ADEL E. ALSHAYJI. Kuwait University

Transcription

1 ANALYSIS OF HEAT TRANSFER THROUGH MULTI-LAYERS WALL INCLUDING AIR AND POROUS LAYERS. ADEL E. ALSHAYJI Kuwait University Abstract - In this study, heat transfer through a multi-layer ceramic furnace wall was analyzed, the study concentrates on the analysis of an air layer inside the wall, and moister transport from moist porous layer to adjacent air in the air layer. By considering several porosity values ranging from 0.1 to 0.9, the effect of porosity on the total heat transfer thought the wall and the effective thermal conductivity was concluded. this study concludes that increase porosity in the porous layer will reduce the total heat flux through the wall and reduce the effective thermal conductivity in the air and porous layers. Index Terms - Heat Transfer, Moist Air, Multi-layers Wall, Porous Material. I. INTRODUCTION Heat can be transferred into and out of a subject in three forms conduction, convection, and radiation. In some cases, when it comes to air, convection is considered the highest denominator in the heat transfer equation when compared with conduction, which is very insignificant. All over the world insulations are used to control the heat transfer rate through various systems and the effectiveness of these insulations vary with the significance of the media it is preserving, for an example a high temperature operating furnace requires a huge amount of insulation in order to minimize the heat loss from the furnace. Air gaps are used in most of the insulating walls in these kind of applications due to its very low conducting property. On the other hand, any air gap that is used as an insulation must be accounted for its natural convection capability depending on the thickness and shape of this gap, and in this study furnace wall with four different layers including an air gap, and moist porous layer, is going to be designed and analyzed to minimize heat transfer rate out of the system. Ceramic based products are very popular and highly required in the industrial world, in one stage of the ceramic production the ceramic must go through a baking process in large furnaces, and this baking process would require the inside of the furnace to reach a high temperature of 900 C. For environmental purposes as well as to maintain a high efficiency the outside temperature of the furnace must not exceed room temperature 27 C. Orhan Aydın [1] studied the conjugate heat transfer through a double pane window numerically using finite difference method, the study aimed to determine the optimum air layer thickness between the panes for four different climates in four different cities in turkey, the author assumed constant temperature and convection as the two different boundary conditions for the outer surface of the pane. The study showed that increasing the forced convection in the outer surface did not show much effect on the heat transfer, and also that using gas with lower thermal conductivity instead of air decreases the insulating value of the window. M. Darbandi and S. F. Hosseinizadeh [3] solved the free convection problem of a vertical cavity for different thicknesses and wall temperatures and hence different Rayleigh numbers, a novel numerical algorithm was used to solve the compressible flow equations using a primitive incompressible method instead of Boussinesq approximation due to the variation of temperature gradients. The study showed that the maximum Nusselt number depends on both the ratio between the length and the high of the cavity and Rayleigh number, where it initially increases then decreases with increasing length-to-high ratio and constant Rayleigh number. The study also showed that using Boussinesq approximation instead of the current method would create a large error in the results since the effect of compressibility in the fluid would be neglected. A.A. Ganguli, A.B. Pandit, and J.B. Joshi [2] performed a CFD simulations on a rectangular enclosure in order to predict the variation in heat transfer coefficient setup by natural convection, the height, length, and temperature difference were varied in the study using ranges found from previous studies in the literature, the results found from the simulation were very close to those from the literature with only a small variation. From further simulation it was found that using smaller ranges of the previously mentioned parameters gave results that were much closer to the results found from the literature, the study also listed some of the short comings that were found in the literature. II. PROBLEM DEFINITION This research concerned on the design of a multi-layer 45

2 wall with an air gap, and moist porous layer, that operates between an inside surface temperature of 27 C (300 K) and an outside surface temperature of 900 C (1173 K). This study is based on a previously published study by Gallegos-Munoz Armando, Balderas-Bernal J. Armando, Violante-Cruz Christian, V.H Rangel-Hernandez, J.M Belman-Flores [4] that concentrated mainly on the air layer between a four layers wall, where the air layer was studied for two thicknesses (L=0.08 m and L=0.1 m). In the first part of this work is simulated and verify the results of the previous work, where the thickness was taken to be 0.1 m, as shown in Figure (1). The second part of this study is concerned about studying alternative designs in order to further more decrease the heat transfer through the wall and thus increasing the wall efficiency. The chambers can be designed by introducing ceramic based moist porous layer and allow the extra heat to vaporize the water in this moist porous layer into the air layer. After that the designs are evaluated depending on the amount of air circulation inside the air layer, the heat flux through the wall, and the mean effective conductivity. Further details will be shown in the result analysis and discussion section below. combined the heat transfer in solid layers and fluid layer ( air layer ). The equations were used to solve for the energy balance through the wall and for the gravitational force applied on the air due to the shift in the density inside the air layer. Table 1: Porous layer properties Table 2: Solid layers properties In the momentum equation it was assumed that the laminar flow is incompressible and that the air inside the layer is an ideal gas and the gravity effect is only applied in the vertical directions. Continuity equation: III. MODEL DESCRIPTION The model used in the analysis of this study, as described in figure (1), consist of four layers. The first layer from the left is the outer layer of the furnace wall; this layer is made of common brick with a constant thickness of 0.21 m. The second layer, which is the most important and most considered layer in the wall is the air layer, the thickness of the air layer is 0.1 m. The third layer is made of porous ceramic fiber with a thickness of m. Table (1) show the constant properties of the porous layer. Momentum equation: (1) (2) The porosity of this layer will be variable in this study ranging from 0.1 to 0.9 and will be saturated with at the beginning of the simulation. The forth and last layer is the inner layer of the furnace which is exposed to the highest temperatures in the wall, this layer is made of Firebrick with a thickness of m. Table (2) show the constant properties of the three solid layers of the furnace wall. The height of the whole wall H is constant during this simulation and have a value of 1.3 m in order to maintain constant aspect ratio especially in the air layer where the natural convection heat transfer take place. IV. MATHEMATICAL FORMULATION The analysis of the multi-layer wall with the air gap, and moist porous layer was done for equations that (3) Energy equation: (4) The heat flux across the wall is determined by this equation: (5) 46

3 Where l is the width of each layer and k eff is the effective conductivity that represents within it the combination of conduction and natural convection in the moist air and moist ceramic layers. in all points of the layer, which can cause a lot of change in the average convection coefficient inside the air layer. However, the simulation results in very good agreement with the paper and the percentage differences was found to be less than 3%. Figure 1: Geometry of the furnace wall. V. BOUNDARY AND INITIAL CONDITIONS Figure 2: Temperature distrubition in furnace wall. The model was set at a certain boundary and initial conditions. The model was initially set at room temperature 27 C (300 K) for all the layers and at zero atmospheric pressure for the air layer. On the other hand, the model was set at the following boundary conditions : 1- T o = 27 C (300 K) for the outer surface of the wall. 2- T i = 900 C (1173 K) for the inner surface of the wall. 3- No-slip condition for the walls inside the air layer. 4- Adiabatic boundary condition at the upper and lower horizontal surfaces. VI. VALIDATION To validate the results of this study, we compare the average heat flux, and the mean effective conductivity, with the results of a simpler case obtained by G. Armando, B. Armando, V. Christian, V. Hernandez, J. Flores [4] for air layer thickness of L=0.1 m. In their work they considered air layer without moister transport and without porous layer. By computing the heat flux through the air layer, we can compute the mean effective conductivity k eff. When comparing the heat flux and effective conductivity values between the paper and the simulation, a slight variation is found due to the mentioned assumption of constant pressure Figure 3: Velocity distrubition in air and porous layers. VII. RESULTS ANALYSIS AND DISCUSSION After validating the results with the ones obtained by G. Armando, B. Armando, V. Christian, V. Hernandez, J. Flores [4, the effects of both of porosity in the porous layer, and moister transport in air layer, on heat transfer rate and mean effective thermal conductivity is examined. 47

4 Porosity variation between 0.1 and 0.9 in the porous ceramic layer is considered in this study. Figure (2) shows the temperature distribution inside the furnace wall, while figure (3) shows the velocity magnitude inside and the porous and air layer for ceramic porosity of 0.5. From these upper part or the layer due to bouncy effect and air in the layers. From these figures we can notice that the flow circulation inside the air and porous layer and its effect on the temperature distribution. Flow circulation due to bouncy effect help to redistribute the temperature inside the air and porous layer and therefore the heat transfers Figure 4: Moist air concentration in air and porous layers. Figure 6: Velocity magnitude variation between air and porous layers. Figure 5: Temperature variation between air and porous layers. figures we can notice that the flow circulation inside the air and porous layer and its effect on the temperature distribution. Flow circulation due to bouncy effect help to redistribute the temperature inside the air and porous layer and therefore the heat transfers through the wall. The moist air concentration in the air and porous ceramic layers are shown in figure (4) for ceramic porosity of 0.5. This figure shows that the moister is concentrated in the Figure 7: Moist air concentration variation between air and porous layers. through the wall. The effect of porosity on the temperature variation, velocity circulation, moist air concentration between the air and porous layer are examined and shown in figures (5), in figures (6), and in figures (7). The velocity magnitude of the circulated moist air and the concentration of the moist air will increase when decreasing the porosity. As a result, porosity variation will have direct impact on the total heat flux 48

5 Figure 9: Effective thermal conductivity variation with porocity. through the wall as seen in figure (8). Higher porosity will help in reducing the total heat flux and therefore enhance the insulation. As a result, the mean effective conductivity in the air and porous layers will drop by increasing the porosity and this will enhance the insulation effect. CONCLUSION In this study we focused of the effect of porosity of heat transfer thought multilayer wall. The effect of the porosity is profound and significant. Porous layer tends to have the ability to affect the air circulation and moister content in the air and porous layers. This study concludes that increasing porosity will decrease the total heat transfers in this wall by reducing the effective thermal conductivity. REFERENCES Figure 8: Total heat flux variation with porocity. [1] Orhan Aydin, Conjugate heat transfer analysis of double pane windows, Building and Environment 41 (2006), [2] A.A. Ganguli, A.B. Pandit, and J.B. Joshi, CFD simulation of heat transfer in a two-dimensional vertical enclosure, chemical engineering research and design 87 (2009), [3] M. Darbandi and S. F. Hosseinizadeh, Numerical Study of Natural Convection in Vertical Enclosures Using a Novel Non-Boussinesq Algorithm, Numerical Heat Transfer, Part A: Applications, 52: 9, [4] G. Armando, B. Armando, V. Christian, V. Hernandez, J. Flores, Analysis of the Conjugate Heat Transfer in a Multi-layer Wall Including an Air Layer, Applied Thermal Engineering 30, 2010,