Abstract: The problem of conjugate free convection in a square
cavity filled with nanofluid and heated from below by spatial wall
temperature is studied numerically using the finite difference method.
Water-based nanofluid with copper nanoparticles are chosen for the
investigation. Governing equations are solved over a wide range
of nanoparticle volume fraction (0 ≤ φ ≤ 0.2), wave number
((0 ≤ λ ≤ 4) and thermal conductivity ratio (0.44 ≤ Kr ≤ 6). The
results presented for values of the governing parameters in terms of
streamlines, isotherms and average Nusselt number. It is found that
the flow behavior and the heat distribution are clearly enhanced with
the increment of the non-uniform heating.
Abstract: The study of mixed convection is, usually, focused on the straight channels in which the onset of the mixed convection is well defined as function of the ratio between Grashof number and Reynolds number, Gr/Re. This is not the case for a complex channel wherein the mixed convection is not sufficiently examined in the literature. Our paper focuses on the study of the mixed convection in a complex geometry in which our main contribution reveals that the critical value of the ratio Gr/Re for the onset of the mixed convection increases highly in the type of geometry contrary to the straight channel. Furthermore, the accentuated secondary flow in this geometry prevents the thermal stratification in the flow and consequently the buoyancy driven becomes negligible. To perform these objectives, a numerical study in complex geometry for several values of the ratio Gr/Re with prescribed wall heat flux (H2), was realized by using the CFD code.
Abstract: A three-dimensional numerical simulation of flow
through mini and microchannels with designed roughness is
conducted here. The effect of the roughness height (surface
roughness), geometry, Reynolds number on the friction factor, and
Nusselt number is investigated. The study is carried out by
employing CFD software, CFX. Our work focuses on a water flow
inside a circular mini-channel of 1 mm and microchannels of 500 and
100 m in diameter. The speed entry varies from 0.1 m/s to 20 m/s.
The general trend can be observed that bigger sizes of roughness
element lead to higher flow resistance. It is found that the friction
factor increases in a nonlinear fashion with the increase in obstruction
height. Particularly, the effect of roughness can no longer be ignored
at relative roughness height higher than 3%. A significant increase in
Poiseuille number is detected for all configurations considered. The
same observation can be done for Nusselt number. The transition
zone between laminar and turbulent flow depends on the channel
diameter.
Abstract: A solar receiver is designed for operation under
extremely uneven heat flux distribution, cyclic weather, and cloud
transient cycle conditions, which can include large thermal stress and
even receiver failure. In this study, the effect of different oil velocity
on convection coefficient factor and impact of wind velocity on local
Nusselt number by Finite Volume Method will be analyzed. This
study is organized to give an overview of the numerical modeling
using a MATLAB software, as an accurate, time efficient and
economical way of analyzing the heat transfer trends over stationary
receiver tube for different Reynolds number. The results reveal when
oil velocity is below 0.33m/s, the value of convection coefficient is
negligible at low temperature. The numerical graphs indicate that
when oil velocity increases up to 1.2 m/s, heat convection coefficient
increases significantly. In fact, a reduction in oil velocity causes a
reduction in heat conduction through the glass envelope. In addition,
the different local Nusselt number is reduced when the wind blows
toward the concave side of the collector and it has a significant effect
on heat losses reduction through the glass envelope.
Abstract: The objective of the paper is a numerical study of heat
transfer between perforated metal plates and the surrounding air
flows. Different perforation structures can nowadays be found in
various industrial products. Besides improving the mechanical
properties, the perforations can intensify the heat transfer as well. The
heat transfer coefficient depends on a wide range of parameters such
as type of perforation, size, shape, flow properties of the surrounding
air etc. The paper was focused on three different perforation
structures which have been investigated from the point of the view of
the production in the previous studies. To determine the heat
coefficients and the Nusselt numbers, the numerical simulation
approach was adopted. The calculations were performed using the
OpenFOAM software. The three-dimensional, unstable, turbulent and
incompressible air flow around the perforated surface metal plate was
considered.
Abstract: In this study, we investigated numerically heat
transfer by mixed convection coupled to radiation in a square cavity;
the upper horizontal wall is movable. The purpose of this study is to
see the influence of the emissivity ε and the varying of the
Richardson number Ri on the variation of average Nusselt number
Nu. The vertical walls of the cavity are differentially heated, the left
wall is maintained at a uniform temperature higher than the right
wall, and the two horizontal walls are adiabatic. The finite volume
method is used for solving the dimensionless Governing Equations.
Emissivity values used in this study are ranged between 0 and 1, the
Richardson number in the range 0.1 to 10. The Rayleigh number is
fixed to Ra=104 and the Prandtl number is maintained constant
Pr=0.71. Streamlines, isothermal lines and the average Nusselt
number are presented according to the surface emissivity. The results
of this study show that the Richardson number Ri and emissivity ε
affect the average Nusselt number.
Abstract: In this numerical study, effects of using Al2O3-water
nanofluid on the rate of heat transfer have been investigated. Physical
model is a square enclosure with insulated top and bottom horizontal
walls, while the vertical walls are kept at different constant
temperatures. Two appropriate models are used to evaluate the
viscosity and thermal conductivity of nanofluid. The governing
stream-vorticity equations are solved using a second order central
finite difference scheme, coupled to the conservation of mass and
energy. The study has been carried out for the nanoparticle diameter
30, 60 and 90 nm and the solid volume fraction 0 to 0.04. Results are
presented by average Nusselt number and normalized Nusselt number
in different range of φ and D for mixed convection dominated
regime. It is found that different heat transfer rate is predicted when
the effect of nanoparticle diameter is taken into account.
Abstract: In the present study, analysis of heat transfer is carried
out in the slip flow region for the fluid flowing between two parallel
plates by employing the asymmetric heat fluxes at surface of the
plates. The flow is assumed to be hydrodynamically and thermally
fully developed for the analysis. The second order velocity slip and
viscous dissipation effects are considered for the analysis. Closed
form expressions are obtained for the Nusselt number as a function of
Knudsen number and modified Brinkman number. The limiting
condition of the present prediction for Kn = 0, Kn2 = 0, and Brq1 = 0
is considered and found to agree well with other analytical results.
Abstract: The present study focused on the investigation of the
effects of roughness elements on heat transfer during natural
convection in a rectangular cavity using numerical technique.
Roughness elements were introduced on the bottom hot wall with a
normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic
behaviors were studied using computational method based on Lattice
Boltzmann method (LBM). Numerical studies were performed for a
laminar flow in the range of Rayleigh number (Ra) from 103 to 106
for a rectangular cavity of aspect ratio (L/H) 2.0 with a fluid of
Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness
elements caused a minimum to maximum decrease in the heat
transfer as 7% to 17% respectively compared to smooth enclosure.
The results are presented for mean Nusselt number (Nu), isotherms
and streamlines.
Abstract: In this numerical work, mixed convection and entropy
generation of Cu–water nanofluid in a lid-driven square cavity have
been investigated numerically using the Lattice Boltzmann Method.
Horizontal walls of the cavity are adiabatic and vertical walls have
constant temperature but different values. The top wall has been
considered as moving from left to right at a constant speed, U0. The
effects of different parameters such as nanoparticle volume
concentration (0–0.05), Rayleigh number (104–106) and Reynolds
numbers (1, 10 and 100) on the entropy generation, flow and
temperature fields are studied. The results have shown that addition
of nanoparticles to the base fluid affects the entropy generation, flow
pattern and thermal behavior especially at higher Rayleigh and low
Reynolds numbers. For pure fluid as well as nanofluid, the increase
of Reynolds number increases the average Nusselt number and the
total entropy generation, linearly. The maximum entropy generation
occurs in nanofluid at low Rayleigh number and at high Reynolds
number. The minimum entropy generation occurs in pure fluid at low
Rayleigh and Reynolds numbers. Also at higher Reynolds number,
the effect of Cu nanoparticles on enhancement of heat transfer was
decreased because the effect of lid-driven cavity was increased. The
present results are validated by favorable comparisons with
previously published results. The results of the problem are presented
in graphical and tabular forms and discussed.
Abstract: This paper presents a computational study of steady
state three dimensional very high turbulent flow and heat transfer
characteristics in a constant temperature-surfaced circular duct fitted
with 900 hemispherical inline baffles. The computations are based on
realizable k-ɛ model with standard wall function considering the
finite volume method, and the SIMPLE algorithm has been
implemented. Computational Study are carried out for Reynolds
number, Re ranging from 80000 to 120000, Prandtl Number, Pr of
0.73, Pitch Ratios, PR of 1,2,3,4,5 based on the hydraulic diameter of
the channel, hydrodynamic entry length, thermal entry length and the
test section. Ansys Fluent 15.0 software has been used to solve the
flow field. Study reveals that circular pipe having baffles has a higher
Nusselt number and friction factor compared to the smooth circular
pipe without baffles. Maximum Nusselt number and friction factor
are obtained for the PR=5 and PR=1 respectively. Nusselt number
increases while pitch ratio increases in the range of study; however,
friction factor also decreases up to PR 3 and after which it becomes
almost constant up to PR 5. Thermal enhancement factor increases
with increasing pitch ratio but with slightly decreasing Reynolds
number in the range of study and becomes almost constant at higher
Reynolds number. The computational results reveal that optimum
thermal enhancement factor of 900 inline hemispherical baffle is
about 1.23 for pitch ratio 5 at Reynolds number 120000.It also shows
that the optimum pitch ratio for which the baffles can be installed in
such very high turbulent flows should be 5. Results show that pitch
ratio and Reynolds number play an important role on both fluid flow
and heat transfer characteristics.
Abstract: Experimental study of natural convection heat transfer
inside smooth and rough surfaces of vertical and inclined equilateral
triangular channels of different inclination angles with a uniformly
heated surface are performed. The inclination angle is changed from
15º to 90º. Smooth and rough surface of average roughness (0.02mm)
are used and their effect on the heat transfer characteristics are
studied. The local and average heat transfer coefficients and Nusselt
number are obtained for smooth and rough channels at different heat
flux values, different inclination angles and different Rayleigh
numbers (Ra) 6.48 × 105 ≤ Ra ≤ 4.78 × 106. The results show that
the local Nusselt number decreases with increase of axial distance
from the lower end of the triangular channel to a point near the upper
end of channel, and then, it slightly increases. Higher values of local
Nusselt number for rough channel along the axial distance compared
with the smooth channel. The average Nusselt number of rough
channel is higher than that of smooth channel by about 8.1% for
inclined case at θ = 45o and 10% for vertical case. The results
obtained are correlated using dimensionless groups for both rough
and smooth surfaces of the inclined and vertical triangular channels.
Abstract: The convective heat and mass transfer in nanofluid
flow through a porous media due to a permeable stretching sheet with
magnetic field, viscous dissipation, chemical reaction and Soret
effects are numerically investigated. Two types of nanofluids, namely
Cu-water and Ag-water were studied. The governing boundary layer
equations are formulated and reduced to a set of ordinary differential
equations using similarity transformations and then solved
numerically using the Keller box method. Numerical results are
obtained for the skin friction coefficient, Nusselt number and
Sherwood number as well as for the velocity, temperature and
concentration profiles for selected values of the governing
parameters. Excellent validation of the present numerical results has
been achieved with the earlier linearly stretching sheet problems in
the literature.
Abstract: The thermal control in many systems is widely
accomplished applying mixed convection process due to its low cost,
reliability and easy maintenance. Typical applications include the
aircraft electronic equipment, rotating-disc heat exchangers, turbo
machinery, and nuclear reactors, etc. Natural convection in an inclined
square enclosure heated via wall heater has been studied numerically.
Finite volume method is used for solving momentum and energy
equations in the form of stream function–vorticity. The right and left
walls are kept at a constant temperature, while the other parts are
adiabatic. The range of the inclination angle covers a whole revolution.
The method is validated for a vertical cavity. A general power law
dependence of the Nusselt number with respect to the Rayleigh
number with the coefficient and exponent as functions of the
inclination angle is presented. For a fixed Rayleigh number, the
inclination angle increases or decreases is found.
Abstract: Meeting the growth in demand for digital services
such as social media, telecommunications, and business and cloud
services requires large scale data centres, which has led to an increase
in their end use energy demand. Generally, over 30% of data centre
power is consumed by the necessary cooling overhead. Thus energy
can be reduced by improving the cooling efficiency. Air and liquid
can both be used as cooling media for the data centre. Traditional
data centre cooling systems use air, however liquid is recognised as a
promising method that can handle the more densely packed data
centres. Liquid cooling can be classified into three methods; rack heat
exchanger, on-chip heat exchanger and full immersion of the
microelectronics. This study quantifies the improvements of heat
transfer specifically for the case of immersed microelectronics by
varying the CPU and heat sink location. Immersion of the server is
achieved by filling the gap between the microelectronics and a water
jacket with a dielectric liquid which convects the heat from the CPU
to the water jacket on the opposite side. Heat transfer is governed by
two physical mechanisms, which is natural convection for the fixed
enclosure filled with dielectric liquid and forced convection for the
water that is pumped through the water jacket. The model in this
study is validated with published numerical and experimental work
and shows good agreement with previous work. The results show that
the heat transfer performance and Nusselt number (Nu) is improved
by 89% by placing the CPU and heat sink on the bottom of the
microelectronics enclosure.
Abstract: In this paper, effects of using Alumina-water
nanofluid on the rate of heat transfer have been investigated
numerically. Physical model is a square enclosure with insulated top
and bottom horizontal walls, while the vertical walls are kept at
different constant temperatures. Two appropriate models are used to
evaluate the viscosity and thermal conductivity of nanofluid. The
governing stream-vorticity equations are solved using a second order
central finite difference scheme, coupled to the conservation of mass
and energy. The study has been carried out for the Richardson
number 0.1 to 10 and the solid volume fraction 0 to 0.04. Results are
presented by isotherms lines, average Nusselt number and normalized
Nusselt number in different range of φ and Ri for forced, combined
and natural convection dominated regime. It is found that higher heat
transfer rate is predicted when the effects of nanoparticle is taken into
account.
Abstract: Numerical studies were conducted using Lattice
Boltzmann Method (LBM) to study the natural convection in a square
cavity in the presence of roughness. An algorithm based on a single
relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice
Boltzmann Method (LBM) was developed. Roughness was
introduced on both the hot and cold walls in the form of sinusoidal
roughness elements. The study was conducted for a Newtonian fluid
of Prandtl number (Pr) 1.0. The range of Ra number was explored
from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic
behavior of fluid was analyzed using a differentially heated square
cavity with roughness elements present on both the hot and cold wall.
Neumann boundary conditions were introduced on horizontal walls
with vertical walls as isothermal. The roughness elements were at the
same boundary condition as corresponding walls. Computational
algorithm was validated against previous benchmark studies
performed with different numerical methods, and a good agreement
was found to exist. Results indicate that the maximum reduction in
the average heat transfer was 16.66 percent at Ra number 10^5.
Abstract: An analysis is carried out to investigate the effect of
magnetic field and heat source on the steady boundary layer flow and
heat transfer of a Casson nanofluid over a vertical cylinder stretching
exponentially along its radial direction. Using a similarity
transformation, the governing mathematical equations, with the
boundary conditions are reduced to a system of coupled, non –linear
ordinary differential equations. The resulting system is solved
numerically by the fourth order Runge – Kutta scheme with shooting
technique. The influence of various physical parameters such as
Reynolds number, Prandtl number, magnetic field, Brownian motion
parameter, thermophoresis parameter, Lewis number and the natural
convection parameter are presented graphically and discussed for non
– dimensional velocity, temperature and nanoparticle volume
fraction. Numerical data for the skin – friction coefficient, local
Nusselt number and the local Sherwood number have been tabulated
for various parametric conditions. It is found that the local Nusselt
number is a decreasing function of Brownian motion parameter Nb
and the thermophoresis parameter Nt.
Abstract: In the present study, mixed convection in a horizontal
rectangular duct using Al2O3 is numerically investigated. The effects
of different Rayleigh number, Reynolds number and radiation on
flow and heat transfer characteristics are studied in detail. This study
covers Rayleigh number in the range of 2 × 10^6 ≤ Ra ≤ 2 × 10^7 and
Reynolds number in the range of 100 ≤ Re ≤ 1100. Results reveal that
the Nusselt number increases as Reynolds and Rayleigh numbers
increase. It is also found that the dimensionless temperature
distribution increases as Rayleigh number increases.
Abstract: In this paper the effect of wall waviness of side walls
in a two-dimensional wavy enclosure is numerically investigated.
Two vertical wavy walls and straight top wall are kept isothermal and
the bottom wall temperature is higher and spatially varying with
cosinusoidal temperature distribution. A computational code based on
Finite-volume approach is used to solve governing equations and
SIMPLE method is used for pressure velocity coupling. Test is
performed for several different numbers of undulations. The Prandtl
number was kept constant and the Ra number denotes that the flow is
laminar. Temperature and velocity fields are determined. Therefore,
according to the obtained results a correlation is proposed for average
Nusselt number as a function of number of side wall waves. The
results indicate that the Nusselt number is highly affected by number
of waves and increasing it decreases the wavy walls Nusselt number;
although the Nusselt number is not highly affected by surface
waviness when the number of undulations is below one.