Published at : 18 Jan 2023
Volume : IJtech Vol 14, No 1 (2023)
DOI : https://doi.org/10.14716/ijtech.v14i1.3660
|Eko Siswanto||Mechanical Engineering Departmen,t Faculty of Engineering, Brawijaya University, Jalan MT. Haryono No. 167, Malang 65145, Indonesia|
|Denny Widhiyanuriyawan||Mechanical Engineering Departmen,t Faculty of Engineering, Brawijaya University, Jalan MT. Haryono No. 167, Malang 65145, Indonesia|
|Mochammad Agus Choiron||Mechanical Engineering Departmen,t Faculty of Engineering, Brawijaya University, Jalan MT. Haryono No. 167, Malang 65145, Indonesia|
|Djarot Bangun Darmadi||Mechanical Engineering Departmen,t Faculty of Engineering, Brawijaya University, Jalan MT. Haryono No. 167, Malang 65145, Indonesia|
|Yasuo Katoh||Mechanical Engineering Department, System Design and Engineering, Yamaguchi University, Tokiwadai 2-16-1, Yamaguchi 7558611, Japan|
This study aims to obtain the local heat penetration and local heat convection characteristics in a system where a flow of heated vapour cedes thermal energy to a horizontal heat-sink plate. The heat penetrates a bed of porous materials with variations in the thermal conductivity inside a sudden-enlargement-contraction-channel. The two non-dimensional parameters of interest are the local Nusselt and Metais-Eckert numbers. The solid particles used for the porous bed are copper, carbon steel, and ceramics. The study is conducted numerically via the software package Ansys-Fluent to solve the Navier-Stokes equation for the conservation of mass, momentum, and energy to obtain the profiles of local temperature and velocity, both in the porous bed and in the vapour stream. Results of this study show that the overall effective-thermal-conductivity of porous materials filled with vapour mainly affects the local Nusselt number. The local Nusselt number increases with increasing overall effective thermal conductivity of porous materials. The sudden enlargement-contraction of the channel affects the local Metais-Eckert number. This finding is proven by the average Metais-Eckert number's variation along the duct and by its non-proportionality to the overall-effective-thermal-conductivity of each porous material. Together with the local Reynolds number, the local Metais-Eckert number describes the flow regimes that locally occur in the system, namely, transitional-combined-convection, laminar-combined-convection, and laminar-forced-convection. Additionally, based on the local Nusselts number, this study locates the critical point of change from enlargement-affected-zone to contraction-affected-zone at 80 mm along the duct's axis, which means that the switchover-point is not at the centre of the channel.
Effective thermal conductivity; Metais-Eckert number; Porous materials bed; Sudden enlargement-contraction channel
Because of their importance in industrial applications, research and development projects on porous materials are carried out. Among the most notable research works in the literature is the paper by Zulkarnain, Sharudin, and Ohshima (2022). They show that polymer foams have superior properties in low density by using, as basic material, thermoplastic elastomer Polystyrene-b-polybutadiene-b-polystyrene (SEBS) foams. Successively, Zulkarnain, Fadzil, and Sharudin (2017) have developed a pores distribution model for the thermal conductivity analysis and measurement of polypropylene porous materials. In addition, Muharam et al. (2018) researched porous adsorbents used for natural gas adsorption in gas storage technologies.
In line with the development of science and technology on heat transfer, the usage of porous or permeable materials has replaced the extended solid slab method (Kundu et al., 2012; Bassam and Hijleh, 2003; Kiwan and Al-Nimr, 2001). The idea behind the slab method of increasing the heat transfer by expanding the surface area available to the heat transfer through solid slabs finds its limitation in space availability. In contrast, a porous material provides a much bigger surface area for heat transfer.
A good knowledge of a system's local heat transfer characteristics is required to create a more accurate design and better control of heat release from a heat source to a heat sink. This is the case, for example, in heat exchangers at the inlet and outlet sections or in a heat releaser's regions where sudden changes in shape occur. In a porous media system, heat penetration and heat convection play a dominant role in heat transport (Siswanto, Katsurayama, and Katoh, 2011a). Therefore, the present study focuses on determining the characteristics of local heat penetration and local heat convection in a system where a heated vapour moves inside a sudden-enlargement-contraction-channel and transfers its thermal energy to a horizontal heat-sink plate penetrating a bed of porous materials. The study also accounts for variations in the porous material's thermal conductivity.
Porous materials have porous and capillary holes scattered throughout a solid volume, resulting in cavities where flows of mass and energy can occur. Slabs made from porous materials have a higher ratio of surface area to volume than those built out of a continuum solid. Several experimental and numerical studies on fluids used as heat sources flowing tangentially over porous material bed layers exist in the literature. Among the experimental studies are worth mentioning those by Nagata et al. (2013), Siswanto, Katsurayama, and Katoh (2011b), Siswanto, Katsurayama, and Katoh (2010) where the heat transfer on laminar condensation using a bed of porous materials was indagated. More specifically, in the experiments carried out, the authors did flow a saturated vapour stream over glass beads and alumina balls with different thermal conductivity and wettability to obtain the characteristic curves of condensate-propagation and heat-flow that penetrates the porous materials bed in a channel. Results allowed the authors to understand how the propagation characteristics of the condensate flow are affected by the materials' wettability. Propagation can be linear dominant, nonlinear dominant, or chaotic. However, this level of information about the heat flow characteristics in the system is still inadequate. The heat flow characterization made in terms of its Jacob or Kutaleladze numbers or via some perturbation parameters like those determined by Kaviany (Siswanto, Katsurayama, and Katoh, 2011a) is still based on some non-dimensional numbers generally defined by differences between the average temperature values along the channel.
The studies mentioned above on heat transfer with saturated vapour (Siswanto et al., 2016; Nagata et al., 2013; Siswanto, Katsurayama, and Katoh, 2011a; Siswanto, Katsurayama, and Katoh, 2010) report Jacob number values of less than 100. This finding means that, although the propagation of condensate into the porous media is affected by the wettability of materials, the condensation from saturated vapour to liquid is predominantly controlled by heat transfer rather than by viscous inertia (Siswanto, Katsurayama, and Katoh, 2011a). Those studies though, do not present the effect and contribution of the effective-thermal-conductivity on the local heat transfer. Hence, this study focuses on the effect of the materials' effective-thermal-conductivities (instead of wettability) on the local heat transfer in a channel where a stream of saturated vapour flows over a bed made from various porous materials
Yamaguchi, Katoh, and Kurima (2007) and Katoh et al. (2007) measured the effective thermal conductivity of porous materials in the presence of two different thermodynamic states of the fluid flowing through the voids inside two thicknesses of a layer of porous material. Based on Yamaguchi's work, the measurements of effective-thermal-conductivity of porous material in this study are correlated as in equations (1), (2), and (3):
The term in expression (1) is the
effective thermal conductivity of the average thickness of the bed upper layer
To better explore the influence of the bed material thermal conductivity on results, we have selected for the present study three materials which cover a broad spectrum of thermal conductivity values, namely copper with kCu=385 (W/mK), carbon steel with kcs=43 (W/mK), and ceramics with kcer=1.298 (W/mK). The selected materials represent high, medium, and low thermal conductivities, respectively. The choice of these materials is made to obtain clear information on the effect of thermal conductivity and does not involve changes in wettability, as in already cited previous studies, which made use of materials with only slightly different values of thermal conductivity, (i.e., glass beads with kgb=1.035 (W/mK) and alumina balls with kab=18.84 (W/mK)).
To obtain details on the local heat transfer characteristics along the channel, for the porous bed upper surface and the inside (i.e., void) of the porous material bed the overall effective thermal conductivity k ef is used. In the present study, the Navier-Stokes system of equations for the conservation of mass, momentum, and energy in the saturated vapour flow is solved. With this approach, an ideally infinite number of observation points can be obtained, with detailed information such as local temperatures, local pressures, local velocities, and some local properties of the saturated vapour for a variety of pressure and temperature values.
2.1. Materials, Procedures, and Test section
This investigation uses three
different porous beds made of copper (Cu), carbon steel (cs), and
ceramics (cer) particles with thermal conductivity
Figure 1 Test section
previously stated, the saturated vapour flow is subjected to a sudden expansion
as it enters the chamber.
depicts the installation of the porous bed, the channel of saturated vapour,
and the chamber of the test section. The same figure shows the glass-made test
section walls (with a thickness
2.2. Computation, Governing Equations, and Flowchart of Model
The software ANSYS Workbench 18.1 (Academic Research license) is used to compute the local temperature gradient, local property parameters, and heat transfer both in the porous materials bed and the saturated vapour stream. Brick-type 8-node-elements are used for meshing the porous materials bed, the volume occupied by the saturated vapour, the chamber walls, and the bottom of the copper plate (ANSYS Inc., 2017). The CONTA174 (ANSYS Inc., 2017) allows us to define the contact and sliding regions between the saturated vapour stream and the porous bed upper surface, between walls and vapour, between walls and porous material bed, and between the porous bed and copper plate. This method allows for an analysis of the coupled field at the contact region. Figure 1 also shows the contact region between the vapour and the upper surface of the porous bed.
This ANSYS solves the Navier-Stokes conservation equation for mass, momentum, and energy in the saturated vapour flow with heat transfer. The following paragraphs give a brief review of those equations.
Under the hypothesis that no other mass is added to the system, the mass conservation equation for the compressible saturated vapour writes (ANSYS Inc., 2017; Welty et al., 2008),
Figure 2 Flowchart of model
Under the assumption that no heat source exists in the test section
other than the heated saturated vapour, the energy conservation equation in
terms of sensible enthalpy
Finally, Figure 2 shows the model’s flowchart for the current study.
3.1. Local Nusselts Numbers
The local Nusselt
For the transitional flow, local Nusselt numbers Nux
Finally, the average local Nusselts number
Figure 3 shows the
one can drive an important piece of information from the local Nusselt numbers
We can further
validate the simulation results by comparing the average local Nusselt numbers
Figure 3 The local Nusselt
3.2. Metais-Eckert Numbers
An experiment from
Metais and Eckert provides the value of the Metais-Eckert numbers (ME)
by measuring the magnitude of the vapour's convection heat rate against the
length of the channel. The study also correlates the local Metais-Eckert number
Analysis of Figure
4 shows that inside area A the porous material with the highest
With reference to
equation (16) and under the assumption that DHx
Therefore, by assuming constant the gravity
3.3. Convection and Flow Regimes
this part of the study, mapping of the convective flow regimes based on the
value of local Metais-Eckert numbers MEx
Local convection exists along
the first 40 (mm) in the channel, i.e., evaluated at x=20 (mm) and x=40
(mm). For all types of porous materials, the local Reynolds number range is and the local Metais-Eckert number range is As for Metais's and Eckert's experiment (Holman, 2010), if
Figure 5 Mapping of laminar forced convection, laminar combined convection, and transition combined convection regimes based on Metais and Eckert
inside the channel and at the axial coordinate ranges of
local Reynolds and Metais-Eckert numbers are 437.22464.78 and 8,715.32 19,305.57 respectively. As per the references (Holman, 2010), if
non-uniform local convection regime occurs in the channel at x = 220 (mm). At
this point, the values of for porous copper and ceramic materials are (18,458.33; 440.04) and
(14,288.95; 465.61), respectively. This finding puts the local convection for
porous-copper and porous ceramics materials in the combined convection regime
with laminar flow due to
Finally, we can summarize the results of the present study. Table 1 presents a recapitulation of what has been found in the course of the study.
Table 1 Recapitulation of results obtained in the present study
results and discussion allow us to establish relations between the effective
thermal conductivity of porous materials under saturated vapour in a sudden
enlargement-contraction channel with the local Nusselts numbers, the local
Metais-Eckert numbers, and the local convection flows regimes. The local
Nusselt numbers in the channel are
affected by the porous material overall-effective-thermal-conductivity , where the term can also represent the heat penetrability of
the porous materials. Variations of the local Metais-Eckert numbers
authors are obliged to thank the Brawijaya University, Malang, Indonesia, for
providing the laboratory facilities, ANSYS Academic Research license software
and the Ministry of Research, Technology, and Higher Education, Indonesia, via
the Engineering Faculty of Brawijaya University, for the financial support to
the present research under the grant number 134/UN10.F07/PN/2018.
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