A heat sink for cooling computer chips is fabricated from copper (k s = 400 W/m' K), with machined micro channels passing a cooling fluid for which T_∞ = 25°C and h = 30,000 W/m² ∙ K. The lower side of the sink experiences no heat removal, and a preliminary heat sink design calls for dimensions of a = b = w_s = w_f = 200μm. A symmetrical element of the heat path from the chip to the fluid is shown in the inset.

(a) Using the symmetrical element with a square nodal network of ∆x = ∆y = 100μm, determine the corresponding temperature field and the heat rate q to the coolant per unit channel length (W/m) for a maximum allowable chip temperature T_{c, max} = 75°C. Estimate the corresponding thermal resistance between the chip surface and the fluid, R_t,c-f(m ∙ K/W). What is the maximum allowable heat dissipation for a chip that measures 10 mm x 10 mm on a side?

(b) The grid spacing used in the foregoing finite-difference solution is coarse, resulting in poor precision for the temperature distribution and heat removal rate. Investigate the effect of grid spacing by considering spatial increments of 50 and 25μm.

(c) Consistent with the requirement that a + b = 400μm, can the heat sink dimensions be altered in a manner that reduces the overall thermal resistance?

Chips, T. Sink, k, Microchannel Te h Insulation W. 2 2