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The research dealt with conjugate natural convection in a geometry whose inner and outer walls were both elliptically and vertically configured. The focus was on the influence of geometry parameters on heat and flow patterns. The parameters of interest investigated were: Radius ratios (Rar), annular eccentricities (Ea), eccentricities of ellipse (Ee), innerwall thickness (δI) and outerwall thickness (δo). In solving the problem, a finite different analogue was developed and results generated using a code written in Qb64. Air of Prandtl, Pr=0.7 was used as the working fluid. The simulated results indicated that for eccentric elliptic annuli of Ea > 0, more heat was transferred as compared to the circular geometry already studied (Nu=4.821). The results showed that the more collapsed the ellipse, the more the heat transferred, and the more the velocity of flow. It was also discovered that the heat absorbed,Q increased with increase in annular eccentricities. The outcome of the study highlighted that, the inner walls of the ellipse transferred more heat than the outer walls, particularly for an aspect ratio greater than 0.5. It was deduced from the computed results that the degree of hotness of the fluid is higher along the periphery of minor radius as compared to that of the major radius. The velocity around the wider gap of the annulus was higher than the one at the vicinity of the thinner walls, where there was an exhibition of higher level of temperature. Beyond a critical value of Rar = 0.4, the flow rate and the heat absorbed decreased sharply. When eccentricity of the ellipse, Ee is greater than 0.55, there was no additional effectiveness in heat transfer from the source. The rate of heat transfer by convection, Nu seized to reduce further as the Rar increased beyond 0.7. The heat transfer rate by convection had its critical value at Ea = 0.6 where heat transfer rate sharply increased. Keywords: Conjugate, convection, heat transfer, vertical, ellipse.