Proceedings of COBEM 2005 18th International Congress of Mechanical Engineering Copyright © 2005 by ABCM November 6-11, 2005, Ouro Preto, MG A NUMERICAL COMPARISON BETWEEN AXISYMMETRIC AND 2-D FINITE VOLUME FORMULATIONS USED IN THE THERMAL ANALYSIS OF OCULAR TISSUES Rita de C. F. de Lima Dep. de Engenharia Mecânica, CTG, UFPE, Av. Acadêmico Hélio Ramos, s/n, 50740-530, Recife, PE, Brasil ritalima@ufpe.br Paulo R. M. Lyra Dep. de Engenharia Mecânica, CTG, UFPE, Av.Acadêmico Hélio Ramos, s/n, 50740-530, Recife, PE, Brasil prmlyra@ufpe.br Giselle M. L. L. da Silva Dep. de Energia Nuclear, CTG, UFPE, Av Prof. Luis Freire, 1000, 50740-540, Recife, PE, Brasil gisellemlls@aol.com Darlan K. E. de Carvalho Dep. de Engenharia Civil, CTG, UFPE, Av. Acadêmico Hélio Ramos, s/n, 50740-530, Recife, PE, Brasil dkarlo@uol.com.br Abstract. In this paper, the analysis of heat transfer in human eyes is done using the Finite Volume Method that was developed for solving two-dimensional model problems with unstructured meshes and later extended to deal with axisymmetric applications. Both formulations use a vertex centered finite volume method implemented using an edge- based data structure. Results of the finite volume thermal analysis in ocular tissues are presented, without the presence of thermal loads, and compared with results obtained using an axisymmetric finite element formulation. Such analysis demonstrates the improvement obtained by using a more realistic axisymmetric formulation. Further, the axisymmetric model will be used in the analysis of the eye with retinal implants. Keywords: finite volume method, axisymmetric, hyperthermia, unstructured meshes 1. Introduction Retinitis pigmentosa (RP) and age-related macular degeneration (AMD) are some of the leading causes of blindness in the population. Both involve a degeneration of the photoreceptor cells, rendering the visual system insensitive to light (Peachey & Chow, 1999). An alternative approach towards function restoration of the visual system involves the appli- cation of external electrical stimulus. The development of retinal prosthesis is based on this concept (Chow & Chow, 1997; Margalit et al., 2002). The retinal prosthesis or implants consist of small chips composed by electrodes that create an electrical current which stimulate adjacent areas and so activate the visual system. Electrical stimulation of the retina through injection of current dissipates power and heart. In patients with degenerative retinal disorders, the choriocapillaris, wich normally provides heat dissipation in the retina, is damaged. The heat generated by the electronic sensors can damage the adja- cent neuronal tissue and also the implant. Furthermore, the temperature increase can produce an environment suitable to proliferate bacteria that could cause infections (Schwiebert et al., 2002). Energy dissipation and temperatures must be carefully controlled to avoid damages in retina and adjacent tissues that could disturb retinal capillary blood flow. Blood flow perturbations in the retina is a feature of many ocular diseases, including diabetic retinopathy, age related maculapathy and glaucoma (Guan et al., 2003). Actually, two kind of implants are being developed in United States, Germany and Japan: the epiretinal and the subretinal. These implants substitute different physiological functions. The subretinal substitutes the degenerated photo- receptors cells while the epiretinal stimulate directly the ganglion cells (Margalit et al., 2002). Consequently, the two kinds of chips are implanted in different places. The subretinal is located under the retina’s surface, between the pig- ment epithelium and the photoreceptors cells, while the epiretinal one is fixed in the internal surface of the retina (Mar- galit et al., 2002; Schwiebert et al., 2002; Zrenner, 2002). In this paper, the analysis of heat transfer in human eyes is done using an unstructured Finite Volume Method (FVM) that was developed for solving two-dimensional model problems and later extended to deal with axisymmetric applications. When studying complex problems using numerical analysis, bi-dimensional models may become quite limited. On the other hand, a fully three dimensional model may lead to heavy computational requirements which may sometimes turn the analysis unfeasible. In some situations the tri-dimensional modeling of a problem may be avoided due to its axisymmetric characteristic. Here, the 2-D and axisymmetric FVM solutions are compared through the analysis of the thermal distribution in ocular tissues in the absence of thermal loads. Results of the finite volume thermal analysis in ocular tissues are pre-