Numerical Study of MHD Natural Convection in Trapezoidal Enclosure Filled With (50%MgO-50%Ag/Water) Hybrid Nanofluid: Heated Sinusoidal from Below

Numerical simulation of MHD free convection in a two-dimensional trapezoidal cavity of a hybrid nanofluid has been carried out in this research. The cavity is heated sinusoidal from the bottom wall, and the inclined walls are cooled while the top wall is isolated. The hybrid nanofluid (MgO-Ag/water) has been used as a working fluid. The numerical simulation has been validated with past papers and met a good agreement. The considered parameters are a range of Rayleigh number (Ra= 103 to 106), Hartmann number (Ha= 0 to 60) and volume fraction (f= 0 to 0.02). The results are presented as isotherms, stream functions, local and average Nusselt numbers, from which it is observed that the strength of the stream functions and isotherms increases with the increase of the Ra and ϕ while the increase in Hartmann number reduce the circulation of the flow and increases the isotherms strength. Also, the Nusselt number is increases with Ra and ϕ while it decreases with Ha.

Numerical Analysis of Natural Convection Driven Flow of a Non-Newtonian Power-Law Fluid in a Trapezoidal Enclosure with a U-Shaped Constructal

Placement of fins in enclosures has promising utilization in advanced technological processes due to their role as heat reducing/generating elements such as in conventional furnaces, economizers, gas turbines, heat exchangers, superconductive heaters and so forth. The advancement in technologies in power engineering and microelectronics requires the development of effective cooling systems. This evolution involves the utilization of fins of significantly variable geometries enclosed in cavities to increase the heat elimination from heat-generating mechanisms. Since fins are considered to play an effective role in the escalation of heat transmission, the current study is conducted to examine the transfer of heat in cavities embedding fins, as well as the effect of a range of several parameters upon the transmission of energy. The following research is supplemented with the interpretation of the thermo-physical aspects of a power-law liquid enclosed in a trapezoidal cavity embedding a U-shaped fin. The Boussinesq approximation is utilized to generate the mathematical attributes of factors describing natural convection, which are then used in the momentum equation. Furthermore, the Fourier law is applied to formulate the streaming heat inside the fluid flow region. The formulated system describing the problem is non-dimensionalized using similarity transformations. The geometry of the problem comprises a trapezoidal cavity with a non-uniformly heated U-shaped fin introduced at the center of the base of the enclosure. The boundaries of the cavity are at no-slip conditions. Non-uniform heating is provided at the walls (l1 and l2), curves (c1,c2 and c3) and surfaces (s1 and s2) of the fin; the upper wall is insulated whereas the base and sidewalls of the enclosure are kept cold. The solution of the non-dimensionalized equations is procured by the Galerkin finite element procedure. To acquire information regarding the change in displacement w.r.t time and temperature, supplementary quadratic interpolating functions are also observed. An amalgam meshing is constructed to elaborate the triangular and quadrilateral elements of the trapezoidal domain. Observation of significant variation in the flow configurations for a specified range of parameters is taken into consideration i.e., 0.5≤n≤1.5 and 104≤Ra≤106. Furthermore, flow structures in the form of velocity profiles, streamlines, and temperature contours are interpreted for the parameters taken into account. It is deduced from the study that ascending magnitude of (Ra) elevates level of kinetic energy and magnitude of heat flux; however, a contrary configuration is encapsulated for the power-law index. Navier–Stokes equations constituting the phenomenon are written with the help of non-dimensionalized stream function, temperature profiles, and vortices, and the solutions are acquired using the finite element method. Furthermore, the attained outcomes are accessible through velocity and temperature profiles. It is worth highlighting the fact that the following analysis enumerates the pseudo-plastic, viscous and dilatant behavior of the fluid for different values of (n). This study highlights that the momentum profile and the heat transportation increase by increasing (Ra) and decline as the viscosity of the fluid increases. Overall, it can be seen from the current study that heat transportation increases with the insertion of a fin in the cavity. The current communication signifies the phenomenon of a power-law fluid flow filling a trapezoidal cavity enclosing a U-shaped fin. Previously, researchers have studied such phenomena mostly in Newtonian fluids, hence the present effort presents novelty regarding consideration of a power-law liquid in a trapezoidal enclosure by the placement of a U-shaped fin.

Marangoni convection of nanofluid in a wavy trapezoidal enclosure

The purpose of this study is to investigate the behaviour of natural convection in a wavy trapezoidal enclosure that is filled with nanofluid. The left wavy wall has wavelength, l, and amplitude, A. The top and bottom walls are adiabatic while the side walls are set to constant temperature, and shear stress occurs at the top of the enclosure. The numerical approach used in this study in order to discretize the governing equations with its boundary conditions is the finite element method where the Galerkin technique is adopted. The solutions obtained are for various values of the Marangoni number, Rayleigh number, and solid particle volume fraction. The graphs of the streamlines, isotherms, local Nusselt, and average Nusselt numbers are then presented and discussed.

Computational study of laminar free convection inside tilting irregular cavity of a batch-type solar collector

Batch-type solar collector is a tilt-able water-heating solar-thermal system comprising an isosceles-trapezoidal enclosure housing a circular-cylinder absorber at the bottom wall, insulated side-walls, and flat-top glazing. Free convection of air inside such trapezoidal enclosure is studied numerically by varying the tilt angle of the whole enclosure from 0o-70o. The influence of tilt on the flow field has been demonstrated by plotting the streamlines and isotherms. The present study successfully identifies the importance of enclosure-tilt in quantifying heat-loss between absorber and glazing by developing a computational correlation between Nusselt and Rayleigh as a function of tilt. The correlation trend is non-monotonic over the range of angular Rayleigh numbers numerically experimented with having a peak around angular Rayleigh number 3?105 corresponding to the tilt-angle 30 degrees. The irregular-shaped cavity implies that the heat-transfer correlations already existing for regular-shaped cavities may not be used otherwise they will draw implausible conclusions and this argument identifies the novelty of the present study.

ANALYSIS OF ENTROPY GENERATION FOR MIXED CONVECTION FLUID FLOW IN A TRAPEZOIDAL ENCLOSURE USING THE MODIFIED BLOCKED REGION METHOD

In this research, analysis of entropy generation for mixed convection fluid flow in a trapezoidal enclosure is numerically investigated. To achieve this goal, the influences of Grashof number, Reynolds number and inclination angle of enclosure side walls on the distributions of the velocity and temperature fields and the values of entropy generation and Bejan numbers are examined with full details. The Boussinesq approximation is used to calculate the buoyancy force. Also, the entropy generation numbers are calculated according to the second law of thermodynamics. In addition, the modified blocked region method is applied to accurately simulate the diagonal walls of the trapezoidal enclosure. The results of numerical solution show that the maximum values of the flow irreversibility in the whole computational domain of the enclosure are related to the case with the highest values of Grashof number, Reynolds number and inclination angle of side walls.