Computer simulation of Cu:AlOOH/water in a microchannel heat sink using a porous media technique and solved by numerical analysis AGM and FEM

Extensive improvements in small-scale thermal systems in electronic circuits,automotive industries,and microcomputers conduct the study of microsystems as essential.Flow and thermic field characteristics of the coherent nanofluid-guided microchannel heat sink are described in this perusal.The porous media approximate was used to search the heat distribution in the expanded sheet and Cu:γ-AlOOH/water.A hybrid blend of Boehme copper and aluminum nanoparticles is evaluated to have a cooling effect on the microchannel heat sink.By using Akbari Ganji and finite element methods,linear and non-linear differential equations as well as simple dimensionless equations have been analyzed.The purpose of this study is to investigate the fluid and thermal parameters of copper hybrid solution added to water,such as Nusselt number and Darcy number so that we can reach the best cooling of the fluid.Also,by installing a piece of fin on the wall of the heat sink,the coefficient of conductive heat transfer and displacement heat transfer with the surrounding air fluid increases,and the efficiency of the system increases.The overall results show that expanding values on the NP(series heat transfer fluid system maximizes performance with temperatures)volume division of copper,as well as boehmite alumina particles,lead to a decrease within the stream velocity of the Cu:AlOOH/water.Increasing the volume fraction of nanoparticles in the hybrid mixture decreases the temperature of the solid surface and the hybrid nanofluid.The Brownian movement improves as the volume percentage of nanoparticles in the hybrid mixture grows,spreading the heat across the environment.As a result,heat transmission rates rise.As the Darcy number increases,the thermal field for solid sections and Cu:AlOOH/water improves.

Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method

A simple and highly accurate semi-analytical method, called the differential transformation method(DTM), was used for solving the nonlinear temperature distribution equation in solid and porous longitudinal fin with temperature dependent internal heat generation. The problem was solved for two main cases. In the first case, heat generation was assumed variable by fin temperature for a solid fin and in second heat generation varied with temperature for a porous fin. Results are presented for the temperature distribution for a range of values of parameters appearing in the mathematical formulation(e.g. N, εG, and G). Results reveal that DTM is very effective and convenient. Also, it is found that this method can achieve more suitable results in comparison to numerical methods.

Analytical investigation of Jeffery-Hamel flow with high magnetic field and nanoparticle by Adomian decomposition method

In this study, the effects of magnetic field and nanoparticle on the Jeffery- Hamel flow are studied using a powerful analytical method called the Adomian decomposition method （ADM）. The traditional Navier-Stokes equation of fluid mechanics and Maxwell＇s electromagnetism governing equations are reduced to nonlinear ordinary differential equations to model the problem. The obtained results are well agreed with that of the Runge-Kutta method. The present plots confirm that the method has high accuracy for different a, Ha, and Re numbers. The flow field inside the divergent channel is studied for various values of Hartmann ：number and angle of channel. The effect of nanoparticle volume fraction in the absence of magnetic field is investigated.

伴有磁场和纳米固体颗粒时的Jeffery-Hamel流动解析研究--Adomian分解法

用一种强有力的解析方法,称为Adomian分解法(ADM),来研究磁场和纳米颗粒对Jeffery-Hamel流动的影响.将该问题模型的控制方程,即将传统的流体力学Navier-Stokes方程和Maxwell电磁方程,简化为非线性的常微分方程.该方法得到的结果与Runge-Kutta方法得到的数值结果相一致,结果用表格列出.不同α,Ha和Re数下的图形表明,本方法可以得到高精度的结果.首先对不同的Hartmann数和管壁倾角,研究喇叭形管道中的流场;最后在没有磁场作用时,研究纳米固体颗粒体积率的影响.

CFD analysis of Al_(2)O_(3)-syltherm oil nanofluid on parabolic trough solar

In this paper,in order to improve the performance of a linear parabolic collector,the thermal effects of using Al_(2)O_(3)-syltherm oil nanofluid with different concentrations and new flange-shaped turbulators are investigated.The simulation was performed by ANSYS-FLUENT-18.2 commercial software using Realizable k-εtwo-equation turbulence model.In accordance with the results,it was realized that increasing the volume fraction of nanoparticles(to 5%)and number of turbulators causes the heat transfer coefficient(h)of the fluid to elevate and ultimately the uniform temperature is created in the absorber.For instance,at a flow rate of 4.5kg/s and an inlet temperature of 350 K,the value of h increases by about 8.5%by changing the number of turbulators from 10 to 15 sets.On the other hand,the results indicate that by changing the arrangement of the turbulators,the heat transfer efficiency of the collector can be increased by 5%for 350 K,3.5%for 450 K and 1%for 550 K inlet temperature.

Thermal energy storage inside the chamber with a brick wall using the phase change process of paraffinic materials:A numerical simulation

Phase change materials are one of the potential resources to replace fossil fuels in regards of supplying the energy of buildings.Basically,these materials absorb or release heat energy with the help of their latent heat.Phase change materials have low thermal conductivity and this makes it possible to use the physical properties of these materials in the tropical regions where the solar radiation is more direct and concentrated over a smaller area.In this theoretical work,an attempt has been made to study the melting process of these materials by applying constant heat flux and temperature.It was found that by increasing the thickness of phase change materials’layers,due to the melting,more thermal energy is stored.Simultaneously it reduces the penetration of excessive heat into the chamber,so that by increasing the thickness of paraffin materials up to 20 mm,the rate of temperature reduction reaches more than 18%.It was also recognized that increasing the values of constant input heat flux increases buoyancy effects.Increasing the Stefan number from 0.1 to 0.3,increases the temperature by 6%.

Numerical investigation on convective heat transfer over two heated wall-mounted cubes in tandem and staggered arrangement

In this study, laminar convective heat transfer over two heated wall-mounted cubes is investigated.Two cubes, which are under constant heat flux, are placed in different tandem and staggeredarrangements on a base plate. This problem is studied for different streamwise and spanwisedistances between two cubes in different Renolds number （Re）, by using finite-volume method.Effects of these parameters are considered on flow and heat transfer characteristics. The resultsshow that the temperature distribution is strongly dependent on flow structure and varies with anychange of flow pattern in different arrangements of cubes. In addition, it is observed that the dragcoefficient, which is influenced more by pressure forces, in staggered arrangement, is greater thantandem arrangement. Results show that by increasing the spanwise distance the amount of meanNusselt number （Nu） of Cube 2 becomes the same as Cube 1.

Forced convection heat transfer due to different inclination angles of splitter behind square cylinder

A numerical investigation is carried out to study the effect of splitter＇s inclination angle behind an inclined square cylinder on the forced convection heat transfer in a plan channel using the lattice Boltzmann method （LBM）. The simulations are conducted for the pertinent parameters in the following ranges： the Reynolds number Re=50-300, the gap ratio G/d = 2, and the splitter＇s inclination angle 8 = 0°-90°. The results show that with the increase in the angle of the splitter, the drag coefficient initially decreases and then increases. Moreover, the time-averaged Nusselt number at a certain angle increases noticeably.

Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method

In this paper, a non-Newtonian third-grade blood in coronary and femoral arteries is simulated analytically and numerically. The blood is considered as the third- grade non-Newtonian fluid under the periodic body acceleration motion and the pulsatile pressure gradient. The hybrid multi-step differential transformation method （Hybrid-Ms- DTM） and the Crank-Nicholson method （CNM） are used to solve the partial differential equation （PDE）, and a good agreement between them is observed in the results. The effects of the some physical parameters such as the amplitude, the lead angle, and the body acceleration frequency on the velocity and shear stress profiles are considered. The results show that increasing the amplitude, Ag, and reducing the lead angle of body acceleration, 9, make higher velocity profiles on the center line of both arteries. Also, the maximum wall shear stress increases when Ag increases.

Metal foam and fin implementation into a triple concentric tube heat exchanger over melting evolution

It is believed that it is going to be a sizeable mismatch between supply and demand when it comes to renewable resources.Lately,researchers are on course to compensate for the unpredictabilityof such resources by the employment of phase change materials(PCMs).Having multiple advantages,PCMs generally suffer from inadequate thermal conductivity which causes prolonged transition procedures.To tackle this issue,this study is fixated on two parameterswhich are linked to fins addition and porous media incorporation in a melting process within a triple concentric tube heat exchanger(TCTHX).The results provided by multiple cases underlined the significance of natural convection in the bare system,although finned and copper-metal-foam cases outshine buoyancy forces by roughly 45%and 97%,respectively.Material is a major determent when it comes to the selection of porous media as Al_(2)O_(3) registered the weakest performance among SiC,Ni and Cu,however,it managed to speed up the process by 75%which still is much higher than the finned system,implying that porous media is of higher priority over fins.The best scenario transpiredwhile fins and copper metal foam were integrated as 26%and 97%soars in efficacy have been obtained compared to individual incorporation of porous media and fins,respectively.

Investigation of nanofluid flow in a vertical channel considering polynomial boundary conditions by Akbari-Ganji’s method

In this research,a vertical channel containing a laminar and fully developed nanofluid flow is investigated.The channel surface’s boundary conditions for temperature and volume fraction functions are considered qth-order polynomials.The equations related to this problem have been extracted and then solved by the AGM and validated through the Runge-Kutta numerical method and another similar study.In the study,the effect of parameters,including Grashof number,Brownian motion parameter,etc.,on the motion,velocity,temperature,and volume fraction of nanofluids have been analyzed.The results demonstrate that increasing the Gr number by 100%will increase the velocity profile function by 78%and decrease the temperature and fraction profiles by 20.87%and 120.75%.Moreover,rising the Brownian motion parameter in five different sizes(0.1,0.2,0.3,0.4,and 0.5)causes lesser velocity,about 24.3%at first and 4.35%at the last level,and a maximum 52.86%increase for temperature and a 24.32%rise for ψ occurs when N b rises from 0.1 to 0.2.For all N_(t) values,at least 55.44%,18.69%,for F(η),andΩ(η),and 20.23%rise for ψ(η)function is observed.Furthermore,enlarging the N r parameter from 0.25 to 0.1 leads F(η)to rise by 199.7%,fluid dimensionless temperature,and dimensional volume fraction to decrease by 18%and 92.3%.In the end,a greater value of q means a more powerful energy source,amplifying all velocity,temperature,and volume fraction functions.The main novelty of this research is the combined convection qth-order polynomials boundary condition applied to the channel walls.Moreover,The AMG semi-analytical method is used as a novel method to solve the governing equations.

Hydrothermal analysis of hybrid nanofluid flow on a vertical plate byconsidering slip condition

Hybrid nanofluids have attracted burgeoning attention owing to their outstanding capacity to improve heat transfer.The influence of velocity and temperature slip parameter and nanoparticls’(NPs’)volume fraction on a vertical plate in the existence of suction has been explored in this work.The investigation’s controlling partial differentiation equations were transformed into a conventional differential equation mechanism using resemblance modifications.Equations were then solved employing the fifth-order Runge-Kutta method.The skin coefficient of friction,temperature,and temperature gradient all rise when the volume percentage of NPs increases from 0 to 2%.Furthermore,a rise in the temperature slip variable was linked to a drop in the Nusselt number(heat transfer).The Nusselt number increased 0.15%and 5.63%respectively when the velocity slip parameter enhanced from 0 to 5 and the NPs volume percentage were increased from 0 to 1.5%.Furthermore,an increase in the temperature slip from 0 to 3 inflated the x-direction skin friction coefficient 8.2%,while inflation in the velocity slip from 0 to 5 was associated with a decline in the x-direction skin friction coefficient 95%.

Importance of induced magnetic field and exponential heat source on convective flow of Casson fluid in a micro-channel via AGM

The study of the natural convective flow of a fluid in the presence of an induced magnetic field has always been of considerable importance due to its many applications in various areas of science,technology,and industry,such as the operation of magnetohydrodynamic generators.This study addresses an analysis of exponential heat source and induced magnetic field on the second-class convection of Casson fluid in a microchannel.The flow is in a vertical microchannel organized by two vertical plates.The answer to governing equations has been grabbed for temperature field,induced magnetic field,and velocity via Akbari-Ganji’s method(AGM).Nusselt number,skin friction coefficient,and current density are approximated.Graphs that describe the conclusion of influential physical variables on velocity,temperature,current density,induced magnetic field,and skin friction coefficient distributions are shown.Comparison of results with numerical method(Runge-Kutta-Fehlberg,RKF-45),homotopy perturbation method,and AGM confirms the accuracy of answers obtained with AGM.

Study on motion of rigid rod on a circular surface using MHPM

In this paper motion of rigid rod on a circular surface is studied analytically.A new analytical method called modified homotopy perturbation method(MHPM)is applied for solving this problem in different initial conditions to show capability of this method.The goveming equation for motion of a nigid rod on the circular surface without slipping have been solved using MHPM.The efficacy of MHPM for handling nonlinear oscillation systems with various small and large oscillation amplitudes are presented in comparison with numerical benchmarks.Outcomes reveal that MHPM has an excellent agreement with numerical solution.The results show that by decreasing the oscillation amplitude,the velocity of rigid rod decreases and for A=w3 the velocity profile is maximum.

Application of Exp-function Method to Wave Solutions of the Sine-Gordon and Ostrovsky Equations

In this work, the Exp-function method is employed to find new wave solutions for the Sine-Gordon and Ostrovsky equation. The equations are simplified to the nonlinear partial differential equations and then different types of exact solutions are extracted by this method. It is shown that the Exp-function method is a powerful analytical method for solving other nonlinear equations occurring in nonlinear physical phenomena. Results are presented in contour plots that show the different values of effective parameters on the velocity profiles.

Motion of a spherical particle in a fluid forced vortex by DQM and DTM

In this study, coupled equations of the motion of a particle in a fluid forced vortex were investigated using the differential transformation method （DTM） with the Pad6 approximation and the differential quadrature method （DO_M）. The significant contribution of the work is the introduction of two new, fast and efficient solutions for a spherical particle in a forced vortex that are improvements over the previous numerical results in the literature. These methods represent approximations with a high degree of accuracy and minimal computational effort for studying the particle motion in a fluid forced vortex. In addition, the velocity profiles （angular and radial） and the position trajectory of a particle in a fluid forced vortex are described in the current study.

Approximate solution of the nonlinear heat transfer equation of a fin with the power-law temperature-dependent thermal conductivity and heat transfer coefficient

In this paper,differential transform method(DTM)is used to solve the nonlinear heat transfer equation of a fin with the power-law temperature-dependent both thermal conductivity and heat transfer coefficient.Using DTM,the differential equation and the related boundary conditions transformed into a recurrence set of equations and finally,the coefficients of power series are obtained based on the solution of this set of equations.DTM overcame on nonlinearity without using restrictive assumptions or linearization.Results are presented for the dimensionless temperature distribution and fin efficiency for different values of the problem parameters.DTM results are compared with special case of the problem that has an exact closed-form solution,and an excellent accuracy is observed.

Propulsion and launching analysis of variable-mass rockets by analytical methods

In this study,applications of some analytical methods on nonlinear equation of the launching of a rocket with variable mass are investigated.Differential transformation method(DTM),homotopy perturbation method(HPM)and least square method(LSM)were applied and their results are compared with numerical solution.An excellent agreement with analytical methods and numerical ones is observed in the results and this reveals that analytical methods are effective and convenient.Also a parametric study is performed here which includes the effect of exhaust velocity(C_(e)),bum rate(BR)of fuel and diameter of cylindrical rocket(d)on the motion of a sample rocket,and contours for showing the sensitivity of these parameters are plotted.The main results indicate that the rocket velocity and altitude are increased with increasing the C_(e) and BR and decreased with increasing the rocket diameter and drag coefficient.

Unsteady time-dependent incompressible Newtonian fluid flow between two parallel plates by homotopy analysis method(HAM),homotopy perturbation method(HPM)and collocation method(CM)

Analytical and numerical analyses have performed to study the problem of the flow of incompressible Newtonian fluid between two parallel plates approaching or receding from each other symmetrically.The Navier–Stokes equations have been transformed into an ordinary differential equation using a similarity transformation.The powerful analytical methods called collocation method(CM),the homotopy perturbation method(HPM),and the homotopy analysis method(HAM)have been used to solve nonlinear differential equations.It has been attempted to show the capabilities and wide-range applications of the proposed methods in comparison with a type of numerical analysis as fourth-order Runge–Kutta numerical method in solving this problem.Also,velocity fields have been computed and shown graphically for various values of physical parameters.The objective of the present work is to investigate the effect of Reynolds number and suction or injection characteristic parameter on the velocity field.

Application of volume of fluid method for simulation of a droplet impacting a fiber

In the present work,impact of a Newtonian drop on horizontal thin fibers withcircular cross section is simulated in 2D views.The numerical simulations of the phenomenaare carried out using volume of fluid(VOF)method for tracking the free surface motion.Impacting of a Newtonian droplet on a circular thin fiber(350 um radius)investigatednumerically.The main focus of this simulation is to acquire threshold radius and velocity of adrop which is entirely captured by the fiber.The model agrees well with the experiments anddemonstrates the threshold radius decreased generally with the increase of impact velocity.Inother words,for velocity larger than threshold velocity of capture perhaps only a small portionof fluid is stuck on the solid and the rest of the drop is ejected for impact velocity smaller thancritical velocity the drop is totally captured.This threshold velocity has been determined whenthe impact is centered.