A cold plate is an active cooling device that is attached to a heat-generating system in order to dissipate the heat while maintaining the system at an acceptable temperature. It is typically fabricated from a material of high thermal conductivity, k_cp, within which channels are machined and a coolant is passed. Consider a copper cold plate of height H and width W on a side, within which water passes through square channels of width w = h. The transverse spacing between channels δ is twice the spacing between the sidewall of an outer channel and the sidewall of the cold plate.

 

Consider conditions for which equivalent heat-generating systems are attached to the top and bottom of the cold plate, maintaining the corresponding surfaces at the same temperature T_s. The mean velocity and inlet temperature of the coolant are um and T_m,i, respectively.

(a) Assuming fully developed turbulent flow throughout each channel, obtain a system of equations that may be used to evaluate the total rate of heat transfer to the cold plate, q, and the outlet temperature of the water, T_m,o, in terms of the specified parameters.

(b) Consider a cold plate of width W = 100 mm and height H = 10 mm, with 10 square channels of width w 6=  mm and a spacing of δ = 4 mm between channels. Water enters the channels at a temperature of T_m,i = 300 K and a velocity of u_m = 2 m/s. If the top and bottom cold plate surfaces are at T_s = 360 K, what is the outlet water temperature and the total rate of heat transfer to the cold plate? The thermal conductivity of the copper is 400 W/m∙K, while average properties of the water may be taken to be

this a good cold plate design? How could its performance be improved?