A numerical study of the natural convection of the laminar heat transfers in the stationary state was developed in a horizontal ring and compared between a heated TRAPEZOIDAL internal cylinder and a cold elliptical outer cylinder. This annular space is traversed by a Newtonian and incompressible fluid. The Prandtl number is set to 0. 7 (air case) for different Rayleigh numbers. The system of equations controlling the problem was solved numerically by the calculation of code fluent based on the finite volume method. In these simulations the Boussinesq approximation was considered. The inner and outer surfaces are kept at a constant temperature. The study is performed for Rayleigh numbers ranging from 103 to 105. Indeed, the effects of different numbers of thermal Rayleigh on natural convection were studied. The results are presented in the form of isotherms, isocurrents, local and average numbers of Nusselt. The purpose of this work is to study the influence of the thermal Rayleigh number, and the change of the angle of inclination of the TRAPEZOIDAL lateral walls on the structure of the flow and the distribution of the temperature.

In present study, natural convection heat transfer of a nanofluid in a TRAPEZOIDAL ENCLOSURE saturated by a porous medium is investigated. A local thermal non-equilibrium model including three thermal equations for the phases of fluid, nanoparticles and solid porous matrix is utilized. Moreover, in order to determine comprehensive behavior of dispersed nanoparticles inside the fluid phase, a non-homogeneous model (Buongiorno, s model) is employed. Governing equations in present study are transformed into a non-dimensional form and finally are solved by using the finite element method. The obtained results indicate that the increase of Rayleigh number has a significant increase in the average Nusselt number for the fluid phase and a less significant increase in the average Nusselt number for the nanoparticles. In addition, raising of the buoyancy ratio parameter tends to reduce the average Nusselt number for fluid phase and nanoparticles. In other hand, the variation of Rayleigh number and buoyancy ratio parameter shows a less impact on the average Nusselt number for the phase of porous sold matrix.

The flow under influence of magnetic field is experienced in cooling electronic devices and voltage transformers, nuclear reactors, biochemistry and in physical phenomenon like geology. In this study, the effects of magnetic field on the flow field, heat transfer and entropy generation of Cuwater nanofluid mixed convection in a TRAPEZOIDAL ENCLOSURE have been investigated. The top lid is cold and moving toward right or left, the bottom wall is hot and theside walls areinsulated and their angle from the horizon is 45˚. Simulations have been carried out for constant Grashof number of 104, Reynolds numbers of 30, 100, 300 and 1000(Richardson from 11.11 to 0.01), Hartmann numbers of 25, 50, 75 and 100 and nanoparticles volume fractions of zero up to 0.04. The finite volume method and SIMPLER algorithm have been utilized to solve the governing equations numerically. The results showed that with imposing the magnetic field and enhancing it, the nanofluid convection and the strength of flow decrease and the flow tends toward natural convection and finally toward pure conduction. For this reason, for all of the considered Reynolds numbers and volume fractions, by increasing the Hartmann number the average Nusselt number decreases. Furthermore, for any case with constant Reynolds and Hartmann numbers by increasing the volume fraction of nanoparticles the maximum stream function decreases. For all of the studied cases, entropy generation due to friction is negligible and the total entropy generation is mainly due to irreversibility associated with heat transfer and variation of the total entropy generation with Hartmann number is similar to that of the average Nusselt number. With change in lid movement directionat Reynolds number of 30 the average Nusselt number and total entropy generation are changed, but at Reynolds number of 1000 it hasa negligible effect.

The flow affected by a magnetic field is applied in cooling electronic devices and voltage transformers and in physical phenomenon such as geology. In this study, the effects of magnetic field on the flow field and heat transfer of Cu-water nanofluid natural convection and by considering the Brownian motion of nanoparticles have been studied in a TRAPEZOIDAL ENCLOSURE. The study has been done for Rayleigh numbers 103 to 1010, Hartmann numbers 0 to 100 and the nanoparticles volume fraction of 0 to 0. 04. The governing equations have been solved numerically by use of finite volume method and SIMPLER algorithm. The results showed that by applying the magnetic field and increasing it, the nanofluid convection and the strength of flow decrease and the flow tends toward natural convection and finally toward pure conduction. For all of the Reynolds numbers and volume fractions which are considered, by increasing the Hartmann number, the average Nusselt number decreases.

Laboratory experiments were conducted in smooth TRAPEZOIDAL channel with side slope 1: 1 to measure boundary force and shear stress. Preston tube is used to estimate contribution of wall and bed shear stresses. Available formulas for estimation of boundary shear were evaluated and new formulas were presented. The effect of aspect ratio on wall and bed shear stresses was determined. Results showed that ratio of wall shear force to total shear force decreases as aspect ratio increases.

There are two main methods in fire modeling: zone models and field models. The conservation of mass and energy in ENCLOSURE is the theoretical base of zone models. The models deal with heat release rate, fire plume, mass flow, smoke movement and gas temperature in fires. Theoretical principles of compartment fire zone modeling are presented and the behavior of fire in ENCLOSUREs is discussed. The conservation laws are presented in control volume form and applied to the behavior of fire in ENCLOSUREs. The governing equations are derived and presented. Some zone models and their field of application in fire modeling are also given.

In 2000, exponential TRAPEZOIDAL fuzzy numbers were defined for the first time by Chen and Lie [3] without investigating the definition and properties of fuzzy numbers for them.  Therefore, in this paper first, some necessary definitions and the difference between fuzzy numbers and fuzzy quantities are presented. Then, the correctness of the definition of exponential TRAPEZOIDAL fuzzy numbers is investigated. It is concluded that exponential TRAPEZOIDAL fuzzy numbers do not satisfy general conditions of fuzzy numbers such as bounded amplitude and continuity. In fact, these are fuzzy quantities not fuzzy numbers. As a result, a ranking method is proposed for such quantities to be examined using common tools and test platforms that exist for ranking fuzzy quantities. Moreover, the strength and weaknesses of the method are reported.

Investigation of channel capability for sediment transport is an important factor in sanitary sewer and urban runoff drainage system design. This is because of the undesirable effects arising from the reduced channel hydraulic capacity due to the deposition of sediment particles. Self-cleansing channel designs minimize sediment deposition and، thereby، prevent reduced channel hydraulic capacity. Our literature review revealed no previous report on self-cleansing models yet proposed for channels with TRAPEZOIDAL sections. An experimental study was conducted using a TRAPEZOIDAL channel and a non-deposited bed to investigate the self-cleansing process with four different sediment particle sizes under various slopes and discharge rates. The experimental data were exploited to develop a bed load self-cleansing model for the TRAPEZOIDAL channel considering the specific flow، fluid، sediment، channel، and sediment characteristics. The proposed model was then compared with those reported in the literature for circular and rectangular channels. It was found that channel section geometry is a decisive factor in channel self-cleansing rate. Comparisons revealed that circular and rectangular self-cleansing models produce an error of approximately 15% when employed for designing channels with TRAPEZOIDAL sections. Hence، the model developed in this study is recommended for designing channels with TRAPEZOIDAL sections

The problem of steady, laminar and incompressible natural convection flow in an octagonalENCLOSURE was studied. In this investigation, two horizontal walls were maintained at a constant hightemperature, two vertical walls were kept at a constant low temperature and all inclined walls wereconsidered adiabatic. The ENCLOSURE was assumed to be filled with a Bousinessq fluid. The studyincludes computations for different Prandtl numbers Pr such as 0.71, 7, 20 and 50 whereas the Rayleighnumber Ra was varied from 103 to 106. The pressure-velocity form of Navier-Stokes equations andenergy equation was used to represent the mass, momentum and energy conservations of the fluidmedium in the ENCLOSURE. The governing equations and boundary conditions were converted todimentionless form and solved numerically by penalty finite element method with discretization bytriangular mesh elements. Flow and heat transfer characteristics were presented in terms of streamlines, isotherms and average Nusselt number Nu. Results showed that the effect of Ra on the convection heattransfer phenomenon inside the ENCLOSURE was significant for all values of Pr studied (0.71-50). It wasalso found that, Pr influence natural convection inside the ENCLOSURE at high Ra (Ra > 104).