The article deals with magnetic field of free convective flows in cavities similar to those used in artificial growth of single crystals from melts (horizontal Bridgman configurations) and having aspect ratios an equal to “4”. The combined effect of wall electrical conductivity and vertical direction of the magnetic field on the buoyancy induced flow of mercury was investigated numerically. The validation of the numerical method was achieved by comparison with both experimental and analytical data found in the literature. The plotted results for variation of velocity, temperature and Nusselt number in terms of the Hartmann number Ha and Rayleigh number “Ra” showed a considerable decrease in convection intensity as the magnetic field is increased, especially for values of “Gr” situated around 107. The calculations also showed that the vertically directed magnetic field (perpendicular to the x-z plane) is the most effective in controlling the flow and hence the speed of growth of the crystal. Also, wall electrical conductivity enhances damping by changing the distribution of the induced electric current to one which augments the magnitude of the Lorentz force.

A numerical investigation of laminar mixed convection heat transfer in a shallow two sided lid driven RECTANGULAR ENCLOSURE of aspect ratio 5, (AR=5) is executed. The natural convection effect is sustained by subjecting the bottom wall to a higher temperature than its top counterpart. In addition, the two horizontal walls of the ENCLOSURE are moving in different directions and the two vertical walls of the ENCLOSURE are kept insulate. Discretization of the governing equations is achieved through a finite volume scheme. Fluid flow and heat transfer characteristics are examined in the domain of the Richardson number and Grashof number as 10-3£Ri=Gr / Re2£103 and Gr=10 4 while the bottom side of ENCLOSURE is moving in two different horizontal directions. The working fluid is assigned a Prandtl number of 0.7, 10 and 100 throughout this investigation. Temporal variations of streamlines, isotherms, and Nusselt number are presented in this investigation for various pertinent dimensionless groups.

In this paper, we present an analysis for the unsteady two-dimensional flow of incompressible fractional NTNN model. The purpose of this research is to detect exact solutions for the cosine oscillation inside an oscillating RECTANGULAR duct having fractional fluid. The mixed initial-boundary value problem is simplified by using Laplace and double finite Fourier sine transform. The impacts of pertinent parameters on the velocity profile and the corresponding shear stresses are analyzed through graphical illustrations for cosine oscillation. Our results indicate that the fluid's flow rises in correlation with fractional and rheological factors, such as α,N,ω, and t. As limiting cases of exact solution, the results can also be obtained for the ordinary NTNN and Newtonian fluid.

In this study, the cooling of a hot obstacle in a RECTANGULAR cavity filled with water-CuO nanofuid is examined numerically. This cavity has an inlet and outlet, and the cold nanofluid comes from the left side of the cavity and goes out from the opposite side, after cooling the hot obstacle. All walls are insulated, and the SIMPLER algorithm is employed for solving the governing equations. The effects of fluid inertia, the magnetic field strength, the volume fraction of nanoparticles, and the place of the outlet on the heat transfer rate are scrutinized. According to the results, the average Nusselt number builds up as the outlet place goes down. In other words, when the outlet is located at the bottom of the cavity, the rate of the heat transfer is maximum. Moreover, by increasing the Reynolds number and volume fraction of nanoparticles, the average Nusselt number builds up as well.

Steady, laminar, natural-convection flow in the presence of a magnetic field in an inclined RECTANGULAR ENCLOSURE heated from one side and cooled from the adjacent side was considered. The governing equations were solved numerically for the stream function, vorticity and temperature using the finite-volume method for various Grashof and Hartman numbers and inclination angles and magnetic field directions. The results show that the orientation and the strength and direction of the magnetic field have significant effects on the flow and temperature fields. Counterclockwise inclination induces the formation of multiple eddies inside the ENCLOSURE significantly affecting the temperature field. Circulation inside the ENCLOSURE and therefore the convection become stronger as the Grashof number increases while the magnetic field suppresses the convective flow and the heat transfer rate.

Mixed convection is a fundamentally significant heat transfer mechanism that occurs in selection industrial and technological applications. In this study, first the laminar mixed convection inside RECTANGULAR ENCLOSURE with moving wall and Aspect Ratio=10 is modeled and then the results are compared with other investigate. After showing varity of results, the investigation is continued with turbulent flow using RNG k-e  and standard k-e. The results indicate that the turbulence intensity depends on the position. For example, in vertical walls and boundary layer, the flow is laminar and it is in the center of ENCLOSURE turbulent.

This paper deals with the study of natural convection cooling of a discrete heater array in Cu-EG-water nanofluid filled RECTANGULAR ENCLOSURE. A 3 x 3 array of non-protruding heat sources is embedded on one of the vertical walls of the ENCLOSURE while the top horizontal and opposite vertical walls are assumed to be isothermally cold. The remaining portions in which the heaters are mounted and all other walls are insulated.The above setup is modeled into a system of partial differential equations which are solved numerically using finite volume method based on the Semi-Implicit Method for Pressure Linked Equation (SIMPLE) algorithm and power law scheme. The wide range of parameters for computation are the aspect ratio of the ENCLOSURE, the mixture proportion of Ethylene glycol-water, the solid volume fraction of the nanoparticle along with two different thermal conductivity models. It is observed that the proper choice of the computation parameters and thermal conductivity models could be able to maximize the heat transfer rate from the heater array. Also, the results obtained in this study will provide new guidelines in the field of electronic equipment cooling.

In this study, the variation of aspect ratio (height to width) and nanoparticles volume fractions of on natural convection heat transfer of Alumina-water nanofluid in ENCLOSUREs was investigated. It is supposed that the nanofluid are applied as incompressible fluid and single phase base on water (as basefluid) include Alumina (Al2O3), with volume fraction (concentration) 0-4%, under laminar flow. Governing equations were solved numerically by finite volume method (Fluent). Rayleigh number is in the range of 4×105-108 in 2D ENCLOSUREs with specific aspect ratios (0. 6-3. 2) and temperature difference (Δ 𝑇 ). In the present work with due attention to the used models for the viscosity and the nanofluid coefficientof thermal conduction was showed that the Nusselt number of the nanofluid with more concentration, is increasing due to more viscosity and coefficient of thermal conduction rather than pure water. In other words the Nusselt number in every specific aspect ratio, in minimum of concentration equals 0. 3% and in maximum of concentration equals 14% would be decreased. In a specific concentration, The Nusselt number was more related with aspect ratio rather than the coefficientof natural convection heat transfer and thermal conduction.