A composite wall separates combustion gases  at 2600°C from a liquid coolant at 100°C, with gas- and liquid-side convection coefficients of 50 and 1000

(a) Sketch the equivalent thermal circuit corresponding to steady-state conditions. In variable form, label appropriate resistances, temperatures, and heat fluxes.

(b) Under steady-state conditions for which the chip heat dissipation is qc" = 30,000 W/m2, what is the chip temperature?

(c) The  maximum  allowable  heat  flux,  qc",m,  is  deter- mined  by  the  constraint  that  the  chip  temperature must not exceed 85°C. Determine qc",m  for the fore- going conditions. If air is used in lieu of the dielec- tric liquid, the convection coefficient is reduced by approximately an order of magnitude. What is the value of qc",m  for ho  = 100 W/m2 · K? With air cool- ing,  can  significant improvements  be  realized  by using   an   aluminum   oxide   circuit   board   and/or by using a conductive paste at the chip/board inter- face for which Rt", c  = 10-5  m2 · K/W?