Cooling of outdoor electronic equipment such as in telecommunications towers is difficult due to seasonal and diurnal variations of the air temperature, and potential fouling of heat exchange surfaces due to dust accumulation or insect nesting. A concept to provide a nearly constant sink temperature in a hermetically sealed environment is shown below. The cool surface is maintained at nearly constant groundwater temperature (T₁ = 5°C) while the hot surface is subjected to a constant heat load from the electronic equipment (q₂ = 50 W, T₂). Connecting the surfaces is a concentric tube of length L = 10 m with D_i = 100 mm and D_o = 150 mm. A fan moves air at a mass flow rate of m = 0.0325 kg/s and dissipates P = 10 W of thermal energy. Heat transfer to the cool surface is described by q"₁= h₁(T_h,o = T₁) while heat transfer from the hot surface is described by q"₂  = h₂(T₂ T_f,o) where T_f,o is the fan outlet temperature. The values of h₁ and h₂ are 40 and 60 W/m² · K, respectively. To isolate the electronics from ambient temperature variations, the entire device is insulated at its outer surfaces. The design engineer is concerned that conduction through the wall of the inner tube may adversely affect the device performance. Determine the value of T₂ for the limiting cases of 

(i) No conduction resistance in the inner tube wall and 

(ii) Infinite conduction resistance in the inner tube wall. Does the proposed device maintain maximum temperatures below 80°C? 

Transcribed Image Text:

Electronics cabinet Tjo fo Thi Do- D; The L IN VH Hot surface 92, h₂, T₂ D₂ = Do Fan, P -T C,0 Ground level Insulation T c,i Cool surface T₁, h₂ D₁ = Do