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Transformer oil is used to maintain the core and winding of the transformer. The main tasks of transformer oil as an industrial oil are insulation and cooling of a transformer. In the current study, the thermophysical and thermal properties of transformer oil nanofluid with volume percentages of 0.017% and 0.56% have been experimentally investigated which improves the performance of the base fluid due to the high thermal conductivity coefficient of carbon nanotubes compared to transformer oil. Ultrasonic baths and chemically functionalizing techniques were utilized in a two-step process to create nanofluids, which were stabilized by these techniques. In a double-tube carbon steel heat exchanger, the nanofluids were employed, and the thermal characteristics of the base fluid and nanofluids were evaluated. The findings indicated that the effective thermal conductivity improves with increasing temperature and CNT concentration, reaching its maximum value at a temperature of 45 °C in a volume fraction of 0.56. Observations showed that the heat transfer coefficient rose with rising Reynolds number and volume percentage, whereas the friction factor reduced when the hot fluid flowed at an intake temperature of 80 °C compared to the nanofluid in the outer tube. The flow rates for the nanofluids were calculated to be 0.2, 0.3, 0.4 lit/s, and 0.18 lit/s for the hot fluid, respectively. As a general conclusion, carbon nanotubes have a very high potential to improve the thermal performance of transformer oils, which is a serious challenge. [ABSTRACT FROM AUTHOR]

A nanofluid flow under the influence of magnetic field with heat generation/absorption is considered in the cooling of electronic systems, nuclear reactors and physical phenomena such as geology. For the first time, in the present work, natural convection heat transfer in a two-dimensional enclosure with three types of wall shapes filled with a cu-water nanofluid in terms of the effect of Brownian motion of nanoparticles with heat generation/absorption and in the presence of a magnetic field is investigated by using the Lattice Boltzmann Method (LBM). The left vertical wall of the enclosure is examined in two modes: constant temperature heating and linear temperature heating and the cold wall of the enclosure in three different forms (a) diagonal, (b) curved and (c) smooth. The effect of parameters such as the Hartmann number, nanoparticle volume fraction, heat generation/absorption coefficient, cold wall shape and the type of wall heating on the nature of flow and heat transfer is investigated. The results of the authors' research were validated with other sources, and the accuracy of the outputs was ensured. The outcomes of research show that in all instances, increasing the strength of the magnetic field and the heat generation/absorption coefficient decrease the average Nusselt number. In addition, the effect of Hartmann number in various states is different. The highest heat transfer also occurs when the vertical wall has a constant temperature. In this case, the average Nusselt number is about 35% higher on average. The effect of the magnetic field is greater when the cold wall is smooth. By keeping all the parameters constant, the diagonal wall design increases the average Nusselt number by an average of about 30%. The effect of adding nanoparticles to the base fluid on decreasing or increasing the average Nusselt number depends on the Hartmann number and the heat generation/absorption coefficient. Using this numerical simulation, a comprehensive view on the optimal design of heat transfer from equipment can be obtained. [ABSTRACT FROM AUTHOR]

The ultimate goal of the present review paper is to summarize and discuss the findings of the most recently published literature on natural convection of nanofluids in various enclosures. The review covers five different geometries of enclosures: square, circular, triangular, trapezoidal, and unconventional geometries. The core findings of the reviewed papers are summarized and tabulated in a table. Moreover, the relation between the thermophysical properties and the way they affect each other is demonstrated for different geometries of enclosures. Various numerical methods, such as finite difference, finite volume, and finite element methods, as well as different microscopic models, such as single-phase and two-phase models, are considered in this review. [ABSTRACT FROM AUTHOR]

The present examination is considered to discuss the steady, two-dimensional flow of heat and mass transfer of nanofluid flow along with the variable suction under the influence of heat source/sink alongside the viscous dissipation. Because of the stretchable surface, flow is generated. Spectral relaxation technique is used to acquire the numerical solution for the altered nonlinear group of differential equations. Thereafter, outcomes which were obtained from the above numerical technique are validated by comparing with the available outcomes in the existing literature and also with MATLAB inbuilt solver bvp4c. All the acquired results from the above numerical system are shown through graphs and tables to discuss different resulting parameters related to the present analysis. The range of the physical parameters is taken as - 0.1 ≤ f w ≤ 0.5 , 0.1 ≤ N t ≤ 0.7 , 0.1 ≤ N b ≤ 0.7 , 0 ≤ E c ≤ 1.2 , - 0.5 ≤ Q ≤ 0.5 , 1 ≤ P r ≤ 10 , 1 ≤ L e ≤ 5. The main findings are as follows: For the effect of suction parameter, the profiles of velocity, temperature and mass friction are decreased, and the coefficient of skin friction and Nusselt number is declined for the impact of thermophoresis parameter. [ABSTRACT FROM AUTHOR]

In this examination, a mathematical model is developed for Darcy free convection with reference to an isothermal vertical cone along with fixed apex half angle, pointing downward in a nanofluid-saturated porous medium. The aim of this methodology is to offer another sort of primary fluid containing nanoparticles and gyrotactic microorganism's consistence of permeable medium, chemical reaction alongside convective boundary circumstance. The model presents design rules for improvement of imperative fabrication of fertilizer and polymer substance. The present model includes the gyrotactic microorganisms alongside nanoparticles, and cone is dependent on concentration of nanoparticles as well as density of motile microorganisms. Two important impacts Brownian motion as well as thermophoresis are also included in the present model for nanofluids. Reduced system of nonlinear differential equations is derived from governing partial differential of the present flow by using usual transformations along with Oberbeck–Boussinesq approximation. After that, this reduced system is solved numerically with the use of fifth-order Runge–Kutta method in conjunction with the shooting technique. Relevant outcomes are exhibited graphically and talked about quantitatively as for variety in the flow controlling parameters related to the present analysis. Mainly, the observations are bioconvection parameters will in general improve the concentration of the rescaled density of microorganisms and nanoparticles volume fraction and dimensionless motile microorganisms reduce with strong chemical reactions. [ABSTRACT FROM AUTHOR]

The steady flow of a nanofluid (mixture of titanium dioxide and water) in a rectangular channel under the influence of an inclined magnetic field is studied. The channel contains an upstream hot splitter plate in alignment with the upper and lower plates of the channel. It may be said that two incoming channel flows merge to form a single channel flow. This setup may apply to the heating chamber in which titanium dioxide can be used to enhance the thermal transfer rate. It is observed that the position of the splitter plate (that may act as an electric heater) affects the velocity and temperature of the fluid. Therefore, in order to ensure these facts, the examination of the flow behavior and the temperature distributions in the channel if the splitter is placed at different positions in the upstream have been probed. In addition, the effect of nanoparticles on the convection process has been probed. The streamlines are almost similar for a clear fluid as well as for a nanofluid (for low values of solid volume fraction of nanoparticles (i.e. φ < 0.05 )) for all values of the Reynolds number. However, the rise in the temperature is noted for the nanofluid if the concentration of nanoparticles is increased. The increase in the Reynolds number also supports the enhancement of the Nusselt number and, hence, the thermal transfer rate of the nanofluid. The Nusselt number is dominant in the vicinity of the trailing edge of the splitter because the trailing edge exhibits as a stagnation point. In addition, the maximum Nusselt number for nanofluid at moderate Reynolds number (e.g., Re = 100) is enhanced to 0.3% with respect to the clear fluid. Moreover, obtained results for this particular case are compared with the existing literature, and the results compare well. [ABSTRACT FROM AUTHOR]

The aim of the current study is natural convection analysis conjugated with entropy generation analysis in an incinerator shaped permeable enclosure loaded with Al2O3–H2O nanofluid subjected to the magnetic field with a rectangular wavy heater block positioned on the bottom of the cavity wall. The bottom and top horizontal walls are adiabatic; the inclined and vertical walls are thought to be cooled. Firstly, the governing expressions and standard k–ε turbulence model are rewritten from dimensional form to non-dimensional form using dimensionless parameters such as vorticity and stream function. In the next step, the equation of entropy generation is written in dimensionless form. Then, the system of non-dimensional governing equations is solved by the finite volume method (FVM) conjugated with a non-dimensionalization scheme using ANSYS Fluent. Fine grids (wall y+ < 2) with inflated layers have been used for the higher Rayleigh number. The effects of the Rayleigh number in the laminar region (Ra = 103, 104, and 105) and turbulent region (Ra = 108, 0.5 × 109, and 109), Darcy number (Da = 0.01 and 100), Hartmann number (Ha = 0 and 40), and the nanoparticles ( ϕ = 2 % ) on the entropy generation number and natural convection are investigated. The validation results were in good agreement with those of the literature. The results demonstrate that for the laminar region, the Nusselt number and entropy generation number increase as the Rayleigh number and the Darcy number grow, whereas both of them abate as Hartmann number increases. In the turbulent region, the average Nusselt number decreases by ascending the Darcy number. Also, for turbulent region (Ra = 109), convection flow strength decreases 6.28% when Hartmann number increases from 0 to 40, whereas the entropy generation number increases 31.5% at Da = 0.01. [ABSTRACT FROM AUTHOR]

This article unveils the combined impact of heat generation/absorption and Joule heating on MHD flow of Ag-H2O nanofluid into a porous stretching/shrinking divergent/convergent channel with viscous dissipation and solid volume fraction. The mathematical modeling is presented for the existing equations of continuity, momentum, and energy fraction. The reduced boundary value problem is solved numerically employing Runge-Kutta-Fehlberg (RKF) method via shooting scheme and then the outcomes are sketched and interpreted. The results explore that the thermal boundary layer thickness of the stretching divergent and the shrinking divergent channels enhance by increasing the value of the Eckert number, while the opposite tendency is scrutinized on the momentum boundary layer thickness by increasing the value of the porosity parameter for the stretching divergent and the shrinking convergent channels. [ABSTRACT FROM AUTHOR]

The aim of the current study is to investigate the natural convection heat transfer in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. The governing equations that are expressed in dimensionless form are solved by means of control volume finite element method employing a validated FORTRAN code. The dimensionless controlling parameters of the present investigation are shape factor of nanoparticles (m), Hartmann number (Ha), Rayleigh number (Ra), and nanoparticle volume fraction (ϕ). In this study, the amplitude A and number of undulations N are fixed at a constant value of 0.2 and 8, respectively. The obtained results portray that in the presence of waves on the inner wall of the annulus, the heat transfer rate is an ascending function of Rayleigh number, nanoparticle volume fraction and less obvious function of their shape factor, while it is a descending function of the Hartmann number. [ABSTRACT FROM AUTHOR]

Mixed convective heat transfer of Cu–water nanofluid in a porous cavity with non-uniform temperature profiles on vertical sidewalls in the presence of thermal radiation and magnetic field is examined numerically. The vertical sidewalls are heated sinusoidally. Thermally insulated walls are considered at the remaining sides of the cavity. The magnetic field is applied parallel to the horizontal walls uniformly. The SIMPLE algorithm based on finite volume approach is applied to solve the governing equations. The numerical outcomes are discussed in the wide range of the parameters, Richardson number, phase deviation, amplitude ratio, Darcy number, Hartmann number, the thermal radiation, and the solid volume fraction. It is found that the average Nusselt number is decreased in value with the raise in the either Hartmann number or Richardson number in the presence of thermal radiation. The average heat transfer rate is enhanced with an augment in the solid volume fraction, and this enhancement is more effective in the presence of thermal radiation than that of in the absence of thermal radiation. The highest heat transfer rate is obtained for φ = 0 in the forced convection regime, whereas it is maximum at φ = 3 π / 4 in the mixed and free convection regimes. [ABSTRACT FROM AUTHOR]

The paper presents the mixed convection heat transfer and entropy generation of a nanofluid containing carbon nanotubes, flowing in a 3D rectangular channel, subjected to opposed buoyant forces. The governing equations, including the continuity, momentum and energy equations, have been numerically solved using the finite volume technique. The results, including the contours of the axial velocity and temperature, have been presented for different values of the opposed buoyancy parameter (− 300 < Ω < − 100). The outcomes show that with an increase in the opposed buoyancy parameter, the nanofluid velocity near the channel wall drastically reduces and, therefore, causes a reduction in the Nusselt number. In addition, due to the occurrence of backflow phenomenon, an increment of the opposed buoyancy parameter enhances the total entropy generation along the channel. In brief, the friction-induced entropy generation is negligible compared with the entropy generation due to heat transfer. Finally, by increasing the value of the opposed buoyancy parameter, the ratio of the heat transfer rate to irreversibility decreases within the system. [ABSTRACT FROM AUTHOR]

Bioconvection in magneto-nanoliquid embedded with gyrotactic microorganisms across an elongated sheet with velocity slip of second order is addressed. Nonlinear thermal radiation and chemical reaction aspects are retained in energy and concentration equations. Numerical simulations for the modeled problem are proposed via Runge–Kutta–Fehlberg-based shooting technique. Special attention is given to the impact of involved parameters on the profiles of motile microorganisms, nanoparticle volume fraction, temperature and velocity. Our simulations figured out that assisting flow generates more heat transfer than the opposing flow situation. The motile microorganism's boundary layer decayed for higher bioconvection Peclet and bioconvection Lewis numbers. [ABSTRACT FROM AUTHOR]

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This study provides numerical analysis of the free convection of copper-water-based nanofluid filling a triangular cavity with semicircular bottom wall. The cavity sidewalls are maintained at cold temperature, while the semicircular wall is maintained at hot temperature. The other wall segments are thermally insulated. To control the energy transport within the cavity, a uniform magnetic field is applied horizontally. The physical domain is discretized according to the control volume finite element method which has been used to solve the governing equations. The physical and geometrical aspects of the current problem are investigated by inspecting the impacts of Rayleigh number, Hartman number, aspect ratio and the volume fraction of the Cu nanoparticles. Decreasing the radius of the hot semicircle enlarges the average Nusselt number at the absence of the magnetic field. When the magnetic field is applied, this effect is conversed within Ra ≤ 104. This conversed impact does not hold up when Ra is raised to 105. The numerical results are correlated in a sophisticated correlation of the average Nusselt number with other parameters. [ABSTRACT FROM AUTHOR]

In this work, magneto-hydrodynamic natural convection of a nanofluid in a wavy cavity considering Brownian motion is studied numerically using the control volume finite element method. The effective viscosity and thermal conductivity of the nanofluid are defined by the correlation in which the impact of Brownian motion on the thermal conductivity is considered. The considered wavy cavity is heated from the left side and it cooled from the right side. Also, the top and bottom walls of the considered wavy cavity are assumed adiabatic. The impacts of various controlling parameters such as the Rayleigh number, wavy contraction ratio, Hartmann number and undulation number are examined on the contour maps of the streamlines and the isotherms. Further, the average and local Nusselt numbers are calculated and presented graphically and discussed. The findings narrate that the strength of the convective flow has a direct relationship with the Rayleigh number and also it has a reverse relationship with the wavy contraction ratio. [ABSTRACT FROM AUTHOR]

This paper carries on investigation to study the effects of variable magnetic field and thermal radiation on free convective flow of an electrically conducting incompressible nanofluid over an exponential stretching sheet. The model implemented in the present study significantly enriches the thermal conductivity and hence more heat transfer capability of nanofluids. The transformed governing equations have been solved numerically using fourth-order Runge-Kutta method along with shooting technique. The influence of variable magnetic field and thermal radiation associated with thermal buoyancy on the dimensionless velocity, temperature, skin friction and Nusselt number have been analyzed. The obtained numerical results in the present study are validated and found to be in excellent agreement with some previous results seen in the literature. The present study contributes to the result that augmented Hartmann number belittles the fluid flow and enhances the fluid temperature and the related thermal boundary layer thickness. [ABSTRACT FROM AUTHOR]

In this study, natural convection of CuO-water nanofluid in a square cavity with a conductive partition and a phase change material (PCM) attached to its vertical wall is numerically analyzed under the effect of an uniform inclined magnetic field by using finite element method. Effects of various pertinent parameters such as Rayleigh number (between 105 and 106), Hartmann number (between 0 and 100), magnetic inclination angle (between 0∘ and 90∘), PCM height (between 0.2H and 0.8H), PCM length (between 0.1H and 0.8H), thermal conductivity ratio (between 0.1 and 100) and solid nanoparticle volume fraction (between 0 and 0.04) on the fluid flow and thermal characteristics were numerically analyzed. It was observed that when magnetic field is imposed, more reduction in average Nusselt number for water is obtained as compared to nanofluid which is 31.81% for the nanofluid at the highest particle volume fraction. The average heat transfer augments with magnetic inclination angle, but it is less than 5%. When the height of the PCM is increased which is from 0.2H to 0.8H, local and average Nusselt number reduced which is 42.14%. However, the length of the PCM is not significant on the heat transfer enhancement. When the conductivity ratio of the PCM to the base fluid within the cavity is increased from 0.1 to 10, 29.5% of the average Nusselt number enhancement is achieved. [ABSTRACT FROM AUTHOR]

In this study, mixed convection and entropy generation in a nanofluid filled triangular cavity under the influence of rotating cylinder and flexible sidewall were numerically analyzed with finite element method. The inclined sidewall was cooled while the left vertical wall is partially heated. Heat transfer rate enhances as the values of Rayleigh number, angular rotational velocity of the cylinder, elastic modulus of the flexible sidewall and solid nanoparticles volume fraction increase. Nusselt number enhances more in the counter-clockwise direction of the cylinder as compared to clockwise directional rotation and 13.55% of average heat transfer enhancement was achieved for Ω=3000 when compared to motionless cylinder. Average Nusselt number increases by about 30.50% when the elastic modulus of the flexible wall is changed from 500 to 105. The changes in the velocity profiles are significant for the lower part of the triangular enclosure with respect to changes in angular rotational velocity and elastic modulus as compared to upper part of the cavity. Adding nanoparticles increases heat transfer especially for the lower part of the cavity and 49.63% of heat transfer enhancement was achieved for the highest volume fraction when compared to base fluid. Normalized total entropy generation rates enhance for higher values of elastic modulus of the flexible wall, angular rotational speed of the circular cylinder and nanoparticle volume fractions. [ABSTRACT FROM AUTHOR]

Numerical simulation of mixed convection heat transfer in a lid-driven triangular cavity filled with power law nanofluid and with an opening was performed under the effect of an inclined magnetic field. The left vertical wall of the cavity moves in + y-direction, and the bottom wall of the cavity is partially heated. Galerkin weighted residual finite element method was used to solve the governing equations. Influence of Richardson number, Hartmann number, inclination angle, opening ratio and nanoparticle volume fraction on the fluid flow and heat transfer is examined for various power law indices. It was observed that average heat transfer deteriorates as the value of Richardson number and Hartmann number enhances. At the lowest value of Richardson number, the discrepancy between the average heat transfer corresponding to different power law indices is higher. The inclination angle of the magnetic field where the minimum of the average Nusselt number is seen depends on the fluid type. Average heat transfer number is the highest for the highest value of the opening ratio. The average Nusselt number enhances with solid particle volume fraction, and there are slight variations in the reduction in the average Nusselt number when base fluid and nanofluid are considered for various power law indices. [ABSTRACT FROM AUTHOR]

In this paper, the effect of a baffle on free convection heat transfer of a water-Fe3O4 nanofluid in a C-shaped enclosure in the presence of a magnetic field is investigated numerically. The enclosure is subjected to a constant magnetic field. The vertical wall on the left side is maintained at a constant hot temperature of Th, and the right one is kept at a constant cold temperature of Tc. The rest of the walls are insulated. The governing equations are discretized by the control volume method and solved simultaneously by the SIMPLE algorithm. The numerical results show very good agreement with other published works. The results indicate that by increasing the enclosure's aspect ratio, the Nusselt number is increased. It is also found that the volume fraction of nanoparticles can be raised in order to achieve increased cooling in the enclosure. By increasing the aspect ratio, the effect of the nanoparticles on the enhancement of the Nusselt number is more pronounced. Also, the maximum effect of the baffle on the heat transfer is seen at the bottom of the hot wall. Generally, increasing the baffle length produces increases in the Nusselt number. The maximum cooling level is occurred for AR = 0.7 and Bf = 0.2. [ABSTRACT FROM AUTHOR]

In this study, fluid flow and heat transfer in a vertical lid-driven CuO-water nanofluid filled square cavity with a flexible fin attached to its upper wall under the influence of an inclined magnetic field are numerically investigated. The left vertical wall of the cavity is colder than right vertical wall, and it moves in + y direction with constant speed. Horizontal walls of the cavity are insulated. The governing equations are solved with finite element method. The arbitrary Lagrangian-Eulerian method is used to describe the fluid motion within the cavity for the flexible fin in the fluid-structure interaction model. The influence of Richardson number (between 0.01 and 100), Hartmann number (between 0 and 50), inclination angle of the magnetic field (between 0 and 90%), nanoparticle volume fraction (between 0 and 0.05) and Young's modulus of flexible fin (between 250 and 5000) on the flow and heat transfer were numerically studied. It is observed that the presence of the elastic fin affects the flow field and thermal characteristics of the cavity. The local and average heat transfer enhance as the Richardson number, solid volume fraction of the nanoparticle increase whereas deteriorate as the value of the Hartmann number and inclination angle of the magnetic field increases due to the dampening of the fluid motion with Lorentz forces. The addition of the nanoparticles is more effective along the lower part of the right vertical wall where the heat transfer process is effective. The average heat transfer increases by 28.96% for solid volume fraction of 0.05% compared to base fluid when the flexible fin is attached to the upper wall. The average heat transfer deteriorates by 10.10% for cavity with and without fin at Hartmann number of 50 compared to the case without magnetic field. The average heat transfer enhances as the Young's modulus of the flexible fin decreases and the average Nusselt number increases by 13.24% for Young's modulus of 250 compared to configuration for the cavity having the Young's modulus of 5000. [ABSTRACT FROM AUTHOR]