Simulation of Free Convection with Conjugate Heat Transfer

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1 Simulation of Free Convection with Conjugate Heat Transfer Hong Xu, Chokri Guetari, Kurt Svihla ANSYS, Inc. Abstract This study focuses on free convective and conjugate heat transfer in a naturally ventilated, rectangular cavity, in which a vertical, isothermal plate is placed. The impact of the following parameters on the local sselt number is studied: spacing between the isothermal plate and the cavity walls (i.e. the channel width); location and number of openings. This paper presents predictions of Local sselt number distribution obtained using ANSYS CFX software. A series of test cases have been computed and compared to the experimental data. Results are in good agreement with the experimental data. Introduction Heat exchangers are found in a number of different industrial sectors where the need to transport heat from medium to medium exists. They also have an important role in everyday life, as they are one of the basic elements of heating, cooling, refrigerating and air-conditioning installations. The prediction of heat transfer in buoyancy influenced flows is important for a number of engineering applications, including cooling of electronics, heating and cooling of buildings, process heat transfer (e.g., heat exchangers), and safety applications (e.g., heat transfer from fires). In many of these applications, mixed convection exists in which both forced and free convection contributes to the heat transfer. Free or natural convection heat transfer has always been of particular interest among heat transfer problems. Examples of free convection include a single-phase closed loop thermosyphon (roughly the condition in a nuclear reactor immediately after pump failure), a Trombe wall (a passive solar heating device), and the shimmering visible above a paved highway on a hot summer day. In natural or free convective heat transfer, heat is transferred between a solid surface and a fluid moving over it, where fluid motion is entirely caused by the buoyancy forces arising from density changes that result from the temperature variations in the fluid. In reality this is a combination of diffusion and bulk motion of molecules. Near the surface the fluid velocity is low, and diffusion dominates. Away from the surface, bulk motion increases in influence and dominates. Fluid movement by natural convection can be either laminar or turbulent. However, because of the low velocities that usually exist in natural convection, laminar flow occurs more frequently than turbulent flow. Most of the phenomena related to a temperature difference involve more than one mechanism of heat transfer. Therefore, a very complex theoretical set of equations is required to study them. Among the known mechanisms, natural convection is one of the most complex ones. Therefore, experimental methods have been developed to study these problems and provide quantitative information about the temperature fields and the rates of heat transfer. Many experimental studies have been performed during the last three decades and interesting results have been presented. Heat transfer in free convection situations depends on surface temperature, ambient temperature, air properties and the geometry of the heat transfer surface. Theses dependencies demonstrate the importance of a representative dimension which best describes the geometry and correlates the heat transfer parameters. The current study will focus on free convective and conjugate heat transfer characteristics of a naturally ventilated, rectangular cavity in which a vertical, isothermal plate is placed. The local sselt number varies when:

2 the spacing between the isothermal plate and the cavity walls (i.e. the channel width) varies; the location and the number of openings changes. The main objective of this study is to calculate the local sselt number distribution for difference case and to compare the simulation results with experimental data. Procedure merical Method Since the dimension along the plate length is much larger than the other two directions, a 2-dimensional computational model will be used. Furthermore, the experimental data is measured at the midpoint in the length direction. The working fluid in the cavity and surrounding the cavity is air, which will be treated as an ideal gas. The equation of state is: ρ = w ( p + p R T where w is the molecular weight of the gas, and R is the Universal Gas constant. The following governing equations of mass, momentum and energy are solved at steady-state conditions (1) : ref ) ρ U t ρ + ( ρ U ) = t + ( ρ U U ) = ( pδ + µ ( U + ( U ) ρ h t tot p + ( ρ U htot ) = ( λ T ) + S t T E ) + S M where h tot is defined as the specific total enthalpy, which is defined in terms of the specific static enthalpy, h, by: 1 htot = h + U 2 Two different types of lateral walls were considered in this case: 1. 6 mm-thick Plexiglas walls with a 2 cm polystyrene thermal insulation mm-thick Plexiglas walls without thermal insulation Also the top and bottom cavity walls are made of 2 cm-thick wood pieces. All solids are treated as conducting domains. Within solid regions, the conservation of energy equation is simplified by removing the convection terms. Therefore, the energy equation in solids becomes: 2

3 ( ρ C T ) = ( λ T ) + t p S E where ρ, Cp and λ are the density, specific heat capacity and thermal conductivity of the solid, respectively. The sselt number, is defined as follows (2) : = hh k = ( T '' q H T ) w a * where h is the heat transfer coefficient, H is a characteristic length, T w and T a are the wall and ambient temperatures, q is the heat flux, and k is the thermal conductivity of the fluid. k Analysis The four cavity configurations considered in this study are summarized in Table 1. Table 1: Dimensions and locations of the cavity openings. Please refer to Figure 1 for the various parameters. Config. No. openings on each side H mm H mm Xin mm Xout mm Xmid mm B C E E Table 2: Geometric information (mm). Plate length H Plate width D Cavity length H c Cavity width Wc or 2 Wc varies in order to have different values of the internal wall spacing to plate height ratio W/H=.,.21 where W=(Wc-D)/2. A total of 9 cases were analyzed. A summary of these is listed in Table 3. These cases have been selected to study the following parameters: the presence or absence of insulation on some of the external walls; the size of the openings; opening locations; position of the heat source with respect to the openings; cavity width.

4 Table 3: Summary of cased analyzed. Without Insulation (W/H=.) With Insulation (W/H=.) Without Insulation (W/H=.21) Config B Yes Yes - Config C Yes Yes Yes Config E2 Yes Yes - Config E4 Yes Yes - The temperature on all isothermal plate surfaces is maintained at 32 K, and the ambient air temperature is set to 3 K. All simulations were done assuming steady state conditions. A completely hexahedral mesh was generated for all cases using ANSYS ICEM CFD Hexa meshing package. The material physical properties used are summarized in Table 4. Table 4: Material properties. Molar Mass (kg/kmol) Density (kg/m^3) Dynamic Viscosity (kg/m s) Thermal Conductivity (W/m K) Specific Heat Capacity (J/kg K) Air Ideal Gas E Plexiglas Wood Analysis Results & Discussion In this study, the experimental setup of Francesco Devia et al (3) was modeled numerically. Figure 3 shows the boundary condition settings for the numerical simulation. Tables 1 and 2 list the dimensions of the geometry and cavity configurations. Based on the symmetry in the geometry, only half of the geometry is meshed. The resulting mesh size was on the order of 3, elements.

5 Figure 1. Schematic view of the rectangular cavity. Ambient region is not shown here. Figure 2. Geometry and boundary conditions.

6 Figure 3. Computational mesh for Configuration B with no thermal Insulation (N-I).

7 Figure 4a. Temperature contours for Configuration B with insulation (a) and without Insulation (b), W/H=.. Figure 4b. Temperature contours for Configuration C with insulation (a) and without Insulation (b), W/H=..

8 Figure 4c. Temperature contours for Configuration C without Insulation, W/H=.21. Figure 4d. Temperature contours for Configurations E2 & E4 with insulation, W/H=..

9 Figure 4e. Temperature contours for Configurations E2 & E4 with no insulation, W/H=.. The temperature contours and vector fields for all cases analyzed are shown in Figure 4 and. Figure a. Vector plots for Configuration B with insulation (a) and without Insulation (b), W/H=..

10 Figure b. Vector plots for Configuration C with insulation (a) and without Insulation (b), W/H=.. Figure c: Vector plot for Configuration C without Insulation, W/H=.21.

11 Figure d. Vector plots for Configurations E2 & E4 with insulation, W/H=.. Figure e. Vector plots for Configurations E2 & E4 with no insulation, W/H=..

12 Figure 6 compares the isotherms for configuration C to experimental data. The agreement between the two is good and shows similar patterns of hot and cold areas. The presence of insulation results in hot spots in the top corners of the cavity. In all the cases shown in Figure 6, the simulated results are in good agreement with the experiments, but the agreement deteriorates towards the top of the cavity. Figure 6. Isotherms for Configuration C. The values shown are for the ratio of the temperature and the heated plate temperature. Figure 7 shows that the sselt number decreases along the height of the heated plate. Furthermore, insulation results in a further decrease in the sselt number towards the top due to the hot spots that are generated in the top corners. Figures 7c and 6d show the impact of the additional opening located across the middle of the plate. The heat transfer improves temporarily and then decreases again. Figure 8 highlights the impact of increasing the size of the openings by %. The simulation and experiments show very little impact on the overall heat transfer characteristics of the problem. The location of the openings does have an important impact on the heat transfer as shown in Figure 9. The location of the top opening has a larger impact and does reduce the heat transfer as the opening is moved further up. The presence of the third opening in the middle does improve the heat transfer somewhat and the impact is local in nature, as shown in Figure 1.

13 Config B, W/H= CFX results, I case Experimental data, I case CFX results, N-I case Experimental data, N-I case (a) Local distributions for Config. B, W/H=. Config C, W/H= CFX results, I case Experimental data, I case CFX results, N-I case Experimental data, N-I case (b) Local distributions for Config. C, W/H=.

14 Config E2, W/H= CFX result, I case Experimental data, I case CFX result, N-I case Experimental data, N-I case (c) Local distributions for Config. E2, W/H=. Config E4, W/H= CFX results, I case Experimental data, I case CFX results, N-I case Experimental data, N-I case (d) Local distributions for Config. B, W/H=. Figure 7. Effects of insulation on local distribution.

15 Config B & C, I case, W/H= CFX results, Config B Experimental data, Config B CFX results, Config C Experimental data, Config C (a) Local distributions for Config. B and C, with thermal insulation Config B & C, N-I case, W/H= CFX results, Config C Experimental data, Config C CFX results, Config B Experimental data, Config B (b) Local distributions for Config. B and C, without thermal insulation Figure 8. Impact of the height of the openings on local distribution for W/H=..

16 Config E2 & E4, I case, W/H= CFX results, Config E2 Experimental data, Config E2 CFX results, Config E4 Experimental data, Config E (a) Local distributions for Config. E2 and E4, with thermal insulation Config E2 & E4, N-I case, W/H= CFX results, Config E2 Experimental data, Config E2 CFX results, Config E4 Experimental data, Config E (b) Local distributions for Config. E2 and E4, without thermal insulation Figure 9. Impact of the openings locations on local distributions for W/H=..

17 Config E2 & E4 & B, I case, W/H= CFX results, Config E2 Experimental data, Config E2 CFX results, Config E4 Experimental data, Config E4 CFX results, Config B Experimental data, Config B (a) Local distributions for Config. B, E2 and E4, with thermal insulation Config E2 & E4 & B, N-I case, W/H= CFX results, Config E2 Experimental data, Config E2 CFX results, Config E4 Experimental data, Config E4 CFX results, Config B Experimental data, Config B (b) Local distributions for Config. B, E2 and E4, without thermal insulation Figure 1. Impact of the third opening on local distributions for W/H=..

18 Figure 11 shows that increasing the cavity width will help with heat transfer. Figure 11. Impact of the width of the cavity on local distributions for W/H=.. Conclusion In this paper, nine cases of free convective conjugate heat transfer have been presented. The results from ANSYS CFX have been compared to experimental data for various configurations and the impact of various parameters has been examined. The computational results are in good agreement with experimental data. The impact of cavity width, and the placement, size and number of openings on the heat transfer from the heated plate have been analyzed. The placement of the openings and the size of the cavity have a larger impact on heat transfer then the other parameters. References 1. CFX Solver manual 2. Patrick H. Oosthuizen, et al., The Effect of heat Generation in Inclined Slats on The Natural Convective Heat Transfer from an Isothermal heated Vertical Plate. 24 ASME International Mechanical Engineering Congress and Exposition 3. G. Tanda et al., Experimental heat transfer from a vertical plate within a naturally ventilated cabinet. Heat and Mass Transfer, Volume 36, November 2.