Shear $$rate $$and $$shear $$stress $$data $$of $$a $$Bingham $$plastic $$fluid $$at $$two $$different $$temperatures $$are $$given $$in $$the $$table $$below$.$Using $$the $$Herschel Bulkley $$equation$,$determine;

a$)$ Yield $$stress $$and $$consistency $$index $$at $303$ and $313$K$.$

b$)$ The $$activation $$energy $$of $$the $$fluid $$in kj$/$kg$.$

Table:$$

$($shear rate$=106\mathrm{.}2$ shear stress at $303$K$=6\mathrm{.}2$ shear st at $313$K$=5\mathrm{.}9)$

$($shear rate$=208\mathrm{.}9$ shear st at $303$ K $=10\mathrm{.}9$ shear st at $313$K$=9\mathrm{.}8)$

$($shear rate$=311\mathrm{.}6$ shear st at $303$K$=15\mathrm{.}6$ shear stress at $313$K$=13\mathrm{.}7)$

$($shear rate $=408\mathrm{.}9$ shear stress at $303$K $=20\mathrm{.}3$ shear stress at $313$K $=17\mathrm{.}6)$

$($shear rate $=511\mathrm{.}6$ shear stress at $303$K $=25\mathrm{.}0$ shear stress at $313$K $=21\mathrm{.}5)$

$($shear rate $=614\mathrm{.}3$ shear stress at $303$K $=29\mathrm{.}7$ shear stress at $313$K $=25\mathrm{.}4)$

$($shear rate $=717\mathrm{.}0$ shear stress at $303$K $=34\mathrm{.}4$ shear stress at $313$K $=29\mathrm{.}3)$

$($shear rate $=819\mathrm{.}7$ shear stress at $303$K $39\mathrm{.}1$ shear stress at $313$K $=33\mathrm{.}2)$