Experimental investigation on the evaporation of a wet porous layer inside a vertical channel with resolution of the heat equation by inverse method
Introduction
The phenomena of heat and mass transfer during the flow of a liquid film on a heated wall has a considerable interest in the engineering field, which was translated into many applications, such as the refrigeration [1], air conditioning [2], photovoltaic [3], energy-saving [4] and the cooling of electronic components. In order to understand the heat and mass transfer, different geometries were studied. Firstly, the flow of a liquid was examined on a horizontal flat plate [5]. We cite Siow et al. [6], who studied the evaporation of a laminar model within a horizontal channel. Yuan et al. [7] conducted a study on the coupled heat and mass transfer from a thin film of water subjected to a flow of moist air.
Thereafter, several studies addressed the case of a vertical plate in order to improve the flow of the liquid. Ben Jabrallah et al. [8] studied the coupled heat and mass transfer in a rectangular cavity that acts as a distillation cell. Cherif et al. [9] realised an experimental study on the natural and forced convection evaporation of a thin liquid film that flows on the inner faces of the plates of a vertical channel. Fahem et al. [10] conducted a numerical analysis on the heat and mass transfer within a distillation cell. Debbissi et al. [11] studied the evaporation of water by free and mixed convection into humid air and superheated steam. Min and Tang [12] conducted a theoretical study to analyze the characteristics of transient evaporation of a water film attached to an adiabatic solid wall.
Later on, other researchers have studied evaporation on an inclined plane [14], [15], [16], [13], which affects gravitational forces and decreases the rate of fluid flow. We cite Zeghmati and Daguenet [17] who realised a study of transient laminar free convection over an inclined wet flat plate. Agunaoun and Daif [18] studied the evaporation of a thin film of water flowing on an inclined plate surface at a constant temperature that is higher than the air temperature.
From what was stated above, it is clear that researchers have studied different geometries and conducted parametric studies at almost all input parameters that may influence the heat and mass transfers.
On the other hand, alternative solutions, such as the use of binary fluids, have also been proposed to improve transfer. Cherif and Daif [19] conducted a numerical study on the heat and mass transfer between two vertical flat plates in the presence of a binary liquid film that flows on one heated plate. Debbissi et al. [20] studied the evaporation of a binary liquid film in a vertical channel.
However, obtaining a homogenous liquid film over the entire plate constitutes a major discrepancy between the theoretical and experimental studies. Despite efforts made in the field of modeling and numerical simulation, we still see a difference between calculations and experiments. In a previous work, Cherif et al. [21], have studied the two aspects of the evaporation of a liquid film: experimental and numerical. A difference was reported. They believe that this difference is caused by the difficulty of making a falling film on a vertical plate. In fact, the film could not be controlled if it was directly adhered to the plate. To analyze the effect of dry zones on the plate, Debbissi et al. [22] realised a numerical study of the evaporation along an inclined plate. This plate is composed of two wet zones separated by a dry zone. The results of this study showed that the length of the dry zone plays an important role.
More recent studies have explored various techniques to solve this problem. For example, several researchers used rough surfaces, or interposed obstacles [23]. For example, Zheng and Worek [24] realised numerical and experimental studies on the evaporation of a liquid film inside an inclined channel. They fixed glass rods on the plate to disrupt the flow of liquid, thus improving the heat and mass transfer.
We believe that the best way to achieve a falling film on a flat plate and control its characteristics is the application of a porous layer that plays the role of a support for the liquid film. Few studies have theoretically examined the effect of the presence of a porous medium during evaporation [25], [26] and as far as we now here is not an experimental study that have examined the case of a liquid film evaporation along a vertical plate that is covered with a porous layer. As a result, this work focuses on the study of the evaporation of a wet porous layer inside a vertical channel. The main objective of this study is to evaluate the variation of the temperature and the evaporated flow rate as well as to determine the best operating conditions for a better performance of the system. We have also solved the heat equation by inverse method to determine the local variation of the evaporated flow rate and thereafter the local variation of the latent and sensible Nusselt numbers.
Section snippets
Setup
To conduct the study we realised an experimental setup which we represent in Fig. 1, Fig. 2. It is composed of:
An aluminium plate which the dimensions are 1 × 0.5 × 0.012 m. the front face of the plate was covered by a porous layer which is a copper metal foam represented in Fig. 3. Its caracteristiques are summarized in Table 1.
A heating system composed of 12 electrical resistors distributed homogeneously over the entire rear face of the plate and connected to a generator.
An isolation system
Resolution of the heat equation by the inverse method
Certainly, knowing the temperature at any point of the wet wall requires special interest in understanding the phenomena of evaporation. But the knowledge of the local variation of the evaporated flow is essential. For that reason, and from the values of the measured temperatures, we must solve the heat equation on the plate. This resolution allows us to determine the values of the exchange coefficient at the wet wall and determine subsequently the variation of evaporated flow.
Results and discussions
During the tests, the effect of water inlet flow rate was examined. To analyze its influence, we present in Fig. 7 the local variation of temperature for two water inlet flows and .
First of all, we note that the temperature profiles are divided into two areas. The first area starts at the top of the plate to the point where the temperature reaches its maximum. In this part of the plate, the water film receives a sensible heat flux which increases the liquid
Conclusion
In this paper, we conducted an experimental study on the flow of a liquid film on one of the plates of a vertical channel. This plate was covered with a porous layer. With the realised experimental dispositif, we measured the temperature throughout the plate and the average evaporated flow rate. From these measurements, we solved the heat equation by inverse method which allowed us to determine the local variation of the evaporated flow rate, the latent Nusselt number and the sensible Nusselt
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2022, Energy Conversion and ManagementCitation Excerpt :Alongside the efforts in material development [10], proposed applications span from wearable electronics [16–19] to low-power IoT devices [18], exploiting different methods such as plasmonic heating or composite polymers to improve the evaporation rate and power generation in the device [20,21]. Water transport and evaporation in porous materials has been extensively studied [22–27] and applied for example in food and earth sciences [28–30], and the theory has since been applied to solar steam generation with porous materials [31]. However, the connection between the water evaporation and electricity generation in a porous film remains poorly understood.
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2022, International Journal of Thermal SciencesCitation Excerpt :They established a numerical model to estimate heat transfer coefficients and verified it using experimental results [7]. Terzi et al. experimentally investigated the cooling performance of air flow between wet parallel porous layers [8]. Sellami et al. established a theoretical model for the same experimental setup by Terzi et al. and compared the results for validation [9].
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2019, International Journal of Thermal SciencesExperimental study of active phase change cooling technique based on porous media for photovoltaic thermal management and efficiency enhancement
2019, Energy Conversion and ManagementCitation Excerpt :Meantime, a combination of using forced convection (active) and vapor phase change cooling (passive) with the aid of porous media is not available in the open literature. The evaporation of water on a wet porous layer inside a vertical channel and using a wet porous cooling plate for building wall cooling were studied in [21–23]. However, they only considered the high boiling point coolant-water as the working fluid but were not aware of the potential for using low boiling point coolant (such as ethanol).
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2019, Chemical Engineering Research and DesignCitation Excerpt :Consider the corrected pressure as the new estimated pressure value; go back to step 2 and repeat the entire procedure until you reach the convergence of the solution. A good accordance is noticed between our results and those of Terzi et al. (2016a), as the relative difference is less than 3%. The comparison shows the variation of local temperature throughout the plate for inlet mass flow mL0 = 2.77 g s−1 m−2 and mL0 = 4.44 g s−1 m−2.