by similarity substitutions into two nonlinear ordinary differential equations, which are then solved numerically using Maple. The MR-Solve technique in the built-in Maple package was used. The MR-Solve technique was used to numerically solve highly coupled ordinary differential equation problems. This approach produced highly precise and consistent results. It also provides the best performance while using a minimum amount of CPU and the shortest phrases.

The main conclusions of this study show that axial velocity drops, while radial velocity increases as the mixed convection parameter increases. The rate of heat transmission and skin friction is higher for hybrid nanoparticles with volume fraction percentile (0.01–0.03) than for those with volume fraction percentile (0.1–0.3).

Further research on this topic could examine a broader range of parameter values, suction/injection, entropy, mass equation, micropolar fluid, ternary hybrid nanofluid and Newtonian heating flow on a curved stretching surface.

By investigating a novel physical design that combines the various effect with stagnation flow, this study adds value and offers insights and prospective improvements in the discipline of heat fluid mechanics. Mathematical modeling or experimental studies in a variety of multiphysical contexts can be used to achieve this. Heat exchangers, crystalline procedures, microelectronic machines, systems for conserving energy, integrating operations, food manufacturing, climate control, purification and other engineering domains can all benefit from the geometric configurations investigated in this study. The results of this study greatly aid in optimizing thermal performance in a variety of application domains. This study is novel because it compares several volume fraction percentiles.

A stretching curved surface’s stagnation zone is traversed by hybrid nanofluids, offering insights into how curvature affects heat transfer and fluid flow efficiency. The results aid in the design and improvement of the energy transfer efficiencies for a range of commercial and biological purposes. The results offer possibilities for increased efficiency in a range of applications by developing hybrid nanofluid flow control methods and helping to create ideal thermal systems.

The purpose of this paper is to study numerically the influence of a magnetic field on the transient free convective boundary layer flow of a nanofluid over a moving semi-infinite vertical cylinder with heat transfer

The problem is governed by the coupled non-linear partial differential equations with appropriate boundary conditions. The fluid is a water-based nanofluid containing nanoparticles of copper. The Brinkman model for dynamic viscosity and Maxwell–Garnett model for thermal conductivity are used. The governing boundary layer equations are written according to The Tiwari–Das nanofluid model. A robust, well-tested, implicit finite difference method of Crank–Nicolson type, which is unconditionally stable and convergent, is used to find the numerical solutions of the problem. The velocity and temperature profiles are studied for significant physical parameters such as the magnetic parameter, nanoparticles volume fraction and the thermal Grashof number Gr. The local skin-friction coefficient and the Nusselt number are also analysed and presented graphically.

The present computations have shown that an increase in the values of either magnetic parameter M or nanoparticle volume fraction decreases the local skin-friction coefficient, whereas the opposite effect is observed for thermal Grashof number Gr. The local Nusselt number increases with a rise in Gr and ϕ values. But an increase in M reduces the local Nusselt number.

This paper is relatively original and presents numerical investigation of transient two-dimensional laminar boundary layer free convective flow of a nanofluid over a moving semi-infinite vertical cylinder in the presence of an applied magnetic field. The present study is of immediate application to all those processes which are highly affected by heat enhancement concept and a magnetic field. Further the present study is relevant to nanofluid materials processing, chemical engineering coating operations exploiting nanomaterials and others.

This article presents a numerical study of the heat transfer properties of a nanofluid created using engine oil as the common fluid and Fe3O4 nanoparticles within a square cavity embedded with porous media using the LTNE model in the presence of a Cattaneo–Christov heat flux. To obtain the governing boundary layer equations, the Boussinesq approximation and Darcy model are employed.

By applying the Finite Element method, the modeling equations for dimensionless vorticity, stream function and temperature contours with conforming boundary and initial conditions are scrutinized.

One important finding is that streamlines create a core vortex that is oriented centrally and has longer thermal relaxation times. In contrast, solid state isotherms are hardly affected by growth in thermal relaxation parameter values when compared to fluid state isotherms.

The research work carried out in this work is original and no part is copied from others.

This paper aims to numerically examine the impact of gyrotactic microorganisms and radiation on heat transport features of magnetic nanoliquid within a closed cavity. Thermophoresis, chemical reaction and Brownian motion are also considered in flow geometry for the moment of nanoparticles.

Finite element method (FEM) was depleted to numerically approximate the temperature, momentum, concentration and microorganisms concentration of the nanoliquid. The present simulation was unsteady state, and the resulting transformed equations are simulated by FEM-based Mathematica algorithm.

It has been found that isotherm patterns get larger with increasing values of the magnetic field parameter. Additionally, numerical codes for rate of heat transport impedance inside the cavity with an increasing Brownian motion parameter values.

To the best of the authors’ knowledge, the research work carried out in this paper is new, and no part is copied from others’ works.

Buongiorno’s type nanofluid mass and heat transport appearances inside a cavity filled with gyrotactic microorganisms by captivating thermal radiation is analyzed in the present work. Finite element investigation is instigated to examine the converted momentum, temperature, concentration of microorganisms and concentration of nanofluid equations numerically.

Finite element investigation is instigated to examine the converted momentum, temperature, concentration of microorganisms and concentration of nanofluid equations numerically.

The sway of these influenced parameters on standard rates of heat transport, nanoparticles Sherwood number and Sherwood number of microorganisms is also illustrated through graphs. It is perceived that the rates of heat transport remarkably intensifies inside the cavity region with amplifying thermophoresis number values.

The research work carried out in this paper is original and no part is copied from others’ work.

Using suspended nanoparticles in the base fluid is known as one of the most efficient ways for heat transfer augmentation and improving the thermal efficiency of various heat exchangers. Different types of nanofluids are available and used in different applications. The main purpose of this study is to investigate the effects of using hybrid nanofluid and number of plates on the performance of plate heat exchanger. In this study, TiO₂/water single nanofluid and TiO₂-Al₂O₃/water hybrid nanofluid with 1% particle weight ratio have been used to prepare hybrid nanofluid to use in plate type heat exchangers with three various number of plates including 8, 12 and 16.

The experiments have been conducted with the aim of examining the impact of plates number and used nanofluids on heat transfer enhancement. The performance tests have been done at 40°C, 45°C, 50°C and 55°C set outlet temperatures and in five various Reynolds numbers between 1,600 and 3,800. Also, numerical simulation has been applied to verify the heat and flow behavior inside the heat exchangers.

The results indicated that using both nanofluids raised the thermal performance of all tested exchangers which have a various number of plates. While the major outcomes of this study showed that TiO₂-Al₂O₃/water hybrid nanofluid has priority when compared to TiO₂/water single type nanofluid. Utilization of TiO₂-Al₂O₃/water nanofluid led to obtaining an average improvement of 7.5%, 9.6% and 12.3% in heat transfer of heat exchangers with 8, 12 and 16 plates, respectively.

In the present work, experimental and numerical analyzes have been conducted to investigate the influence of using TiO₂-Al₂O₃/water hybrid nanofluid in various plate heat exchangers. The attained findings showed successful utilization of TiO₂-Al₂O₃/water nanofluid. Based on the obtained results increasing the number of plates in the heat exchanger caused to obtain more increment by using both types of nanofluids.

The purpose of this study is to numerically analyze the thermal and entropy generation characteristics on two-dimensional, incompressible, laminar single-phase flow of Al₂O₃-water nanofluid in a micro-channel subjected to asymmetric sinusoidal wall heating with varying amplitude, length of fluctuation period and phase difference of applied heat flux for Reynolds number in the range of 25-1000.

The numerical computation is based on the Finite Element Method and the Lagrange finite element technique is used for approximating the flow variables within the computational domain.

The average Nusselt number increases with increasing Reynolds number (Re) for all the volume fractions of nanofluid. However, the total entropy generation decreases up to a critical value of Re and increases thereafter. Increase in volume fraction shifts the critical Re towards the lower Re regime. The average Nusselt number and total entropy generation increase with amplitude and length of fluctuation period of heat flux. The optimal choice of volume fraction for lesser entropy generation and higher heat transfer is found to be 3 per cent independent of the value of amplitude, length of fluctuation period and phase difference of the heat flux.

To the best of authors’ knowledge, the interplay of various parameters concerning non-uniform heating in achieving the maximum heat transfer with minimum irreversibility has not been investigated. Focusing on this agenda, 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 inlet Reynolds number, volume fraction of nanofluid, amplitude, length of the period of fluctuation of heat flux and phase difference of applied heat flux.

This study aims to present the experimental and computational performance analysis in compact plate heat exchanger (PHE) using graphene oxide nanofluids at different concentrations and flow rate.

Field emission scanning electron microscope and X-ray diffraction were used to characterize graphene oxide nanoparticles. The nanofluid samples were prepared by varying volume concentration. Zeta potential test was done to check stability of samples. The thermophysical properties of samples have been experimentally measured. The experimental setup of PHE with 60° chevron angle has also been developed. The numerical analysis is done using computational fluid dynamics (CFD) model having similar geometry as of the actual plate. Distilled water at fixed temperature and flow rate is used in hot side tank. Nanofluid at fixed temperature with varying concentration and flow rate is used in cold side tank as coolant.

The numerical and experimental results were compared and found that both results were in good agreement. The results showed ∼13% improvement in thermal conductivity, ∼14% heat transfer rate (HTR), ∼9% in effectiveness and ∼10% in overall heat transfer coefficient at cost of pressure drop and pumping power using nanofluid. Exergy loss also decreased using nanofluid at optimum concentration of 1 Vol.%.

The CFD model can be significant to analyze temperature, pressure and flow distribution in heat exchanger which is impossible otherwise. This study gives ease to predict PHE performance with high accuracy without performing the experiment.