When exact analytical solutions to certain type of heat conduction problems are quite cumbersome or not obtainable, it is important to introduce approximate analytical methods which are simple and useful compared with numerical methods. In this study, therefore, the Heat Balance Integral Method is applied to analysis of steady-state conduction in a straight fin of trapezoidal profile, and the two-dimensional temperature distribution in the fin and the approximate fin efficiency are obtained. Results are compared with those by the one- dimensional analysis and two-dimensional numerical analysis for a wide range of Biot numbers. It is shown that the two-dimensional temperature distribution obtained by the integral method is in good agreement with that by the finite element method at Biot numbers for which the result by the one-dimensional analysis is unreliable.

In this paper, temperature distributions in radial fin of hyperbolic profile for steady -state with no heat generation are obtained by one-dimensional analytical method, finite difference method and experiment respectively. Heat flow rate and fin efficiency from the fin model are obtained by analytical method. To compare the exact solutions obtained by theoretical analysis with the results obtained by finite difference method, cylindrical shape is selected. Particularly, equations of finite difference method for cylindrical shape with irregular boundary are rearranged and formulated. Consequently, temperature distributions in radial fin can certify that are similar to exact solutions. From theoretical analysis, the effects according to heat flow rate and fin efficiency are related to variation of parameters which are fin thickness ${\delta}_o$, fin base temperature $T_o$, thermal conductivity K with same basic dimensions and the fleets are studied and compared.

The heat transfer process with boiling on a fin cannot be treated in a conventional manner of assuming a constant heat transfer coefficient. This report proposes a simplified method for determining fin performance. The heat transfer coefficients in boiling region is approximated by n ty power function of superheat. The results yield the temperature gradient as a function of superheat, fin width, and thermal conductivity of the fin. Computed results for water boiling on fin compare favorably with those obtained from a small-increment numerical solution.

For studying this project, we selected a 2-storied detached house as a sample which was constructed in July 1976, the last year of the 3rd 5-years economic and social development plan and also the middle year between the years of the 1st oil crisis and the 2nd oil crisis, located In Gayang-dong, Daejeon City. The contents and scope of this project was to produce retrofit measures by theoretically analyzing the building energy use between both of pre-retrofit and post-retrofit conditions of this sample house, and to compare and analyze the predicated data with experimented data under post - retrofit condition. It is suggested in this report that we have to develop rational and practical retrofit measures for energy conservations in existing residences.

One-dimensional approximation for fin problems is widely used in current texts and industrial practice. The errors caused by this approximation is analysed for a longitudinal triangular fin by the numerical solution of two-dimensional fin equation. Two-dimensional solution is obtained by the finite element method and com pared with the one-dimensional esact solution. The results show that total heat transfer and fin efficiency are overestimated by the one-dimensional approximation. The factors which cause these errors are the Biot number (Bi) and the ratio of fin length to half the thickness (L/a). When Bi is smaller than 1.0 these errors are smaller than $10\%$, but when Bi is larger than 5.0 they are a few ten percents. Fin efficiency obtaned by one-dimensional and long fin assumption is valid only then Bi is small and L/a is large.