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Heat pipes are crucial in a wide range of applications, ranging from space satellites and industrial systems to electronic cooling and X-ray tube thermal management. This study introduces a method investigation into vapor flows within a flat plate heat pipe, utilizing the collocation method (CM) and the fourth-order Runge-Kutta-Fehlberg (RKF45) method. Building on previous efforts, this work explores the effects of the evaporator-to-condenser length ratio and Reynolds number on velocity and pressure distributions along the entire heat pipe. The significance of this research lies in its ability to elucidate critical parameters that directly influence heat pipe performance, offering deeper insights that are vital for optimizing design and efficiency. The primary motivation of this study is to fill existing gaps in the literature by developing a comprehensive analytical model that accurately characterizes vapor and liquid flow in asymmetrical flat plate heat pipes. The model's validity is confirmed through a satisfactory agreement with numerical results, underscoring the reliability of the methods used. Notably, the findings reveal that higher Reynolds numbers reduce pressure drop and shift the maximum velocity toward the bottom wick in the evaporation section, providing valuable guidance for future design improvements. Additionally, this research presents a powerful method for solving non-linear ordinary differential equations, offering significant time savings and enabling predictive functions. These contributions are poised to enhance the performance of thermal management systems across various engineering disciplines.

A significant factor in the storage and blending of crude oil in reservoirs and its transfer and transmission to the pipeline in cold regions is sufficient heating and blending in the reservoir to reach the desired temperature and quality. Rapid heating and better blending prevent it from becoming sludg and jelly-like in the pipeline and damaging facilities, pumps, etc. The foreign ship, at the right operational time, sends its cargo to the tank or receives it from it and prevents the company from receiving damages due to the ship's time waste. In crude oil storage tanks, considering that crude oil has a low thermal conductivity coefficient, heat transfer in the inner layers of crude oil takes place slowly, so multiple hot crude oil flow nozzles are used to inject into the reservoir to rate up heating and better blending. The blending and homogenization or blending of stored crude oil in storage tanks, its heating takes place at three molecular, vortex, convection, which as a result, the rate of each of them increases, the rate of blending and homogenization and also heating increases. The process of heat transfer and blending is essentially dependent on the buoyancy of the fluid resulting from the hot crude oil jet flow by the nozzles. The Froude number along with the Reynolds number and diffusion number stronger indicates better buoyancy and stronger and faster heat transfer and more homogeneous blending and vice versa. Increasing or decreasing the temperature and output velocity of hot crude oil from the nozzles, changing the arrangement of the nozzles and their number, changing the diameter and angle of the nozzle throw can have a significant effect on increasing or decreasing the Froude and Reynolds numbers and diffusion number and as a result, increase or decrease the rate of heating and blending of stored crude oil inside the tank, which is examined in this activity experimentally and numerically. The finite volume method and standard k − ε turbulence model are used to numerically investigate the heat transfer features of crude oil inside the floating roof tank under the hot crude oil jet flow heating mode. By choosing the correct arrangement of hot jet flow nozzles, the appropriate diameter of the nozzles, the temperature and output velocity of the hot jet flow fluid, the appropriate flow rate of the jet, the appropriate throw angle of the hot jet flow nozzles, etc., the heating and blending rate of the crude oil storage tank can be increased by 50–70 percent compared to when submerged heat exchanger are used inside the tank, which is currently common, and reduce its operational heating and blending time by the same amount.

The objective of this study is to enhance the rate of solidification of Phase Change Materials (PCMs) in Latent Thermal Energy Storage Systems (LTESSs) by incorporating hybrid nanoparticles (MoS2-Fe3O4) and utilizing a unique optimized antenna-shaped fin configuration in a triplex-tube energy storage device. The problem was solved by applying the Finite Element Method (FEM), considering some numerical analysis. For studying the effects of a variety of angles and dimensions of antenna-shaped fins with a radiation parameter during the process of solidification, a computational model validated by historical experimental data is developed. This paper will present an analysis of the effect of different angles and dimensions of antenna-shaped fins in conjunction with the radiation parameter during the solidification process. Results show that the full solidification time (FTS) decreases by 51 % when Rd = 1 compared to zero radiation, indicating a significant improvement in the efficiency of the solidification process. Furthermore, at 4000 s, the average temperatures for Rd = 0 and Rd = 1 differ, showing a noticeable drop of 4.51°. Furthermore, using Taguchi and Response Surface Methodology (RSM), the optimal settings were determined to minimize the full solidification time in the triplex-tube LHESS. Interestingly, a highly accurate and precise correlation for FST was established.

Within this research, we examined the convective flow of a blend of ternary hybrid nanofluids and single nanofluids with a stagnation point caused by a stretched cylinder. The purpose of this study is to investigate the effect of using a ternary hybrid nanofluid instead of a single nanofluid. Water is used as the base fluid in this investigation. The single nanofluid is made of copper and the ternary hybrid nanofluid is made of Molybdenum disulfide, copper, and silver. The impact of the curvature parameter, nanoparticle volume fraction, mixed convection parameter, velocity ratio, shape factor, conjugate number and Eckert number parameters on temperature and velocity profiles has been investigated. Differential equations with partial derivatives were transformed to equations of ordinary differential type. The ODEs were then solved using the RK5th method. The ternary hybrid nanofluid has greater advantages than the single nanofluid and enhances the velocity and temperature compared to the single nanofluid, according to this study. Furthermore, the results showed that when curvature parameter, volume fraction and shape factor improved, so did the velocity and temperature profile. The results showed that moving from a single nanofluid to a ternary hybrid nanofluid at shape factor equal to 16.2 (Lamina) boosts the velocity by 20 %. Also, in Eckert number equal to 0.45, and substituting the ternary hybrid nanofluid boosts the temperature tenfold.

The flow phenomena become more significant and varied when an extra heat source, a chemical reaction, and thermal and solutal buoyancy forces exist. Transport property optimization results from the current demand in several sectors dependent on the solutal reactant and the heat source given. Partial differential equations are transformed into ordinary equations using appropriate similarity transformations. Python was used as an efficient tool to solve equations in this research. According to the available facilities and libraries, Python can efficiently solve various physics and engineering problems. The homotopy perturbation method (HPM) and Akbari-Ganji Method (AGM) have been used to solve differential equations. The results calculated in Python indicate the high accuracy of calculations in Python. The effect of different parameters on the profile of velocity, temperature, and concentration has been investigated graphically. Also, the friction coefficient (Cf), Nusselt number (Nu), and Sherwood number (Sh) have also been investigated in this study. The results show that the velocity profile decreases with increased magnetic field intensity. Also, the porosity parameter has an inverse effect on the velocity and temperature profile, so the growth of the porosity parameter reduces the fluid velocity while improving the temperature profile.

Pin fin heat sinks have garnered considerable attention within the realm of thermal management for high-heat-flux electronics systems. This study advances the understanding of perforated pin fin systems, offering novel insights into heat transfer enhancement. The research explores circular and square perforation geometries located at varying positions along the pin fin length, aiming to enhance heat dissipation and extend the lifespan of electronic components. A parametric analysis examines the impact of perforation quantity on thermal performance with a rigorous comparison against non-perforated pin fins. The investigation incorporates machine learning techniques, including artificial neural networks, to predict cooling system thermal efficiency. Using computational fluid dynamics simulations and Artificial Neural Network modeling, the obtained results indicate the optimal design mode is the use of 3 square holes on the pin fin, which leads to an increase in thermal efficiency by 16.63% compared to the case without pin fins. Additionally, the mean absolute error value calculated across all data extracted from the computational fluid dynamics simulation for predicting thermal efficiency was 2.25%. This low error value further demonstrates the accuracy of the simulation data and neural network model in predicting the heat transfer performance of the pin fin designs.

This article investigates the effect of Rayleigh numbers, Hartmann numbers, and magnetic fields on nanofluid flow behavior and heat transfer. The flow behavior has been analyzed based on the contours and values of the flow function and heat transfer based on the temperature distribution contours and local and average Nusselt number values. Since the effects of the magnetic field are an important parameter in many technical and engineering applications such as cooling of nuclear reactors, extraction of geothermal energy, and induction casting of metals, in this study, its effect on aluminum oxide nanoparticle, Al2O3, and water, H2O, has been analyzed. The governing equations of nanofluid flow, continuity, momentum, and energy equations have been solved using the Galerkin finite element method and coded and simulated using FlexPDE software. The results obtained for both octagonal cavities containing horizontal and vertical Cassini oval barriers with specific boundary conditions show that with the Rayleigh number and nanoparticle volume fraction being constant, the value of the maximum stream function decreases with the increase of the Hartmann number, and when the Hartmann number and nanoparticle volume fraction is constant, with increasing Rayleigh number, its value increases significantly.

Heat exchangers (HE) are one of the vital heat transfer equipment that have various applications in disparate industries. In this regard, countless methods have been implemented to increase and optimize the heat transfer process inside them. However, passive techniques have received more attention due to the absence of external power consumption. In this study, the impact of employing turbulators with various geometries on the overall heat transfer coefficient (HTC), flow pressure drop (PD), and temperature distribution in the shell-and-tube heat exchanger (STHE) has been computationally investigated. Moreover, for a better examination, the effect of variation of the middle diameter of the turbulator on the hydrothermal behavior of the STHE has been scrutinized. To this end, a 1–2 STHE equipped with five baffles on the shell side and turbulators with different configurations inside the tube is considered. The simulation process is carried out with a variable mass flow rate of 0.2–0.565 kg/s on the tube side and a constant mass flow rate of 1.1 kg/s on the shell side. The outcomes disclosed that the single and double-blade turbulators (SBT and DBT) heighten the HTC and PD inside the STHE tubes. For instance, in the mass flow rate of 0.338 kg/s, the HTC ameliorates by 25.41 % and 33.43 % in the presence of SBT and DBT, respectively. Also, for the mass flow rate of 0.45 kg/s, the PDs for the mentioned turbulators increase by 6.32 and 8.62 times, orderly, compared to the base model (HE without turbulator). Additionally, by increasing the middle diameter of the DBT in a constant value of mass flow rate, the HTC and PD increase. In a mass flow rate of 0.338 kg/s, the HTC of DBT with a 4 mm diameter reduces by 1.97 %, and turbulators with a 6 mm diameter improve by 1.96 %, compared to cases with no variations (5 mm). Furthermore, for the mass flow rate equal to 0.45 kg/s, the turbulator with a 4 mm diameter decreases the PD by 13.8 %, and the turbulator with a 6 mm diameter increases it by 17.4 %, in comparison to the turbulator with a 5 mm diameter (without variation).

This paper examined the flow of nanofluids on a curved stretched surface. Three nanoparticles Go (graphene oxide), Cu (Copper) and CeO2 (ceria) and polymer as the basic fluid were used in this investigation. A ternary hybrid nanofluid (THyNF) is created by these nanoparticles and the base fluid. Analysis of irreversibility, entropy generation (SG), and Bejan number (Be) have all been studied in addition to parameter affect velocity and temperature profile. Differential equations with partial derivatives (PDEs) were converted into ordinary differential equations (ODEs) by employing helpful transforms. The RK5th approach was then used to solve the ODEs. Studies demonstrate that curvature parameter (A) enhances the temperature (θ(η)) and velocity profile (f′(η)). The radiation related factor raises the temperature as well. The volume fraction (φ1,φ2,φ3) of nanoparticles and Brinkmann increases the generation of entropy and decreases the Bejan number. The shape factor and radiation also improve entropy and Bejan. Also explored were the effects of volume fraction nanoparticles, shape factor (SF), curvature parameter, and radiation on the surface drag force and the Nusselt number. The findings demonstrate that although surface drag force is unaffected by nanoparticle radiation and shape factor, but Nusselt is improved. The Nusselt value decreases by 37 % when the tested range's curvature parameter is increased.

This paper investigates the mixture of hybrid nanofluid (NF) flow between two concentric cylinders numerically. Ethylene glycol (80%) and water (20%) comprise the base fluid. Additionally, copper oxide (CuO) and silver (Ag) NPs are added. The hybrid NF flows between the two coaxial cylinders is studied. The inner cylinder is fixed and the outer cylinder is rotating. A radial magnetic field also affects fluid flow, and joule heating joule heating is also considered. The transformed system of nonlinear ordinary differential equations is solved numerically using the fifth-order Runge-Kutta method. Numerical solutions are obtained for fluid velocity and velocity gradient, fluid temperature and temperature gradient, pressure, surface friction coefficient and Nusselt number under the influence of different variables. The computer code is validated by comparing the variation of temperature of hybrid nanofluid with the numerical published data, a good agreement was observed. As the magnetic field parameter is increased, the fluid's velocity reduces. The fluid temperature increases as the magnetic field parameter and Brinkman number were increased. The skin friction coefficient increases with the enhancement of volume percentage and the magnetic field parameter. The Nusselt number rises with increasing of the magnetic field and Brinkman number.

Implementing splitters in microchannels enhances fluid distribution, and nanofluids offer a promising approach to improving heat transfer efficiency. This study uses a home-written Lattice Boltzmann code to numerically investigate the integration of splitters and nanofluids in a copper-water-filled channel with varying Reynolds numbers (Re= 10 to 80) and volume fractions (0≤φ≤0.2) including a splitter at different positions and inclination angles under heat flux boundary condition. Results reveal that heat transfer augmentation occurs with an increase in flow and nanofluid usage compared to conventional fluids. The maximum Nusselt number (Nu) is achieved at a vertical position for all splitter plate locations showing a rise to more than 40% by increasing the φ to 0.1. The estimated Nusselt numbers obtained by the two correlation methods agree well with simulation results with a coefficient of determination (R2>0.9). These findings can be coupled with optimization techniques to determine the optimal conditions of splitters, improving heat transfer efficiency for some practical applications such as micro-heat sinks in electronic-cooling devices.

Nowadays, several engineering applications and academic investigations have demonstrated the significance of heat transfers in general and mixed convection heat transfer (MCHT) in particular in cavities containing obstacles. This study's main goal is to analyze the MCHT of a nanofluid in a triangular cavity with a pentagonal barrier using magneto hydrodynamics (MHD). The cavity's-oriented walls are continuous cold temperature, whereas the bottom wall of the triangle and all pentagonal obstacle walls are kept at a constant high temperature. For solving governing equations, we utilized the Galerkin's finite element approach. Four dimensionless factors, Richardson number (0.01 ≤ Ri ≤ 5), Reynolds number (10 ≤ Re ≤ 50), Buoyancy ratio (0.01 ≤ Br ≤ 10) and Hartmann number (0 ≤ Ha ≤20) are examined for their effects on streamlines, isotherms, concentration, velocity, and the Nusselt number. Also, with the help of Taguchi method and Response Surface Method (RSM) the optimization of the studied dimensionless parameters has been done. The optimum values of Ri, Re, Ha and Br are obtained 4.95, 30.49,18.35 and 0.05 respectively. Ultimately, a correlation has been extracted for obtaining the optimum average Nusselt number (Nu) in mentioned cavity.

Phase change materials have wide applications as thermal energy storage systems. Due to the low thermal conductivity of these materials, lots of efforts have been made to increase the thermal conductivity and efficiency of thermal energy storage systems. In this numerical study, convective and radiation heat transfer on a cavity with transparent inner walls have been investigated considering the effects of buoyancy force and viscosity of phase change materials. For this purpose, computational fluid dynamics that have high accuracy in calculations have been used. The considered wall is made of brick, in which the cavity containing phase change materials is included and layers of cement and plaster are placed on the wall. The results indicate that increasing the heat flux increases the effects of convective heat transfer. In addition, by applying radiation effects, the melting process of paraffin materials increases by 31%. Due to the transparency of the inner walls of the cavity, the radiation process occurred surface to surface. Therefore, with increasing amount of molten material, the radiation effects increase, the reason for this is that RT24 material is more transparent in liquid form than solid material. Also, increasing the heat flux from 50 to 100 and 300 (w/m2) increases the speed of the melting process by 19.3% and 27.2%, respectively.

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.

MHD extended flow of second-grade viscoelastic nanofluid is studied in two-dimensional mode on a curve stretching surface. Items like Joule heating and curvature parameter have been applied to inspect the heat transfer and mass transfer rates. To produce the nonlinear ordinary differential system, appropriate transformations are used. The quasi-linearization method is utilized to derive the solutions numerically. The impact of specific variables on the properties of fluid has been studied. Conclusions indicate that the increase in Schmidt number halted the fluid concentration, whereas temperature grew because of an increment in radiation parameter. Viscous fluid velocity and concentration are reduced faster in comparison to viscoelastic fluid. The surface drag force is an increasing function of the non-Newtonian fluid. When values of Nt and Nb are increased, the heat transfer rate of second-grade fluid increases compared to Newtonian fluid. Schmidt number and chemical reaction parameters highly affect the mass transfer of second-grade fluid compared to Newtonian fluid.

In this paper, the authors investigated the shell and helically coiled finned tube heat exchanger numerically and experimentally. At first they investigated the shell and helically coiled finned tube heat exchanger with simple annular fins for the first time. They considered nine cases for experimental investigation, in which three different fluid flow rates are considered for each side. Then they studied the geometry numerically using Ansys Fluent 18.2 software. After validating the numerical model, the authors suggested four new fin geometries. They studied all the geometries numerically and selected the stepped fin geometry as the superior geometry. The fluid flow inside the tube in this work is in the turbulent flow range and the realizable k−ε turbulence model is used. The authors proposed correlations using the response surface methodology and Taguchi method to predict the mean Nusselt number on the shell and tube sides. The presented correlations have good accuracy for calculating the Nusselt numbers (maximum 10% error). The results show that the mean Nusselt number of the coil side is the same in all geometries, and the Reynolds number of each side has almost no effect on the mean Nusselt number of the other side, and with increasing the fin pitch, the mean Nusselt number of the shell side decreases. The mean Nusselt number of the shell side is 80.79% higher for the stepped fin geometry (superior geometry) compared to the simple annular fin at best.

The present study investigated the increase of heat transfer rate of the microchannel (heatsink) with high heat flux using topology structures and CNTs nanofluids. The heat transfers in the heatsink were studied using a three-dimensional finite volume method (FVM). Four nature-inspired topology structures were used: snowflake shape, honeycomb-shaped, ternate veiny, and spider netted, and their results were compared with straight microchannel heatsink (MHS). For testing the effect of nanoparticle concentration and type on heat transfer of heatsinks, two water-based nanofluids (SWCNT-Water) and (MWCNT -Water) were used. The temperature and pressure contours related to the proposed designs and two nanofluids were presented. The spider netted model had the highest heat transfer coefficient and the highest-pressure changes compared to other designs. For Reynolds number 550, the heat transfer coefficient and pump power (Pp) increased by 56.1% and 46.1%, respectively, when using SWCNT- H2O nanofluid. Based on the thermo-hydraulic performance of the models, spider netted increased heatsink performance by an average of 50.2%. The results also showed that nanofluids with a concentration of 5% significantly increase the heat transfer coefficient and pump power in the heatsink.

According to the various and extensive applications of fractional calculus in a range of fields, such as engineering, biology, image processing, material science and economics, researchers have discovered new, simpler-to-use and more accurate approaches to solve these complicated problems today. In this article an analytical method called Akbari–Ganji’s method is proposed to solve nonlinear fractional differential equations. This method was used to solve nonlinear differential equations before but not fractional differential equations. In this method, first, the solution of the differential equation is considered as a polynomial with constant coefficients. Then, with the help of the initial conditions of the problem and also the Akbari–Ganji’s method’s boundary conditions, the final solution of the differential equation obtained by having the constant coefficients of the polynomial. The method was validated by comparing the answers of two nonlinear fractional differential equations to other methods. Some other examples also provided to confirm the strength and validity of the method.

This study is dedicated to the semi-analytical solution of the problem by managing the inclined Lorentz force and variable viscosity impacts on Williamson nanofluid as visco-inelastic fluids on a stretching plate. Varying viscosity is supposed to change with temperature as a linear function. The fundamental mathematical modeled problem, i.e., the system of PDEs, is transformed nonlinear into odes using appropriate transformations. Computational solutions to the issue are also performed through the efficient semi-analytical method. AGM (Akbari-Ganji method) has been used in solving nonlinear coupling equations. Characteristics of some control parameters such as Hartmann number, inclined angle, and stretching index have been considered. Also, the Sherwood number and Nusselt number are described in tables. The results show that the heat transfer rate decreases by increasing the Pr number. Also, increasing the thermophoresis parameter reduces the temperature. Comparing the results obtained from the AGM and previous research shows that the technique used has high accuracy and efficiency.

In this study, shell and tube heat exchanger with non-continuous helical baffles (NCHB-STHX) is modeled numerically. This heat exchanger has varied applications in different fields of science and industry. The ratio of heat transfer coefficient to pressure drop (HTC/ΔP) is obtained from different angles and intensities. Helix angles vary from 20° to 40°, mass flow rate amounts are 0.984, 1.33 and 1.685 kg/s, and hybrid Nanofluid alumina-Cu-water with three different intensities 0.33, 1, and 2% were tested individually. In addition, the results were compared with pure water. Reynolds number ranges are between 25000 and 31000, and the K-ε RNG model was chosen as the most suitable one. Results show that the heat transfer at β = 20° is maximum and the optimum pressure drop occurs at β = 40°. Also, the helix angle β = 20°, 2% intensity of hybrid Nanofluid alumina-Cu-water and 1.685 kg/s flow rate thermal efficiency is maximum for the helix angle. As the Reynolds number increases up to 80%, HTC rises to approximately 84%. On the other hand, it declines gradually as the helix angle raises nearly 50% when it comes to alumina-Cu-water Nanofluid. The ratio (HTC/ΔP) is at its highest and has a 6% improvement compared to the previous study.

In this article, latent heat thermal energy storage (LHTES) is analyzed for nano phase change material enclosed in a hexagonal triplex-tube with solidification acceleration. Optimized curve shape fins are adjusted inside the tube. The shape of the structure is a hexagonal annular. Therefore, both inner hexagonal walls are cold. Corresponding to six vertices of the hexagonal shaped tube, parallel but symmetrically curved fins are adjusted to every corner. Nanoparticles Enhanced Phase Change Material (NEPCM) is filled inside the annulus, and the mathematical model is constructed based upon the system of nonlinear partial differential equations through the heat equation. Single wall carbon nanotubes (SWCNT) and Copper driven through liquid phase and solid phase within the entire duct. Galerkin Finite Element Method (GFEM) is employed to model the solidification procedure. The smaller symmetric fins achieving an angle of 10o≤β1≤45o and the larger symmetric fins making an angle of 10o≤β2≤45o with the vertical rod. However, the length of rod is 10mm≤L≤20mm. It is found that the optimized curve shape fin penetrate the intensity of thermal storage into the Phase change materials (PCM) and the shape of the fin prevents the phase trade manner from final unsolidified PCM near the outer shell, in which the phase alternate front passes the top of the fins. It is further analyzed that at the mean position of the triplex tube, the solidification process is minimum due to the high thermal performance of nanoparticle volume fraction and time perfection.

To tackle global warming, a reliable storage system seems crucial due to unpredictability of renewable energy. As a result, storage units based on Phase Change Material (PCM) are found to be of great worth where latent heat transfer occurring in an almost isothermal condition lay the foundation for far more compact and easy-to-fabricate storage components. Despite their advantageous, one major drawback being weak thermal conductivity needs to be addressed. So, in this study a triplex-tube heat exchanger with tree-like and rectangular fins along with hybrid nanoparticles made of MoS2-TiO2 are put into perspective to dispose of this weakness and Galerkin Finite Element Method (GFEM) is applied using FlexPDE to analyze the solidification process and evaluate the influence of single and combined usage of fins and nanoparticles. Moreover, the credibility of this study and GFEM has been confirmed by an experimental work. The results unveiled that, while the combined usage of nanoparticles and tree-like fins gives the best result by lowering the solidification time by 78% compared to bare tube, tree-like fins claim the best performance taking 1700 s followed by rectangular fins with 3500 s if nanoparticles are out of reach.

Due to the variation in fluid flow behavior in various physical conditions, the presented study have been performed an investigation of cross-fluid flow containing gyrotactic microorganisms and nanoparticles on a horizontal and three-dimensional cylinder considering viscous dissipation and magnetic field. The governing equations of the problem have been solved by the Runge-Kutta fifth-order method. The aim of this study is to inspect the effects of cross fluid, microorganisms, and magnetic field, on velocity, temperature, and concentration profiles. Also, Heat flux and mass flux values for nanoparticles and microorganisms have been calculated in tabular form. In this research, the simultaneous utilization of nanoparticles with motile microorganisms in cross fluid, and three-dimensional assessment on the cylinder has been proposed as an innovation. The results show that, when the Brownian motion parameter varies from 0.1 to 0.4 and at η=4, the concentration of nanoparticle deduces about 80.43%. Furthermore, with the change of bioconvection Lewis number from 0.2 to 0.5, it was observed that the concentration of the microorganisms reduced about 78.38%.

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 Nb rises from 0.1 to 0.2. For all Nt values, at least 55.44%, 18.69%, for F(η), and Ω(η), and 20.23% rise for Ψ(η) function is observed. Furthermore, enlarging the Nr 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.

ABSTRACT: 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.

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%.

In this study, the thermal performance of moving porous fin wetted with hybrid nanofluid with different cross-sections in the presence of a magnetic field is investigated. As an innovation, three different cross-sections) trapezoidal, concave parabolic and convex (have been used. The Shape-factor effect of hybrid nanoparticles is also considered in the equations. After extracting the governing equations and converting the PDE equations to ODE by Similarity solution, the equations are solved by Akbari-Ganji's method. The boundary conditions are an insulated tip with a finite length, and thermal functions for heat transfer coefficient and conductivity have been assumed. The impacts of several characteristics on the dimensionless temperature are thoroughly investigated, including Peclet number, thermal conductivity parameter, emissivity parameter, heat transfer coefficient parameter, convective–conductive parameter, and radiative–conductive parameter. The results show that Akbari-Ganji's method has good accuracy in solving heat transfer equations related to moving porous fin. Also, increasing the Peclet number increases the dimensionless temperature, because increasing the Peclet number causes the fin to move faster.

In this paper, in order to improve the performance of a linear parabolic collector, the thermal effects of using Al2O3-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-ε two-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.

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 Al2O3 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.

Energy storage, particularly thermal energy, is one of the most important issues in responding to human energy needs. In this numerical work, by using the latent heat of the organic paraffin RT26 and its melting and freezing points, an attempt has been made to study thermal and heat energy storage. In this theory, by analyzing different circular and elliptical shapes of heat exchangers and internal tubes, an attempt has been made to increase the thermal efficiency and deal with the slow rate of completing the process, which is mainly based on buoyancy. In this work, by employing MWCNT and GO, it has been tried to increase the thermal conductivity of organic material. The results also show that increasing the eccentricity of the condenser in the melting process causes a thermal equilibrium to be created in heat exchanger area in such a way that by increasing the eccentricity from 0.02 to 0.04, and 0.06, the percentage of heat efficiency of heat exchanger will increase by 27%, 49% and 58%, respectively. It was also found that by reducing the cold wall temperature from 280 K to 270 K, the solidification process is accelerated so that the time required to complete the process is reduced by 17%.

The main part of a gaseous water heater is a shell and tube heat exchanger whereby the heat is transferred between water and hot gases produced by combustion. In this paper, an attempt is made to replace a shell and tube heat exchanger by a finned flat plate in a household water heater to achieve higher efficiency values. Since, the governing equations are highly nonlinear and very hard to implement, an experimental setup is developed to examine a flat plate heat exchanger and compare its performance with the shell and tube ones. Experiments show that the slop of the plate (angles less than 20°) with respect to horizon besides the volumetric flows of water (7.4 L/min) and natural gas (0.013 cubic meter/min) have effective impacts on the efficiency values of the proposed heat exchanger. It is also concluded that the angle 20° corresponds to the highest rate of heat transfer between two fluids. Investigations show that the proposed heat exchanger may help to achieve the higher values of efficiency (increasing between 20% and 50%) for water heaters compared to those including shell and tube configurations.

Increasing heat transfer in the field of thermal management is one of the important features of engineering studies. In many cases, the use of nanoparticles leads to increased heat transfer. Hence in this analysis, Graphene Oxide nanoparticles has been used in the field of Magneto hydro Dynamics as a factor to increase heat transfer. The main objectives of this analytical work is to increase the heat transfer of convective currents on a Williamson non-Newtonian rotating cone with graphene oxide nanoparticles. In this paper, we have converted the governing equations in the PDE form have been converted to the ideal ODE form. From the obtained results, it can be seen that increasing the volume fraction of graphene oxide nanoparticles from 0.01 to 0.04 shows favorable thermal effects. An increase in the Eckert dimensionless number and a decrease in Prandtl lead to an increase in temperature profile. Also, its noted that the concentration decreases with increasing Lewis number parameters and Brownian motion. It was found that with increasing magnetic effects, the rate of velocity profile also increases. This means that the magnetic effects overcome the viscous effects of Williamson fluid and increase the velocity.

In this article, natural convection of MHD fluid flow within a vertical annulus is investigated in existence of radial magnetic field and heat generation or absorption. As an innovation effect of suction and injection has been considered in the velocity and temperature equations. governing equations are solved by Akbari-Ganji's analytical method (AGM) and results are compared with numerical method (Runge-Kutta 4th) and LSM method (least square method) for purpose of showing the accuracy of AGM. Studies were performed for various parameters such as: suction and injection parameter (S), heat generation or absorption (H) and Hartmann number (M) under two boundary conditions isothermal and constant heat flux. Results indicate that with increasing heat generation velocity, temperature and mass flow rate in both boundary conditions are increase while opposite trend are observed for increasing heat absorption. velocity of fluid decreases when Hartmann number increase. Also, it is explained that Nusselt number increases with suction and heat absorption parameters and decreases with injection and heat generation parameters. Phenomenon and parameters studied in this work can give a good insight for cooling electronic equipment such as wire cooling.

Nowadays, due to the global need for energy and the limited amount of fossil fuels, it is required to utilize alternative forms of energy. Thermal energy storage systems together with phase change materials are considered potential options to help achieve renewable energy development goals. Special groups of materials are used for thermal management in thermal processes due to their specific properties such as high latent heat, appropriate phase change temperature, and slight volume change during phase change. In this study, the effects of branch-shaped fins with different thicknesses and lengths on the thermal conductivity of phase change materials are investigated. Furthermore, the different volume ratios is studied. The results show that using thinner branch-shaped fins and hybrid Al2O3 – Cu with volume ratio of 0.04 has greater influence on the speed of the solidification process. The results also illustrate that the use of fins significantly speeds up the solidification process. The comparison between thin and thick fins revealed that the thin fin is a more viable option in increasing heat transfer rate. In this simulation, the finite element method has been employed. Generally, simultaneous use of thin branch-shaped fins and nanoparticles with volume fraction 0.04 leads to maximum efficiency in the simulation.

In this study, flow and heat transfer of Magnetohydrodynamic squeezing nanofluid flow between two infinity parallel plates have been investigated. The fluid is an equal mixture of Ethylene-glycol and water. This paper discusses the hybrid nanoparticle while Particles are Fe3O4 and MoS2. The nonlinear equations have been solved by Akbari- Ganji's method, and the result is compared by the numerical method and reported in figures. The effect of Harman number, base fluid, squeeze number, and Heat source on flow and heat transfer have been computed. The result shows that the Akbari- Ganji's method and the numerical method are in good agreement. Akbari- Ganji's method can be useful for such problems, and we can see that the maximum difference in velocity profile and thermal profile between AGM and the numerical method is less than one percent. The velocity profile reduced by an increase in squeeze number and Hartman number. The thermal profile raised with an increase in squeeze number, but it decreased with increasing in Hartman number and heat source parameter.

In this research, the specification of 3-dimensional flow stagnation point of hybrid Nanofluids passing through circular cylinder with sinusoidal radius are analyzed. C2H6O2, H2O and Engine oil are used as an ordinary liquid, while nano-particles include SWCNT and MWCNT. Fluid stream is taken into account with/without considering the effect of thermal slippage. Higher order non-linear phrases are transformed to ordinary prime-order differential equations and then solved applying the Analytical Method (HPM) in Matlab-14 software. Graphical analysis of the impressive parameters like: Prandtl number, thermal slip parameter, CNTs volume fraction is precisely checked on the profiles of velocity and temperature for various carbon nano-tubes. Consequences display that: cooling process or heat transfer rate can be increased by employing smaller thermal slippage parameter. Further, due to the better thermal conductivity of SWCNT carbon nanotube, the temperature increase in these carbon nanotubes is more than that of MWCNT.

Flow and thermal field features of microchannel heat sink driven by hybrid nanofluid are portrayed in this study. Porous media approach is employed to examine the thermal distribution in extended surface and Cu:γ−ALOOH/Water. Hybrid mixture of nano sized Copper and Boehmite alumina particles are considered to cool the microchannel heat sink. The mathematical expressions are solved numerically via Fourth Fifth order Runge Kutta Fehlberg scheme. The consequences of solid volume fraction of hybrid nanoparticle, porosity and Darcy number on flow field, temperature of fin section and Cu:γ−ALOOH/Water are displayed through graphs. Flow velocity of the hybrid nanofluid is reduced with the addition of hybrid particles with concentration 1−3%. It is emphasized that on augmenting nanoparticle volume fraction of hybrid mixtures the temperature profile declines for both cases. Also, heat liberated is transferred into the ambience due to Brownian motion of the nanoparticles resulting better heat transfer.

Nowadays, with the development of heat transfer in various industrial fields, like as electrical and mechanical fields, we see the more effect of fins in this improvement. The computational price is hidden term of optimizing that can be included of CPU time and material optimizing can be included to modify the profile of fins. So in this paper have been investigated the heat transfer of fins with different profile (Convex, Concave, Triangular, Rectangular) in unsteady condition. The differential transform method (DTM) has been employed to solve this problem due in addition investigation of differences of temperature in fins, computational space become lesser. The boundary conditions are insulated tip with limited length and the thermal functions have been assumed for coefficient of heat transfer and conductivity. Then has been investigated the effect of relationship parameters like as (ε,β,θ,M). In unsteady condition these parameters are limited to one number that is useful in making optimum number. When β are increasing the temperate plot going in the upper level that show the efficiency going upper. In unsteady condition this parameter is limited to one number that it is very important for optimization by to build fins. Keywords: Rectangular fin, Convex fin, Concave fin, Triangular fin, DTM, Temperature-dependent thermal conductivity

This paper studies a steady two-dimensional stagnation-point flow of nanofluids over a nonlinearly stretching/shrinking sheet in the presence of blowing/suction. The effects of different nanoparticle materials, namely copper, alumina and titania on the flow and heat transfer rate are investigated. Employing similarity variables, the governing partial differential equations including continuity, momentum and energy have been reduced to ordinary equations and are solved numerically via Runge-Kutta-Fehlberg scheme. It is shown that two solutions exist for shrinking sheets in both blowing and impermeable cases, while an additional solution appears in the case of suction (there are three solutions). Moreover, the effects of nonlinearly parameter β, blowing/suction S, and solid volume fraction ϕ on the heat and fluid flow characteristics are investigated in details. Keywords: Nano-fluid, Stagnation-point flow, Stretching/shrinking sheet, Similarity solution, Multiple solutions

This article investigates the theoretical study of steady stagnation point flow with heat transfer of a nanofluid towards a stretching surface. It is assumed that the fluid impinges on the wall obliquely. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The basic partial differential equations are reduced to ordinary differential equations which are solved numerically using the fourth-order Runge–Kutta method. Numerical results are obtained for distributions of velocity, temperature and concentration, as well as, for the local Nusselt number and local Sherwood number for several values of governing parameters. The results indicate that the local Nusselt number decreases with an increase in both Brownian motion parameter Nb and thermophoresis parameter Nt. However, the local Sherwood number increases with an increase in both thermophoresis parameter Nb and radiation effect R, but it decreases as the values of Nt increase. Keywords: Nanofluid, MHD stagnation flow, Stretching sheet, Thermal radiation effects, Heat and mass transfer

In this article, TiO2-ethylene glycol nanofluid flow over a porous stretching sheet in presence of non-uniform generation or absorption of heat and convective boundary condition is investigated. The concentration of solute is set by the means of an isothermal model of homogeneous-heterogeneous reactions. The governing equations were simplified to ordinary differential equations and solved using Runge-Kutta-Fehlberg shooting method of fifth order. Effects of different variables such as nanoparticle volume fraction, porosity variable, and Schmidt number were studied and the results are graphically presented. The results showed that the stretching rate ratio has inverse effect of velocities in both directions. According to plots, nanoparticle volume fraction as well as convective heat intensity has a direct relation with wall heat flux, in the contrary, heat generation has an inverse effect on it. Keywords: Ethylene glycol, Titanium dioxide, Heat generation/absorption, Nonlinear stretching sheet

Direct Simulation Monte Carlo (DSMC) method is applied to evaluate the performance of a new micro gas sensor (MIKRA) for mass analysis of ammonia in the rarefied gas. In order to simulate a rarefied gas inside the micro gas detector, Boltzmann equation is applied to obtain high precision results. This study performed comprehensive studies to reveal the main mechanism of force generation and applied this for the analysis of the gas mixture. Our findings show that value of generated Knudsen force significantly varies when the percentage of the NH3 varies in the mixture. According to obtained results, the maximum Knudsen force increases when the fraction of the ammonia decreases. Our findings reveal that the effect of gap size varies with the pressure of the domain. In addition, the increase of temperature gradient from 40 K to 100 K rises the maximum Knudsen force more than 400% on the shuttle arm. Keywords: Ammonia, Knudsen force, DSMC, Low-pressure gas sensor, MEMS

In this paper, mixed convection on MHD flow of casson nanofluid over a non-linearly permeable stretching sheet has been investigated and analyzed numerically. The effects of thermal radiation, chemical reaction, heat generation/absorption, viscous dissipation, suction and Joule heating are considered. The Brownian motion and thermophoresis phenomenon are used to model nanoparticles (Buongiorno's model). After converting PDEs governing the problem to ODEs, they have been solved by Runge-Kutta Fehlberg fourth-fifth order method. Obtained results of investigating the effects of different parameters changes on velocity, temperature, and concentration profiles are reported as diagrams. Fluid flow velocity reduction by increase in Hartman number (magnetic field parameter) is due to existence of Lorentz drag force against flow, flow velocity reduction due to increase in casson fluid parameter, increase in temperature profile due to increase in radiation parameter, and nanoparticle concentration profile reduction due to increase in chemical reaction parameter are some of valuable obtained results. Also, in final section of this paper effects of different parameters on skin friction coefficient, local Nusselt and Sherwood numbers are investigated that positive and ascending behavior for all three are reported. Keywords: Magnetohydrodynamic (MHD), Casson nanofluid, Buongiorno's model, Thermal radiation, Chemical reaction, Heat generation/absorption, Suction, Joule heating effect

In this paper, convective-conductive heat transfer processes between the all components of geothermal borehole heat exchanger (BHE) such as pipe-in, pipe-out and grout have been studied. A set of coupled partial differential equations subjected to general initial and boundary conditions are governed to this problem. Modified Homotopy perturbation method (MHPM) is a hybrid of discrete Fourier Transform, spectral analysis and Homotopy Perturbation Method that is developed in order to solve the partial differential equations of geothermal borehole systems. The results of MHPM are compared with the numerical solution for validation and, furthermore, the effectiveness and accuracy of the applied method have been shown. Keywords: Borehole heat exchanger, Heat conduction-convection, Discrete Fourier transformation, Homotopy perturbation method

Flow and heat transfer of MHD micro-polar nanofluid in a channel with penetrable walls and considering thermal radiation impact are investigated. A similarity transformation is utilized to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The gained non-linear ordinary differential equations are solved by Duan–Rach Approach (DRA). This method allows us to detect a solution without applying numerical methods to evaluate the unspecified coefficients. The impacts of diverse active parameters such as the micro-polar parameter, the magnetic parameter, the volume fraction of nanofluid and the radiation parameter on the velocity and temperature profiles are examined. Furthermore, the value of the Nusselt number is calculated and presented through figures. Keywords: Micro-polar nanofluid, Penetrable channel, MHD, Thermal radiation, Duan-Rach Approach (DRA)

Geothermal energy is one of the well-known types of renewable energies that can be considered as a promising alternative to fossil fuels in order to mitigate the CO2 emission in atmosphere. Geothermal energy has recently been used for heating and cooling systems in many countries of the world. Therefore, studying such kind of energy seems important and necessary. This paper studies the heat transfer processes in a borehole heat exchanger (BHE). The flow of fluid in a BHE has been considered with different geometries and heat transfer processes are modeled numerically and in a finite volume method through convection and conductivity. First, a single U-shaped BHE was modeled and its thermal properties were investigated and then other geometries were studied to obtain the best geometry and heat transfer efficiency. In order to increase the heat transfer in the inner part of the pipes, the fin with the given specifications was used and the modeling was carried out and the thermal parameters were compared for three BHE’s with different geometries. In the final part, optimization results are presented, and the interaction of parameters on the Nusselt number and friction coefficient have been investigated. Also, the desirability of optimization and reliability is given to the results presented in percentage terms. Comparing the results of this article with the results of previous research shows a very good agreement and therefore the applied method is reliable and accurate. Keywords: Borehole heat exchangers, Numerical method, Heat transfer processes, Geothermal energy, Finite volume analysis

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. Keywords: Homotopy analysis method (HAM), Collocation method (CM), Homotopy perturbation method (HPM), Parallel porous plates, Unsteady flow

In this paper, uniform magnetic field impact on nanofluid flow between two circular cylinders is investigated analytically using AGM. Two phase model is applied for nanofluid. Analytical procedures are examined for various active parameters namely aspect ratio, Hartmann number, Eckert number, Reynolds number, thermophoresis and Brownian parameters and Schmidt number. Results indicate that velocity reduces with augment of Lorentz forces but it rises with augment of Reynolds number. Temperature gradient enhances with rise of Hartmann number but it decreases with augment of other parameters. Keywords: Nanofluid, AGM, Rotating cylinders, Brownian motion, Magnetic field

In this research, the mixed convection stationary point flow of an incompressible viscous Nano fluid into a vertical permeable circular cylinder along with electric conductivity is analyzed. Ethylene glycol is used as an ordinary liquid, while nanoparticles include copper and silver. The problem has been calculated without the presence of an inductive and electrical magnetic field while taking into account homogeneous and heterogeneous reactions. The strong nonlinear systems calculations are presented using the Numerical Method after non-dimensionalization. Graphical analysis of the effective parameters such as Prandtl number (Pr), permeability parameter (Vw), Schmidt number (Sc), magnetic parameter (M), mixed convection parameter (λ) and curvature parameter (γ) is precisely investigated on the profiles of velocity, concentration and temperature for different nanoparticles. Conclusions indicate that: The thickness of the thermal boundary layer changes more than the thickness of the hydro-dynamic boundary layer for injection and suction. Also, due to the higher thermal conductivity of silver nanoparticles, the temperature increase in these nanoparticles is more than that of copper. In fact, this paper shows that the heat transfer rate increases with the addition of nanoparticles. In addition, the role of the curvature parameter (γ) on the concentration profile shows that the concentration profile decreases with the gradual increase of γ. Keywords: Nano fluids, Mixed convection, Vertical permeable cylinder, Stagnation point flow, Magnetic field