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Question 9.12: Repeat problem [9.10] for a plutonium fueled sodium cooled f......

Repeat problem [9.10] for a plutonium fueled sodium cooled fast reactor with the parameters: Λ = 0.5 × 10^{-6}  s , α = -1.8 × 10^{-5} /°C  M_ƒc_ƒ = 5.0  × 10^6  J/°C , τ = 4.0  s

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β1 := 0.00021          \operatorname{c1}:=\mathbb{\beta 1}\cdot {\frac{\operatorname{P0}}{(\lambda1\cdot\Lambda)}}     \mathrm{c}2:=\beta 2.{\frac{\mathrm{P}0}{(\lambda2\cdot\Lambda)}}

β2 := 0.00142

β3 := 0.00128             \operatorname{c3}:=\mathbb{\beta 3}\cdot {\frac{\operatorname{P0}}{(\lambda3\cdot\Lambda)}}    \mathrm{c}4:=\beta 4.{\frac{\mathrm{P}0}{(\lambda4\cdot\Lambda)}}

β4 := 0.00257

β5 := 0.00075           \operatorname{c5}:=\mathbb{\beta 5}\cdot {\frac{\operatorname{P0}}{(\lambda5\cdot\Lambda)}}    \mathrm{c}6:=\beta 6.{\frac{\mathrm{P}0}{(\lambda6\cdot\Lambda)}}

β6 := 0.00027

Sample calculations shown for $0.10 below using the stiff differential equations solver Radau (Mathcad) to obtain the vector Y.

\mathrm{Rf}:={\frac{\tau}{\mathrm{MfCf}}}=0.8                             dollars := 0.1

Rf.WCp = 48                                        α1 = -1.8 × 10^{-5}

\mathrm y := \begin{pmatrix}P0 \\ c1 \\ c2 \\ c3 \\ c4 \\ c5 \\c6 \\ \mathrm {Tf0} \end{pmatrix}

 

\mathrm{DD(t,y)} := \begin{bmatrix}\frac{\bigg[\mathrm {dollars}\beta + \alpha 1 \cdot (\mathrm {y_7 – Tf0}) – \beta \bigg ]}{\Lambda} \cdot y_0 + \lambda1 \cdot y_1 + \lambda2 \cdot y_2 + \lambda3 \cdot y_3 + \lambda4 \cdot y_4 + \lambda5 \cdot y_5 + \lambda6 \cdot y_6 \\ \begin{matrix}\left({\frac{\beta1}{\Lambda}}\right)\mathbf{y}_0-\lambda1.\mathrm{y_1} \\ \left({\frac{\beta2}{\Lambda}}\right)\mathbf{y}_0-\lambda2.\mathrm{y_2} \\ \left({\frac{\beta3}{\Lambda}}\right)\mathbf{y}_0-\lambda3.\mathrm{y_3}\\ \left({\frac{\beta4}{\Lambda}}\right)\mathbf{y}_0-\lambda4.\mathrm{y_4} \\ \left({\frac{\beta5}{\Lambda}}\right)\mathbf{y}_0-\lambda5.\mathrm{y_5} \\ \left({\frac{\beta6}{\Lambda}}\right)\mathbf{y}_0-\lambda6.\mathrm{y_6} \\ \frac{y_0}{\mathrm{MfCf}} – \frac{(y_7 – \mathrm{Tf0})}{τ}\end{matrix} \end{bmatrix}
Y:=\mathrm{R a d a u}(y,0,800,1000,\mathrm{DD})

n := 0 .. 1000

25 d
26 d

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