Problem 4.32 For a small heat source attached to a large substrate, the spreading resistance associated with multidimensional conduction in the substrate may be approximated by the expression [Yovanovich, M. M., and V. W. Antonetti, in Adv. Thermal Modeling Elec. Comp. and Systems, Vol. 1, A. Bar-Cohen and A. D. Kraus, Eds., Hemisphere, NY, 79-128, 1988] 1 - 1.410A, + 0.34442 +0.0434 + 0.034A; 4ksub AM Rt(sp) = where Ar = As, h/As,sub is the ratio of the heat source area to the substrate area. Consider application of the expression to an in-line array of square chips of width Lh = 5 mm on a side and pitch Sh = 8 mm. The interface between the chips and a large substrate of thermal conductivity ksub = 80 W/mK is characterized by a thermal contact resistance of Rt.c"=0.5x10-4 m2 K/W. Page 4 of 7 Spring 2022 ME407-104 HW4 Top view Substrate, kub Chip, TN Air Side view ---- Substrate RE If a convection heat transfer coefficient of h = 100 W/m2. K is associated with airflow (Too = 15C) over the chips and substrate, what is the maximum allowable chip power dissipation if the chip temperature is not to exceed Th = 85C