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- Natural convection heat transfer in a square cavity induced by heated plate is investigated using the lattice Boltzmann method. A suitable forcing term is represented in the Boltzmann equation. With the representation, the Navier-Stokes equation can be derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Top and bottom of the cavity are adiabatic; the two vertical walls of the cavity have constant temperatures lower than the plate’s temperature. The flow is assumed to be two-dimensional. Air is chosen as a working fluid (Pr=0.71). The study is performed for different values of Grashof number ranging from 103 to 105 for different aspect ratios and position of heated plate. The effect of the position and aspect ratio of heated plate on heat transfer are discussed. With increase of the Grashof number, heat transfer rate is increased in both vertical and horizontal position of the plate. The obtained results of the lattice Boltzmann method are validated with those presented in the literature.

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In this paper, natural convection heat transfer inside an enclosure which is partially filled with porous layer is reported using lattice Boltzmann method. Generalized equations in modeling flow in porous media have been employed which are coupled with the lattice Boltzmann formulation of the momentum and energy equations. The present study investigates the effect of position of porous layer on heat transfer rate for different dimensionless parameters, such as Rayleigh number, Darcy number and porosity of the porous layer. In addition, a modified Rayleigh number is presented as an effective parameter which affects the degree of penetration of the fluid into the porous layers. The obtained results showed that the heat transfer rate in the case of vertical layer is more than that of horizontal porous layers.

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In the present paper,by performing a two-dimensional simulation,the heat transfer from a hot cylinder to a cold square enclosure has been studied parametrically and the consequent effect of changing in cylinder diameter has been investigated. The 2-D governing equations have been solved using the finite volume method and TDMA in an ADI procedure for different diameters of cylinder inside a square enclosure with a constant characteristic length for two different Rayleigh numbers of 104 and 105.Results showed that the patterns of streamlines, isotherms and the Nusselt number values depend strongly on the Rayleigh number and also ratio of cylinder diameter to characteristic length of enclosure (2R/H). In this case, the centers of vortices created around the cylinder appear in bottom half of enclosure in 2R/H=0.4 for Ra=104 and in 2R/H= 0.5 for Ra=105. Moreover, it is observed that increasing the Rayleigh number and 2R/H ratio, the heat transfer rate from the enclosure is also increased.For example,in 2R/H=0.5, by increasing the Rayleigh number from 104 to 105, the average Nusselt enhances about 30 percent of its initial value and in Ra=105, by changing the 2R/H ratio from 0.2 to 0.5, the average Nusselt climbs almost 35 percent of its initial value.

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In this research, two effective techniques to increase mixed convection heat transfer rate within an enclosure subjected to a transverse magnetic field are studied. In order to increase the heat transfer rate, the addition of Al2O3 nanoparticles is concerned as the first strategy and the change in magnetic field inclination angle is considered as the second. In this study, the left and right sides of the enclosure are kept at constant temperature while the top and bottom walls are adiabatic. In this work, the results are obtained with an in-house finite volume code. To validate the code, the results of the present code are compared to that of an existing correlation as well as those of previous works and good agreements are observed. In the present work, Richardson number varies from Ri=0.05 to Ri=50. Results show that the addition of solid particles may increase or decrease the heat transfer rate whereas the increase in magnetic field inclination angle mostly leads to increase in the heat transfer rate.

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In this study forced convection heat transfer in a pebble bed cylindrical channel with internal heat generation was investigated experimentally. Dry air has been used as working fluid in heated spheres cooling process. Internal heating was generated uniformly, by electromagnetic induction heating method in a metallic spheres which have been used in test section. Spheres are made of stainless steel and their diameter is in the range of 5.5-7.5 mm. Present study was performed at steady state and turbulence flow regime, with Re number in the range of 4500-9500. Different parameters resulted by variation of spheres diameter, flow velocity and generated heat on forced convection heat transfer was studied. According to thermal and hydrodynamics studies, it can be said as Re number increases, heat transfer coefficient will increase. Also heat transfer coefficient has been increased by spheres diameter decrement. The generated heat has a little influence on heat transfer coefficient. The effect of pressure variations on forced convection heat transfer can be neglected. Porous channel has greater friction factor in comparison with an empty channel. The friction factor in empty channel is always less than 1 but for porous channel this parameter is in the range of 10-25.

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In this paper, the flow and temperature fields affected by electrohydrodynamic actuator are numerically investigated for the incompressible, turbulent, and steady flow over a backward-facing step. Air is used as working fluid in heated backward-facing step cooling process. The electric field is generated by the wire electrode charged with DC high voltage. The numerical modeling is based for solving electric, flow, and energy equations with finite volume approach. The computed results are firstly compared with the experimental data in case of rectangular flat channel and the results agree very well. Then the effect of different parameters such as the radius of the wire, applied voltage, Reynolds number, and the wire position on the heat transfer coefficient is evaluated. The results show that the heat transfer coefficient with the presence of electric field increases with the applied voltage but decreases when the Reynolds number and the radius of the wire are augmented. Moreover, reduction of emitting electrode angle can significantly effect on the heat transfer enhancement. In consequence, one may able to find an optimum place for the emitting electrode position.

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In this paper, natural convective heat transfer of nanofluids in a uniform magnetic field between the square cavity and inner cylinder, was simulated via Lattice Boltzmann Method. The inner cylinder in square shape, diamond, and circular has been examined. Square cavity walls and inner cylinder surfaces are at a constant cold and warm temperature, respectively. The flow, temperature, and magnetic field is calculated with solving flow, temperature, and magnetic distribution functions simultaneously. D2Q9 lattice arrangement for each distribution function is used. The results clearly show the behavior of fluid flow and heat transfer between the cavity and the cylinder. The results have been validated with available valid results showing relatively good agreement. The effects of Rayleigh number, Hartmann number, void fraction and type of nanoparticles on natural convective heat transfer are investigated. This study shows that for all three geometries used with the same void fraction, type of nanofluid, and Rayleigh number, natural convective heat transfer decreases with Hartmann number. Also, when Hartmann number was had fixed, natural convective heat transferwas increased with Rayleigh number. Thus, to select the right geometry for optimum natural convective heat transfer, our needs to pay special attention to Hartmann and Rayleigh numbers. In addition, viod fraction and type of nanofulid can affect heat transfer directly.

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In the present study the validity of two conventional Nusselt number definitions were investigated using analytical and numerical methods for convection heat transfer in a pipe partially filled with porous media. The first definition is denoted as Nu_1 (x)=(2R(∂T/∂r)_(r=R))⁄((T_w-T_m (x)) ) and the second one follows: Nu_2 (x)=(2Rq_cond^'')⁄(k_ref (T_w-T_m (x)) ). The Nusselt number resulted from these two definitions was investigated analytically in a pipe for different porous configurations. The results show that the calculated Nusselt numbers using these two definitions, are different in porous media boundary arrangement. In the first definition, the heat transferred to the fluid flowing thorough the porous media is not considered, so the Nusselt number which is calculated via this definition cannot demonstrate the physics of heat transfer phenomenon properly. The boundary arrangement of porous in a pipe with turbulent flow is simulated numerically and the Nusselt number was calculated by the two definitions. The calculated Nusselt from the first definition shows that the Nusselt number increases as the heat conduction coefficient of porous grows which is not a proper expression of physics of this problem. So, the first definition of the Nusselt number is not proper for porous boundary arrangement in a pipe. However, with investigating of the second definition, it is seen that with increasing the porous heat conduction coefficient, the Nusselt number increases which this result is physically valid; therefore the second definition is more appropriate for the porous media boundary arrangement.

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Plasma actuator is one of the newest ways in vortex generation and flow control techniques which can enhance heat transfer rate by inducing external momentum to the boundary layer of the flow. In this paper, a 2-D numerical approach was implemented to analyze the presence of plasma actuator on the incompressible, turbulent, steady flow in a flat channel. In this approach, the flow field and heat transfer characteristics such as the stream function and heat transfer coefficient were evaluated through the variety of Reynolds number, at the presence and absence of applied voltages. The present computed results are firstly compared with the numerical data in case of rectangular flat channel and the results agree very well. The numerical results indicate that at a constant Reynolds number with the presence of a plasma actuator, the heat transfer coefficient will be increased but in a constant applied voltage the heat transfer coefficient will increase to the Reynolds of 250 and then will be decreased respectively. In addition, the size of generated vortexes significantly depends on the applied voltage and the upstream flow speed. On the other hand, according to the results, the flow speed affects the size of generated vortex and vanish the actuator effect at high Reynolds. According to the results, there is an optimized point for the applied voltage and flow speed.

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One of the interesting and practical problems in thermo-fluid sciences is referred to finding the shape of a boundary on which a specific distribution of pressure, temperature or heat flux is known. Because solving such problems using experimental, semi-experimental and analytical methods is time-consuming or even impossible in some practical situations, myriad numerical methods have been introduced to solve surface shape design (SSD) problems. In all the numerical algorithms, an initial guess is modified through a numerical process until the desirable distribution of the target variable is achieved. All the numerical algorithms use three computational tools, i.e. grid generator, flow solver and shape updater to solve an SSD problem. In most of numerical algorithms, not only the three mentioned tools work separately but the shape updater is also not derived from the governing equations. In this article, to solve SSD problems containing convection heat transfer, a new shape design algorithm called direct design method is presented in which grid generator, flow solver and shape updater work simultaneously and also the shape updater is directly derived from the governing equations. Some SSD problems containing convection heat transfer in which instead of the boundary shape the distribution of the heat flux is known are solved using the proposed algorithm. The obtained results show the capability of the method in solving SSD problems containing internal convection heat transfer.

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Free convection heat transfer of a non-Newtonian thickening power law fluid in a closed asymmetrical enclosure with fixed aspect ratio was investigated in this study. Many of the previous studies, addressed the case with symmetrical heat transfer enclosure and for a given inclination. The governing equations were established by the finite volume method and solved by the SIMPLEC algorithm. In order to evaluate the code, its results were compared to those of other papers in the field of Newtonian and non-Newtonian fluids. The impact of the enclosure inclination and the Rayleigh number on the heat transfer and the flow field were investigated. It was found that for Rayleigh numbers smaller than , inclination has little impact on heat transfer, while at Rayleigh numbers larger than , the lowest heat transfer was observed at an angle of . Moreover, the results pertaining to Newtonian and non-Newtonian thickening fluids were compared. The results show that heat transfer by thickening non-Newtonian fluids, in addition to other parameters, depends on the parameter (n) and in the case of the angle of inclination , the heat transfer of Newtonian and non-Newtonian thickening fluids is equal. Considering the non-Newtonian behavior of the fluid and nondimensionalization of the problem, a new dimensionless number known as the extended Prandtl number 〖(Pr〗^*) appeared in the equations that depends on fluids characteristics, flow geometry, and the power law exponent . Its optimal value was observed at 〖(Pr〗^*=0.07) where heat transfer from the enclosure was at maximum.

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