Many materials which consist of substances having different thermal conductivities have been used in various engineering fields. It is necessary to obtain the temperature distribution of these materials in order to study the heat transfer problems concerned with these materials. To obtain the temperature distribution, it is necessary to solve the heat conduction equation under appropriate boundary conditions. For the composite materials, however, there are a little cases acquired the results by analytically. When the solution can not be obtained by analytically, it is got generally by using numerical analyses. The iteration or relaxation method which based upon finite difference has the significant advantage among many numerical methods. It is a well known fact that successive over relaxation method (SOR) can be decreases the calculation number (N_c) that is the number until convergence of temperature distribution of steady state. It is common knowledge also that N_c depend upon relaxation parameter (α). On the α, however, there is little investigation on composite materials. Therefore, it is difficult to predict of α for these ones. On the other hand, to minimize of N_c may be very valuable for effective use of computer. From this standpoint, the α of SOR method for composite materials is investigated on various factor affecting to α, and optimum α(α_<opt>) which minimize the N_c is discussed. Main results obtained in this report are as follows: 1) N_c decreases less than about 1/10 compare with successive relaxation (α=1) by selecting α_<opt>. 2) α_<opt> increases with increasing mesh numbers that are parallel to heat flow. 3) On the composite materials, α_<opt> has qualitatively similar tendency to Yamauchi's value which predict to homogeneous field. But there is the difference about from 0.1 to 0.15. 4) N_<c,opt> has not large change in the range the conductivity ratio of armature to matrix less than 0.1 or greater than 10.0. 5) When α_<opt> can not predict exactly, it is safe to select the value of α from 1.7 to 1.8.
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