scholarly journals Numerical Simulation on Heat Flow for Mixed Convection Within a Triangular Enclosure

2019 ◽  
Vol 39 ◽  
pp. 27-43
Author(s):  
Muhammad Sajjad Hossain ◽  
MM Billah ◽  
MZI Bangalee ◽  
MA Alim
Keyword(s):  
Heat Transfer ◽  
Heat Flow ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
The Other ◽  
Bottom Wall ◽  
Bulk Temperature ◽  
Triangular Enclosure

Heat flow for laminar mixed convection in a triangular enclosure with uniformly heated bottom wall is solved using Galerkin weighted residual method of finite element formulation. A fluid with Prandtl number (Pr = 0.71) is also used to investigate the effects of heat flow for Reynolds number(40 ≤ Re ≤ 110) varying Rayleigh number (103≤ Ra ≤ 104) in that enclosure. In the enclosure, the left wall is considered cold; bottom wall is uniformly heated while the other inclined wall is insulated. The geometry of physical problems is represented mathematically by different sets of governing equations along with appropriate boundary conditions. Results are shown in terms of streamlines, isotherms, average Nusselt number and average temperature of the fluid in the cavity for uniform heating of bottom wall. It is seen that heat transfer rate from the heat source is higher for increasing value of Re. On the other hand, average bulk temperature declines significantly. It is also indicated that for fixed Prandtl number and various Ra, the buoyancy force and heat transfer rate inside the enclosure are increased for the greater value of Re. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 27-43

Mixed Convection Falkner–Skan Flow of a Maxwell Fluid

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
T. Hayat ◽  
M. Farooq ◽  
Z. Iqbal ◽  
A. Alsaedi
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Prandtl Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Maxwell Fluid ◽  
Series Solutions ◽  
Newtonian Heating ◽  
Transformation Procedure

We performed a study for the effect of Newtonian heating on the nonsimilar mixed convection Falkner–Skan flow of a Maxwell fluid. Transformation procedure is adopted in obtaining the ordinary differential equations. Homotopic approach is adopted for the series solutions of velocity and temperature. Special emphasis is given to the effects of Prandtl number (Pr) and conjugate parameter (γ) which measure the strength of surface heating. It is observed that temperature and heat transfer rate are enhanced by increasing the conjugate parameter.

Numerical Simulation of Boundary Conditions Effect on Heat Transfer and Entropy Generation in a Square Cavity Filled with Al2O3-Cu -Water Hybrid Nanofluid

2021 ◽  
Vol 406 ◽  
pp. 98-109
Author(s):  
Ilhem Zeghbid ◽  
Rachid Bessaih
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Entropy Generation ◽  
Transfer Rate ◽  
The Other ◽  
Hybrid Nanofluid ◽  
Different Boundary Conditions

A numerical simulation was performed in four geometries with different boundary conditions; two geometries have top walls moving with a constant horizontal velocity U0 in two opposite directions, while the other geometries have vertical walls moving in two opposite directions with a constant vertical velocity V0. These cavities are filled with hybrid nanofluid Al2O3-Cu/water, and heated by two constant flow heat sources placed on the left vertical wall. The moving wall and the other walls are respectively maintained at a local cold temperature Tc. The interest of this work is to see the effects generated by incorporation of hybrid nanofluids on the mixed convection flow, and to make an analysis of the entropy production in the mixed convection problem in order to be able to choose the geometry with different boundary conditions among the four geometries with different boundary conditions that will ensure energy efficiency. The finite volume method was used to solve the heat transfer flow equations across the physical domain with the SIMPLER algorithm. The influence of relevant parameters such as Richardson and Reynolds numbers and volume fraction of nanoparticles on entropy generation and heat transfer rate were studied. It was found that entropy generation decreases with increasing Richardson number, Reynolds number and that incorporation of a hybrid Al2O3-Cu/water nanofluid in the base fluid improves the high heat transfer rate.

A Numerical Study of Three-Dimensional Natural Convective Heat Transfer From a Plate With a “Wavy” Surface

2001 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Matt Garrett
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Surface Waves ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Three Dimensional ◽  
Wavy Surface ◽  
Surface Waviness ◽  
Dimensionless Amplitude ◽  
The Mean

Abstract Natural convective heat transfer from a wide isothermal plate which has a “wavy” surface, i.e., has a surface which periodically rises and falls, has been numerically studied. The surface waves run parallel to the direction of flow over the surface and have a relatively small amplitude. Two types of wavy surface have been considered here — saw-tooth and sinusoidal. Surfaces of the type considered are approximate models of situations that occur in certain window covering applications, for example, and are also sometimes used to try to enhance the heat transfer rate from the surface. The flow has been assumed to be laminar. Because the surface waves are parallel to the direction of flow, the flow over the surface will be three-dimensional. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being treated by means of the Boussinesq type approximation. The governing equations have been written in dimensionless form, the height of the surface being used as the characteristic length scale and the temperature difference between the surface temperature and the temperature of the fluid far from the plate being used as the characteristic temperature. The dimensionless equations have been solved using a finite-element method. Although the flow is three-dimensional because the surface waves are all assumed to have the same shape, the flow over each surface thus being the same, and it was only necessary to solve for the flow over one of the surface waves. The solution has the following parameters: the Grashof number based on the height, the Prandtl number, the dimensionless amplitude of the surface waviness, the dimensionless pitch of the surface waviness, and the form of the surface waviness (saw-tooth or sinusoidal). Results have been obtained for a Prandtl number of 0.7 for Grashof numbers up to 106. The effects of Grashof number, dimensionless amplitude and dimensionless pitch on the mean heat transfer rate have been studied. It is convenient to introduce two mean heat transfer rates, one based on the total surface area and the other based on the projected frontal area of the surface. A comparison of the values of these quantities gives a measure of the effectiveness of the surface waviness in increasing the mean heat transfer rate. The results show that while surface waviness increases the heat transfer rate based on the frontal area, the modifications of the flow produced by the surface waves are such that the increase in heat transfer rate is less than the increase in surface area.

scholarly journals Improved Energy Efficiency of Mixed Convection Heating Process in Eccentric Annulus

2021 ◽  
Vol 13 (8) ◽  
pp. 168781402110391
Author(s):  
Ben Abdelmlek Khaoula ◽  
Ben Nejma Fayçal
Keyword(s):  
Heat Transfer ◽  
Energy Efficiency ◽  
Rayleigh Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Rotation Speed ◽  
Numerical Study ◽  
Heating Process ◽  
Eccentric Annulus

This paper deals with a numerical study of mixed convection heat transfer in horizontal eccentric annulus. The inner cylinder is supposed hot and rotating, however the outer one is kept cold and motionless. The numerical problem was solved using COMSOL Multiphysics® which is based on finite element method. The resolution of the partial differential equations was conducted through an implicit scheme with the use of the damped Newton’s method. The present numerical analysis concerns the effect of eccentricity, rotation speed and Rayleigh number on the flow patterns, heat transfer rate, and energy efficiency of the process. It was found that the heat transfer rate increases with the increase of Rayleigh number. In addition, the heat transfer rate drops with the increase of rotation speed. Finally, we have demonstrated that maximum energy efficiency is achieved not only with higher Rayleigh number but also it is maximum with small eccentricity.

Natural Convection in an Anisotropic Porous Enclosure Due to Nonuniform Heating From the Bottom Wall

2009 ◽  
Vol 131 (7) ◽  
Author(s):  
Ashok Kumar ◽  
P. Bera
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Principal Direction ◽  
Orientation Angle ◽  
Bottom Wall ◽  
Nonuniform Heating ◽  
Material Derivative ◽  
Porous Enclosure

A comprehensive numerical investigation on the natural convection in a hydrodynamically anisotropic porous enclosure is presented. The flow is due to nonuniformly heated bottom wall and maintenance of constant temperature at cold vertical walls along with adiabatic top wall. Brinkman-extended non-Darcy model, including material derivative, is considered. The principal direction of the permeability tensor has been taken oblique to the gravity vector. The spectral element method has been adopted to solve numerically the governing conservative equations of mass, momentum, and energy by using a stream-function vorticity formulation. Special attention is given to understand the effect of anisotropic parameters on the heat transfer rate as well as flow configurations. The numerical experiments show that in the case of isotropic porous enclosure, the maximum rates of bottom as well as side heat transfers (Nub and Nus) take place at the aspect ratio, A, of the enclosure equal to 1, which is, in general, not true in the case of anisotropic porous enclosures. The flow in the enclosure is governed by two different types of convective cells: rotating (i) clockwise and (ii) anticlockwise. Based on the value of media permeability as well as orientation angle, in the anisotropic case, one of the cells will dominate the other. In contrast to isotropic porous media, enhancement of flow convection in the anisotropic porous enclosure does not mean increasing the side heat transfer rate always. Furthermore, the results show that anisotropy causes significant changes in the bottom as well as side average Nusselt numbers. In particular, the present analysis shows that permeability orientation angle has a significant effect on the flow dynamics and temperature profile and consequently on the heat transfer rates.

A comprehensive review on mixed convection for various patterns of kinematically and thermally induced scenarios within cavities

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Leo Lukose ◽  
Tanmay Basak
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Inertial Forces ◽  
Content Type ◽  
Flow Interaction ◽  
Experimental Works ◽  
Solid Obstacles ◽  
S Model

Purpose The purpose of this paper is to address various works on mixed convection and proposes 10 unified models (Models 1–10) based on various thermal and kinematic conditions of the boundary walls, thermal conditions and/ or kinematics of objects embedded in the cavities and kinematics of external flow field through the ventilation ports. Experimental works on mixed convection have also been addressed. Design/methodology/approach This review is based on 10 unified models on mixed convection within cavities. Models 1–5 involve mixed convection based on the movement of single or double walls subjected to various temperature boundary conditions. Model 6 elucidates mixed convection due to the movement of single or double walls of cavities containing discrete heaters at the stationary wall(s). Model 7A focuses mixed convection based on the movement of wall(s) for cavities containing stationary solid obstacles (hot or cold or adiabatic) whereas Model 7B elucidates mixed convection based on the rotation of solid cylinders (hot or conductive or adiabatic) within the cavities enclosed by stationary or moving wall(s). Model 8 is based on mixed convection due to the flow of air through ventilation ports of cavities (with or without adiabatic baffles) subjected to hot and adiabatic walls. Models 9 and 10 elucidate mixed convection due to flow of air through ventilation ports of cavities involving discrete heaters and/or solid obstacles (conductive or hot) at various locations within cavities. Findings Mixed convection plays an important role for various processes based on convection pattern and heat transfer rate. An important dimensionless number, Richardson number (Ri) identifies various convection regimes (forced, mixed and natural convection). Generalized models also depict the role of “aiding” and “opposing” flow and combination of both on mixed convection processes. Aiding flow (interaction of buoyancy and inertial forces in the same direction) may result in the augmentation of the heat transfer rate whereas opposing flow (interaction of buoyancy and inertial forces in the opposite directions) may result in decrease of the heat transfer rate. Works involving fluid media, porous media and nanofluids (with magnetohydrodynamics) have been highlighted. Various numerical and experimental works on mixed convection have been elucidated. Flow and thermal maps associated with the heat transfer rate for a few representative cases of unified models [Models 1–10] have been elucidated involving specific dimensionless numbers. Originality/value This review paper will provide guidelines for optimal design/operation involving mixed convection processing applications.

Numerical simulation of water/alumina nanofluid mixed convection in square lid-driven cavity

2019 ◽  
Vol 30 (5) ◽  
pp. 2781-2807
Author(s):  
Davood Toghraie ◽  
Ehsan Shirani
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Richardson Number ◽  
Hartmann Number ◽  
Two Phase ◽  
Content Type ◽  
Driven Cavity

Purpose The purpose of this paper is to investigate the mixed convection of a two-phase water–aluminum oxide nanofluid in a cavity under a uniform magnetic field. Design/methodology/approach The upper wall of the cavity is cold and the lower wall is warm. The effects of different values of Richardson number, Hartmann number, cavitation length and solid nanoparticles concentration on the flow and temperature field and heat transfer rate were evaluated. In this paper, the heat flux was assumed to be constant of 10 (W/m2) and the Reynolds number was assumed to be constant of 300 and the Hartmann number and the volume fraction of solid nanoparticles varied from 0 to 60 and 0 to 0.06, respectively. The Richardson number was considered to be 0.1, 1 and 5. Aspect ratios were 1, 1.5 and 2. Findings Comparison of the results of this paper with the results of the numerical and experimental studies of other researchers showed a good correlation. The results were presented in the form of velocity and temperature profiles, stream and isotherm lines and Nusselt numbers. The results showed that by increasing the Hartmann number, the heat transfer rate decreases. An increase from 0 to 20 in Hartmann number results in a 20 per cent decrease in Nusselt numbers, and by increasing the Hartmann number from 20 to 40, a 16 per cent decrease is observed in Nusselt number. Accordingly, it is inferred that by increasing the Hartmann number, the reduction in the Nusselt number is decreased. As the Richardson number increased, the heat transfer rate and, consequently, the Nusselt number increased. Therefore, an increase in the Richardson number results in an increase of the Nusselt number, that is, an increase in Richardson number from 0.1 to 1 and from 1 to 5 results in 37 and 47 per cent increase in Nusselt number, respectively. Originality/value Even though there have been numerous investigations conducted on convection in cavities under various configurations and boundary conditions, relatively few studies are conducted for the case of nanofluid mixed convection in square lid-driven cavity under the effect of magnetic field using two-phase model.

scholarly journals Role of Rotating Cylinder toward Mixed Convection inside a Wavy Heated Cavity via Two-Phase Nanofluid Concept

Nanomaterials ◽  
2020 ◽  
Vol 10 (6) ◽  
pp. 1138 ◽  
Author(s):  
Ammar I. Alsabery ◽  
Mohammad Ghalambaz ◽  
Taher Armaghani ◽  
Ali Chamkha ◽  
Ishak Hashim ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Rotating Cylinder ◽  
Alumina Nanoparticles ◽  
Optimum Number ◽  
Two Phase ◽  
Rotation Direction

The mixed convection two-phase flow and heat transfer of nanofluids were addressed within a wavy wall enclosure containing a solid rotating cylinder. The annulus area between the cylinder and the enclosure was filled with water-alumina nanofluid. Buongiorno’s model was applied to assess the local distribution of nanoparticles in the host fluid. The governing equations for the mass conservation of nanofluid, nanoparticles, and energy conservation in the nanofluid and the rotating cylinder were carried out and converted to a non-dimensional pattern. The finite element technique was utilized for solving the equations numerically. The influence of the undulations, Richardson number, the volume fraction of nanoparticles, rotation direction, and the size of the rotating cylinder were examined on the streamlines, heat transfer rate, and the distribution of nanoparticles. The Brownian motion and thermophoresis forces induced a notable distribution of nanoparticles in the enclosure. The best heat transfer rate was observed for 3% volume fraction of alumina nanoparticles. The optimum number of undulations for the best heat transfer rate depends on the rotation direction of the cylinder. In the case of counterclockwise rotation of the cylinder, a single undulation leads to the best heat transfer rate for nanoparticles volume fraction about 3%. The increase of undulations number traps more nanoparticles near the wavy surface.

Numerical Study of Fluid Flow and Heat Transfer Enhancement of Nanofluids over Tube Bank

2013 ◽  
Vol 388 ◽  
pp. 149-155 ◽  
Author(s):  
Mazlan Abdul Wahid ◽  
Ahmad Ali Gholami ◽  
H.A. Mohammed
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Pressure Drop ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Cross Flow ◽  
Bulk Temperature ◽  
Compact Heat Exchanger ◽  
Pure Fluid ◽  
Tube Banks

In the present work, laminar cross flow forced convective heat transfer of nanofluid over tube banks with various geometry under constant wall temperature condition is investigated numerically. We used nanofluid instead of pure fluid ,as external cross flow, because of its potential to increase heat transfer of system. The effect of the nanofluid on the compact heat exchanger performance was studied and compared to that of a conventional fluid.The two-dimensional steady state Navier-Stokes equations and the energy equation governing laminar incompressible flow are solved using a Finite volume method for the case of flow across an in-line bundle of tube banks as commercial compact heat exchanger. The nanofluid used was alumina-water 4% and the performance was compared with water. In this paper, the effect of parameters such as various tube shapes ( flat, circle, elliptic), and heat transfer comparison between nanofluid and pure fluid is studied. Temperature profile, heat transfer coefficient and pressure profile were obtained from the simulations and the performance was discussed in terms of heat transfer rate and performance index. Results indicated enhanced performance in the use of a nanofluid, and slight penalty in pressure drop. The increase in Reynolds number caused an increase in the heat transfer rate and a decrease in the overall bulk temperature of the cold fluid. The results show that, for a given heat duty, a mas flow rate required of the nanofluid is lower than that of water causing lower pressure drop. Consequently, smaller equipment and less pumping power are required.

Effect of a Pair of Horizontal Frame Members on the Convective Heat Transfer With Laminar and Turbulent Flow From a Recessed Window to a Room

2011 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
David Naylor
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Convective Heat Transfer ◽  
Turbulent Flows ◽  
Heat Transfer Rate ◽  
Convective Heat ◽  
Transfer Rate ◽  
Numerical Study ◽  
Wall Functions ◽  
Inner Surface

The horizontal frame members that often protrude from the inner surface of a window can significantly effect the convective heat transfer rate from this inner surface to the room. The purpose of the present numerical study was to determine how the size of a pair of horizontal frame members effect this heat transfer rate. The flow has been assumed to be steady and conditions under which laminar, transitional, and turbulent flows occur are considered. Fluid properties have been assumed constant except for the density change with temperature that gives rise to the buoyancy forces, this being dealt with using the Boussinesq approach. The governing equations have been solved using the FLUENT commercial CFD code. The k-epsilon turbulence model with standard wall functions and with buoyancy force effects fully accounted for has been used. The solution has the following parameters: the Rayleigh number, the Prandtl number, the dimensionless window recess depth, and the dimensionless width and depth of the frame members. Results have been obtained for a Prandtl number of 0.74.

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