Heat Transfer Modelling Using COMSOL: Slab to Radial Fin (Multiphysics Modeling Series) by Layla S. Mayboudi

Author:Layla S. Mayboudi [Mayboudi, Layla S.]
Language: eng
Format: epub
Publisher: Mercury Learning and Information
Published: 2018-07-10T23:00:00+00:00

CHAPTER 9

FIN WITH CIRCULAR CROSS SECTION

This section focuses on another form of the extended surfaces (or fins)—a cylinder (Figure 79). First, a basic design is presented. Next, a more complex design is introduced that embeds a rectangular cooling channel into the cylindrical fin. A cylindrical fin with a finned cooling channel (which may be employed in aerospace applications) concludes the section.

FIGURE 79:Fin with circular cross section.

Figure 79 shows the energy balance for an element within the fin. Equations for three boundary condition cases are displayed in the figure. For the upcoming analyses, the most comprehensive scenario (Case 3) is investigated, in which the surfaces adjoining to the environment are cooled by convection. The effects of forced or natural convection are represented by a multiplier that changes the base condition from the natural to forced convection scenario.

Steps taken to setup the 3D model are similar to those of the previous analyses. You need to create a new model or component on the upper tree, add a 3D component, define physics (heat transfer in solids), and decide which analysis type you are interested in performing (transient analysis). You may either import the 3D geometry using a dedicated CAD tool or create it using the built-in geometry-creation features within the core COMSOL Multiphysics® application. The geometry for this analysis is simple enough to have been created using the latter approach.

Figure 80 shows a block—representing the surface whose heat is to be transferred to the surrounding—and a cylinder of 10 mm diameter and 100 mm length comprising the model geometry. To take advantage of the symmetry, the model may be cut in half by employing a work-plane. Thus, a work-plane parallel to x-z plane is defined that passes through the model center. This plane is then used to partition the model into two halves (indicated by purple line in the figure). The left half is kept, and the right half is discarded to create the final geometry, which takes advantage of symmetry to save on computational time and memory resources.

There are a variety of methods to mesh a cylindrical geometry similar to the one presented in this example; one method is to use the mapped mesh feature by selecting a (source) surface, creating the mapped mesh, and finally sweeping the results to another (destination) surface. Thus, one end surface was meshed first and then used as the source, and the opposite face was used as the destination to perform mapped meshing. One advantage of mapped meshing is that it introduces uniformly distributed surface or volume elements in a geometry, which results in more accurate and efficient solutions. Note that some surfaces need to have the least number of surrounding constraints in order for the mapped mesh to be swept, meaning that the surfaces used as the source or destination to perform mapped meshing cannot be over-constrained (i.e., having too many adjoining surfaces). Figure 81 shows the meshed cylindrical fin; you may start with 0.75 mm mesh size. In this example, the cylindrical curved surface

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