second distribution is a uniform random distribution which generates random numbers whose elements are uniformly distributed in the range of the mean u2212 3 micron the results are compared for these two random distributions two different analyses are considered for modeling the effects of height variation across the thermal interface material in the first analysis it is assumed that the nanotubes which are smaller than the mean height do not contribute to the effective thermal conductivity i e the resistance of the matrix is very high so there is essentially no heat flowing through these tubes k gap 0 001 w mk the second analysis uses equation 1 to determine the resistance of the short tube k gap 4 w mk and then uses the resistance of the matrix material and the spreading resistance of the tube with the matrix material added in the second case the short tubes also contribute to the effective conductivity calculation this results in four different cases 1 normal finite u2014 normal random distribution with finite resistance for the short tube in this case short tubes contribute to the effective thermal conductivity of the tim 2 normal infinite u2014 normal random distribution with infinite resistance for the short tube so that short tubes do not contribute to the effective thermal conductivity of the tim 3 uniform finite u2014 uniform random distribution with finite resistance for the short tube in this case short tubes also contribute to the effective thermal conductivity of the tim 4 uniform infinite u2014 uniform random distribution with infinite resistance for the short tube so that short tubes do not contribute to the effective thermal conductivity of the tim fig1 shows a plot of number.