The steady problem of free convective heat transfer from an isothermal inclined elliptic cylinder and its stability is investigated. The cylinder is inclined at an arbitrary angle with the horizontal and immersed in an unbounded, viscous, incompressible fluid. It is assumed that the flow is laminar and two-dimensional and that the Boussinesq approximation is valid. The full steady Navier-Stokes and thermal energy equations are transformed to elliptical co-ordinates and an asymptotic analysis is used to find appropriate far-field conditions. A numerical scheme based on finite differences is then used to obtain numerical solutions. Results are found for small to moderate Grashof and Prandtl numbers, and varying ellipse inclinations and aspect ratios. <br /><br /> A linear stability analysis is performed to determine the critical Grashof number at which the flow loses stability. Comparisons are made with long-time unsteady solutions.

The steady problem of free convective heat transfer from an isothermal inclined elliptic cylinder and its stability is investigated. The cylinder is inclined at an arbitrary angle with the horizontal and immersed in an unbounded, viscous, incompressible fluid. It is assumed that the flow is laminar and two-dimensional and that the Boussinesq approximation is valid. The full steady Navier-Stokes and thermal energy equations are transformed to elliptical co-ordinates and an asymptotic analysis is used to find appropriate far-field conditions. A numerical scheme based on finite differences is then used to obtain numerical solutions. Results are found for small to moderate Grashof and Prandtl numbers, and varying ellipse inclinations and aspect ratios. <br /><br /> A linear stability analysis is performed to determine the critical Grashof number at which the flow loses stability. Comparisons are made with long-time unsteady solutions.

Submitted by Maria Medeiros (maria.dilva1@ufcg.edu.br) on 2018-09-14T12:44:26Z No. of bitstreams: 1 LAERCIO GOMES DE OLIVEIRA - TESE (PPGEP) 2004.pdf: 4405529 bytes, checksum: 8b65ffb3723d9c3b423cde424d99a1ef (MD5) / Made available in DSpace on 2018-09-14T12:44:26Z (GMT). No. of bitstreams: 1 LAERCIO GOMES DE OLIVEIRA - TESE (PPGEP) 2004.pdf: 4405529 bytes, checksum: 8b65ffb3723d9c3b423cde424d99a1ef (MD5) Previous issue date: 2004-10-08 / Neste trabalho, foram desenvolvidos e apresentados vários modelos matemáticos tridimensionais analíticos e numéricos para estudar a transferência de calor no interior de um reator de leito fixo, usando condição na fronteira do sistema: de equilíbrio ou convectiva, condutividade térmica do reator constante ou variável e sistema com ou sem reação química. A modelagem matemática apresentada tem a flexibilidade de adaptar-se a leitos com forma geométrica variando desde um canal retangular até o cilindro elíptico, incluindo o cilindro circular. A metodologia numérica utilizada para resolver as equações diferenciais que representam o fenômeno físico baseia-se no método dos volumes finitos. Para discretizar a equação geral da conservação da energia foi utilizado o esquema WUDS (Weigthed Upstream Diference Scheme) como função de interpolação para os termos convectivos e difusivos e uma formulação totalmente implícita. O sistema de equações algébricas lineares resultantes da discretização da equação da energia em todos os pontos do domínio computacional é resolvido iterativamente pelo método Gauss-Seidel. Resultados da distribuição de temperatura no interior do reator em função das posições radial e angular, em várias posições ao longo do equipamento são mostradas e analisadas. Várias condições de processo foram estudadas, variando-se o coeficiente convectivo de transferência de calor, a razão de aspecto geométrica do reator, a concentração do reagente, a temperatura do fluido na entrada do sistema e a velocidade superficial do fluido. Como uma aplicação deste trabalho, os modelos matemáticos desenvolvidos foram utilizados para ajustar os dados experimentais de temperatura coletados numa célula de medidas térmicas (reator de leito fixo) de seção transversal cilíndrica circular, visando obter estimativas da condutividade térmica e coeficiente de transferência de calor do leito de partículas sob várias condições experimentais, usando-se a técnica do erro quadrático mínimo. / In this work, various analytic and numeric three-dimensional mathematical models were developed and presented to study heat transfer inside a fixed bed reactor, using a equilibrium or convective boundary condition, constant or variable thermal conductivity of the reactor and system with or without chemical reaction. The mathematical modeling presented has been the flexibility of adapting to beds with geometric shape varying from a rectangular channel to the elliptic cylinder, including the cylinder circular. The numeric methodology used to solve the differential equations that represent the physical phenomenon is based in the finite volume method. For discretize the general conservation energy equation the WUDS (Weighted Upstream Differentiates Scheme) scheme was used as interpolation function for convective and diffusive terms and a totally implicit formulation. The linear algebraic equations system resultant of the discretization of the energy equation in all points of the computational domain is iteratively solved by Gauss-Seidel method. Results of the temperature distribution inside the reactor in function of the radial and angular positions, in different positions along the equipment are shown and analyzed. Several process conditions were studied, varying the heat transfer convective coefficient, the reactor geometric aspect ration, the reagent concentration, the temperature and superficial velocity of the fluid in entrance of the system. As an application of this work, the mathematical models developed were used to adjust the temperature experimental data collected in a thermal measures cell (fixed bed reactor) of cylindrical traverse section, seeking estimate thermal conductivity and heat transfer coefficient of the particles bed under several experimental conditions, using the minimum quadratic error technique.