From Fig.3.6, heat shield with 1mm diameter tungsten rod has a steep
maximum value of 1300K at the stagnation point and decreasing
drastically to 860K within the stagnation region producing a temperature
gradient of 440K within 10mm radius of heat shield. Keeping every other
condition constant and increasing tungsten diameter to 2mm produces
1250K at the stagnation point and decreasing to 1000K within the
stagnation region producing a temperature gradient of 250K within same
10mm radius of heat shield. Similarly, increasing tungsten diameter to
4mm produces 692K at the stagnation point (remaining relatively constant
within 3mm radius) and decreasing to 665K within the stagnation region
producing a temperature gradient of 27K within 10mm radius of heat
shield. Further increasing tungsten diameter to 6mm produces 583.5K at
the stagnation point (increasing to 588.5K within 5mm radius) and
decreasing to 582K within the stagnation region producing a temperature
gradient of 1.5K within 10mm radius of heat shield. Also increasing
tungsten diameter to 8mm produces 497K at the stagnation point and
increasing to 508K within the stagnation region producing a temperature
gradient of -11K within 10mm radius of heat shield. Increasing tungsten
diameter to 10mm produces 438K at the stagnation point and increasing to
453K within the stagnation region producing a temperature gradient of
-15K within 10mm radius of heat shield. In similar manner, increasing
tungsten diameter to 20mm and 40mm produces a temperature gradient of
-1.5K and 0K respectively within 10mm radius of same heat shield. Hence
considering the whole heat shield up to shoulder ends at 25mm radius
creates higher negative values for diameter of tungsten rod greater than
6mm. This analysis indicates that any diameter of cylindrical tungsten
rod greater than 6mm (at this set of conditions) automatically acts as a
heat sink to the heat shield. This is due to the effect of excess
tungsten mass created from increasing diameter and keeping every other
physical condition constant. Therefore in order to create a more
realistic re-entry temperature distribution of heat shields using Joule
heating, the thermal diffusivity of materials have to be considered.
This will allow optimum thickness of heat shield and effective diameter
of tungsten rod to be assembled.