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Convective flowing and heat transference of non-Newtonian liquid comprising nano-encapsulated phase-changing material (NEPCM) suspensions, filled in a square cavity, is numerically investigated. The molecules of NEPCM are cored with [Formula: see text]-octadecane, shelled by polymethyl-methacrylate, and suspended in non-Newtonian fluid. The enclosure is insulated horizontally and heated vertically. Finite element method (FEM) is implemented for the numerical solution under different variables such as nanoparticles volume fraction ([Formula: see text]), Stefan number ([Formula: see text]), the heat capacity ratio ([Formula: see text]) of about (0.4), the temperature of fusion of the NEPCM ([Formula: see text]) and the density ratio ([Formula: see text]) ([Formula: see text]). The results show that the Nusselt quantity is related to the fusion temperature. An improvement in heat transference is observed when the fusion temperature deviates from the wall temperature, which is in the range of [Formula: see text]. For all power law index values ([Formula: see text]), a linear increase of the Nusselt number with the solid volume fraction is detected. The shear-thinning nanofluid ([Formula: see text]) demonstrates higher Nusselt number values than those of [Formula: see text] and 1.4.

Convective heat transfer in a porous cavity conjugated with an active rotating cylinder is investigated in this paper. Copper–water nanofluid fills the porous cavity. The rotating active cylinder is positioned in such a way conveying heat from the cavity and discharges it outside. The vertical walls of the cavity are thermally insulated while the bottom wall is moving to the right and kept at a constant high temperature. The governing equations are facilitated with the ability to study the tilt of the cylinder-cavity assembly. The effects of Richardson number, Darcy number, inclination angle, conductivity ratio, rotational speed, and nanofluid volume fraction are studied at a constant Rayleigh number of 105. Galerkin finite element method of weak formulation is used to solve the dimensionless governing equation with appropriate boundary conditions. Darcy–Brinkman–Forchheimer model is adopted to govern the flow inside porous medium. Results show that the rotation of the cylinder can enlarge the average Nusselt number more than 223%, while ten times increase of thermal conductivity ratio amplifies Nusselt number by 136%. It is also found that the Richardson number plays an adverse role on the average Nusselt number. Physical explanations and thorough validations are given in the paper.

In this study, the heat transfer, fluid flow and heat capacity ratio are analyzed in an annulus enclosure filled with porous and saturated by a suspension of nanoencapsulated phase change materials (NEPCMs). It consists of phase change material core and a polymer or non-polymer shell. The presence of nanoparticles in the base fluid and the phase change capability of the nanoparticle’s core improve the thermal properties of the base fluid and thermal control process. The inner cylinder wall is reserved at hot temperatures where the encapsulated particles absorb the heat, while the outer cylinder wall is reserved at cold temperatures where the encapsulated particles release the heat. A local thermal non-equilibrium model is adopted for the porous medium. The parameters studied are Rayleigh number (104 ≤ Ra ≤ 106), Stefan number (0.2 ≤ Ste ≤ ∞), melting point temperature of the core (0.05 ≤ θf ≤ 1), the concentration of the NEPCM particles (0% ≤ ϕ ≤ 5%), radius ratio (1.67 ≤ Rr ≤ 2.5), eccentricity (− 0.67 ≤ Ec ≤ 0.67), Darcy number (10−4 ≤ Da ≤ 10−1), porosity (0.3 ≤ e ≤ 0.9) and interface heat transfer coefficient (1 ≤ H ≤ 1000). The results show that the dimensionless temperature of fusion (θf) plays the main role in the improvement in NEPCM on the heat transfer process.

The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied numerically. The fluid inside the enclosure is a CuO–water nanofluid layer in the top space of it, while the bottom space includes a CuO–water nanofluid saturated with a porous medium. Both the right and left sidewalls are assumed adiabatic, while the bottom and the top walls of the enclosure are maintained, respectively, at the hot and cold temperatures. The dimensionless governing equations are expressed for velocity and temperature formulation and modeled by using COMSOL code based on the Galerkin finite element method. Parametric studies on the effects of various significant parameters such as Rayleigh number, Darcy number, the inner cylinder radius, the porous layer thickness, the angular rotational velocity, the solid volume fraction and the number of undulations on the flow and thermal fields together with the heat transfer rate have been performed. The highest value of the stream function for (Ra = 103 and Ra = 105) is seen at (R = 0.2 and S = 0.2). The same thing is observed, when the bottom wall is considered wavy. For (Ra = 103 and N = 0) and (0.5 ≤ S ≤ 0.8), it can be seen that as the inner cylinder radius increases from (R = 0.1) to (R = 0.3), the stream function values increase continuously. It is found that the average Nusselt number increases as the Rayleigh and Darcy numbers, the solid volume fraction, inner cylinder radius and the angular rotational velocity of the cylinder increase, while it decreases as the porous layer thickness and the number of undulations increase. Comparisons with previously published numerical works are performed, and good agreements between the results are observed.

This study investigates the effect of Prandtl number on the natural heat convection inside a square cavity filled with two layers of Ag/water nanofluid-saturated porous medium and non-Newtonian fluid separated by a sinusoidal vertical interface. The left wall, which is adjacent to the nanofluid porous layer, has a relatively hot temperature, while the right wall is cold. Other walls of the cavity are thermally insulated. All cavity walls are impermeable except for the sinusoidal vertical interface located between the two layers. Galerkin finite element method was used to numerically solve the governing differential equations. The study examined the effects of power-law index (0.6

In this paper, numerical Galerkin Finite Element Method (GFEM) is applied for conjugate heat-transfer of a rotating cylinder immersed in Fe3O4-water nanofluid under the heat-flux and magnetic field. The outer boundaries of the cavity were maintained at low temperatures while beside the cylinder were insulated. It is assumed that the cylinder rotates in both clockwise and counter-clockwise directions. The dimensionless governing equations such as velocity, pressure, and temperature formulation were analyzed by the GFEM. The results were evaluated using the governing parameters such as nanoparticles (NPs) volume fraction, Hartmann and Rayleigh numbers, magnetic field angle and NPs shapes. As a main result, the average Nusselt number increases by increasing the NPs volume fraction, inclination angle and thermal conductivity ratios, while increasing the Hartmann number decreased the Nusselt number. Furthermore, platelet NPs had the maximum average Nusselt number and spherical NPs made the minimum values of Nusselt numbers among examined NPs shapes.

In this work, effect of adding MgO nanoparticle to base fluid (water) in car radiator has been implemented experimentally. In this investigation, an experimental test rig has been designed to study effect inlet temperature of nanofluid, the flow rate and nanoparticle volume fraction on heat transfer rates. Six different concentrations of nanofluid of 0.125%, 0.25%, 0.5%,1% ,1.5% and 2% have been prepared by mixed of MgO nanoparticles with water. Reynolds number of nanofluid was between 4500 and 19000.Thermal behavior of an automobile radiator worked with nanofluid has been compared with using pure water in it. So, the fluid circulating rate in radiator has been varied in the extent of the range of 1-8 L/min and fluid inlet temperature is also varied for all experimental. Results emphasized that Nusselt number increases with an increase of liquid inlet temperature, nanoparticle volume fraction and Reynolds number. As well as, the enhancement in heat transfer coefficient due to presence of nanoparticles is more than that without noanoparticles. These results can be achieved to optimize the dimension of an automobile radiator. A good agreement was seen with theoretical and experimental results with many authors

The energy loss through building components resulting in higher energy consumption, thus energy saving has become an essential aspect in design and comfort. This study aims to optimize the thermal insulation of red clay bricks used in the walls of buildings by using a multiscale method. The finite element approach in ABAQUS software has been used to simulate the bricks under different configurations and conditions. Due to cost and time challenges and difficulties in simulation and complex calculations, simplified and applicable equations have been derived to calculate thermal insulation properties. The results show that the paper’s brick design has a significant thermal conductivity reduction that could reach more than one-third of the other corresponding studies. The study goes to fill the hollow bricks by the insulation polyurethane foam (PUF) and comparing the results with air hollow bricks. Besides its other advantages, the outcomes reveal that using the PUF has a noticeable desired-influence in thermal insulation when considering the heat transfer by convection and radiation inside the air cavity of bricks.

Experimental study of γ /Al2O3 with mean diameter of less than 50 nm was dispersed in the distilled water that flows through a pipe consist of five sections as work station ,four sections made of carbon steel metal and one sections made of Pyrex glass pipe, with five nanoparticles volume concentrations of 0%,0.1%,0.2%,0.3%,and 0.4% with seven different volume flow rates 100, 200 , 300, 400, 500, 600 ,and 700ℓ/min were investigated to calculated pressure distribution for the cases without rubber ,with 3mm rubber and with 6mm rubber used to support the pipe. Reynolds number was between 20000 and 130000. Frequency value through pipe was measured for all stations of pipe for all cases. The results show that the pressure drop and wall shear stress of the nanofluid increase by increasing the nanoparticles volume concentrations or Reynolds number, the values of frequency through the pipe increase continuously when wall shear stress increases and the ratio of increment increases as nanofluid concentrations increase. Increasing of vibration frequency lead to increasing the friction factor between the pipe and the wall and thus increasing in pressure drop. Several equations between the wall shear stress and frequency for all volume concentration and for three cases without rubber, with rubber has 3mm thickness ,and with rubber has 6mm thickness. Finally, the results led to that γ /Al2O3 could function as a good and alternative conventional working fluid in heat transfer applications. A good agreement is seen between the experimental and those available in the literature

Taking a more complex engineering geometry into account, magnetohydrodynamic natural convection of nanofluid (Cu-water) in a wavy walled enclosure having a circular hot cylinder inside is investigated by employing Galerkin-weighted residual formulation. In order to investigate the flow and heat transfer characteristics from several perspectives and increase the ability of adaptation to various engineering applications, the influences of the Hartmann number, Ha, Rayleigh number, Ra, and nanoparticle concentration are examined in detail. In addition to that, heat generation and heat absorption situations are also considered within the present work, which are simulated by a heat coefficient in a range of −10 ≤ q ≤ +10. The results revealed that increasing Ha has an insignificant effect on Nusselt number, Nu, at low Ra, however, it significantly pulls Nu down up to 33% for higher Ra, because of restricting convection. It is found that the heat coefficient, q, has a remarkable impact on Nu at low Ra, while its significance is diminished when Ra is increased. For q 0) conversely reduces Nu up to 48%. Besides, variation in heat coefficient does not considerably affect the improvement impact of nanoparticles.

This numerical work examines the impact of an external magnetic field on the hydrothermal aspects of natural convection of a power-law non-Newtonian nanofluid inside a baffled U-shape enclosure. The enclosure is heated from the bottom and cooled from the baffles while the other walls are thermally insulated. Sinusoidal profile is chosen to describe the temperature distribution along the bottom wall. A comprehensive analysis is conducted to study the influence of pertinent parameters including Rayleigh number (Ra), Hartmann number (Ha), nanoparticle volume fraction (ϕ), aspect ratio of cold baffles (AR), inclination angle, and power-law index (n) on the flow and heat transfer characteristics in detail by using Galerkin finite element method. The obtained results show that the impact of n on the Nusselt number (Nu) is considerable for Ra=106 and inappreciable below this value. The influence of n and Ha on the heat transfer is significant when Ha is smaller than 30. For Ha

The numerical simulation of MHD mixed convection due to a rotating circular solid cylinder in a trapezoidal enclosure filled with a Cu-water nanofluid saturated with a porous media was presented in the current paper. The midpoint of the top wall of the enclosure is considered as a center of a cylinder which has a different radius. The remaining of this wall is considered adiabatic. The bottom wall is heated with the temperature of Th and moving to the right hand, while sidewalls are kept isolated and stationary. The Hartmann number, thermal conductivity ratio, angular rotational velocity, Richardson number, inclination angle, cylinder radius, Darcy number, nanofluid concentration vary in the ranges of 0 to 100, 1 to 10, -5 to 5, 0.01 to 100, 0° to 90°, 0.2 to 0.4, 10−5 to 10−1 and 0 to 0.1, respectively. While the convection heat transfer coefficient is considered constant at (h = 5). It was found that, the vertical magnetic field decreases the stream function values more than the inclined and the horizontal fields. Also, the inclination angle of the magnetic field has a profound influence on the thermal performance inside the enclosure. The average Nusselt number rises by raising the Hartmann number, thermal conductivity ratio, cylinder radius and Darcy number, while it decreases by increasing the Richardson number. It was found also that, when the cylinder rotates in a counter clockwise direction (i.e., Ω = 5) and (Kr = 10), the Nuave decreases by about (90 %) when the (Ri) increases from 0.01 to 100. While, it increase by about (35 %) when the (Ha) increases from 0 to 100.

The fluid flow and mixed convection heat transfer of a non-Newtonian (Cu–water) nanofluid-filled circular annulus enclosure in a magnetic field are investigated numerically for a two-dimensional, steady-state, incompressible, laminar flow using the Galerkin finite element method (GFEM). The Prandtl number (Pr = 6.2) and Grashof number (Gr = 100) are assumed to be constants, whereas the Richardson number varies within a range of 0 ≤ Ri ≤ 1, the Hartman number within a range of 0 ≤ Ha ≤60, the Power law index within a range of 0.2 ≤ n ≤ 1.4, and the volume fraction within a range of 0 ≤ φ ≤ 1. The enclosure consists of an outer rotating cylinder that is kept at a cold temperature (Tc) and an inner non-rotating cylinder kept at a hot temperature (Th). The ratio of the inner circular diameter to the annulus space length is kept constant at 2. The results depict that the stream function increases with increasing power law index, even up to n = 1, which causes the fluid to behave as a Newtonian fluid. The magnetic field has a critical impact on the fluid flow pattern. The average Nusselt number increases with decreasing Richardson number, owing to the improved heat transfer by forced convection., Mechanical engineering; Computational fluid dynamics; Nanofluidics; Heat transfer; Magnetohydrodynamics; Computational mechanics; Nanoparticles; Magnetic field; Mixed convection; Annulus circular enclosure; Non-Newtonian fluid; Nanofluid

Heatlines visualization of natural convection heat transfer in trapezoidal-shape cavity filled with nanofluid (TiO2-water) and divided by horizontal porous media partition has been studied numerically using finite element method. Non-uniform temperature is applied at the bottom wall and cold temperature applied to the top wall while two inclined vertical walls were insulated. In this work the influence of many parameters such as, Rayleigh number (103≤Ra≤105), partition porous thickness (0.05≤TH≤0.6), partition porous position (0.15≤HD≤0.75), Darcy number (10−5≤Da≤10−1) and volume of fraction (0≤φ≤0.1). Results are exhibited by means heatlines, isotherms, streamlines rather than local and average Nusselt number. The results show that at a constant Rayleigh number equal to (105) and thickness of porous partition (0.1), the percentage enhancement of heat transfer along the bottom wall with the addition of nanoparticles (ϕ=0.1) is greater than enhancement with the base fluid. While, the maximum value of the percentage enhancement of heat transfer is (4.22%) occurred at porous position equal to 0.5. Also, for a constant position of porous partition (HD=0.5) the percentage enhancement of heat transfer with volume fraction of nanoparticles (0.1) along the bottom wall decreases as the thickness of porous partition and Rayleigh number increased. It can be noticed that there is a good agreement between the current study and those of Chamka and Ismeal, with an approximated absolute error 1.829%.

The natural convection of heat transfer is presented numerically using a temperature gradient from the hot inner corrugated cylinder. Different inner corrugated numbers located inside a cooled wavy-walled enclosure filled with two layers were simulated. The right layer is filled with Ag nanofluid and the left with a fully saturated porous media with similar nanofluid. The porous media with the nanofluid was modeled using the Darcy–Brinkman model. The main dimensionless equations are solved numerically using the method of Galerkin. This study considered the following dimensionless parameters: the Rayleigh number (106 ≥ Ra ≥ 103), the Darcy number (0.1 ≥ Da ≥ 0.00001), the vertical location (0.2 ≥ H ≥ −0.2), the number of sinusoidal inner cylinders (6 ≥ N ≥ 3), fraction volume of the nanoparticle (0.1 ≥ ⱷ ≥ 0), and porous layer thickness (0.8 ≥ XP ≥ 0.2). Results suggest that to increase the fluid flow strength, the internal sinusoidal cylinder must move upward to increase the fluid flow strength. Increasing the thickness of the porous layer reduces the average heat transfer. Results indicate further that highest fluid flow strength occurs at N = 4 when the inner sinusoidal cylinder moves downward vertically.