(adsbygoogle = window.adsbygoogle || []).push({}); Steady-state HELP!!

Hi guys, I really need some help with this!

I have this set of equations for an evaporator which I want to calculate x_{0}and u_{0}for the steady state

mdot_{in}(h_{in}- h_{g}) + (B_{1}/L_{tot})*L_{1}(T_{w1}- T_{r1}) = 0

mdot_{out}(h_{g}- h_{out}) + (B_{2}/L_{tot})*L_{2}(T_{w2}- T_{r2}) = 0

mdot_{in}- mdot_{out}= 0

B_{3}(T_{a}- T_{w1}) -B_{1}(T_{w1}- T_{r1})

B_{3}(T_{a}- T_{w2}) -B_{2}(T_{w2}- T_{r2})

where B_{1,2,3}are constant values

T_{a}is the surrounding air on the evaporator

L_{tot}is the total length of the evaporator

L_{2}= L_{tot}- L_{1}

h_{g}the enthalpy of the vapor refrigerant

My state variables are x = [L_{1}P h_{out}T_{w1}T_{w2}] and my control inputs are u = [mdot_{in}mdot_{out}h_{in}] which results in the following set of equations

u_{1}(u_{3}- h_{g}) + (B_{1}/L_{tot})*x_{1}(x_{4}- T_{r1}) = 0

u_{2}(h_{g}- x_{3}) + (B_{2}/L_{tot})*(L_{tot}- x_{1})(x_{5}- T_{r2}) = 0

u_{1}- u_{2}= 0

B_{3}(T_{a}- x_{4}) - B_{1}(x_{4}- T_{r1}) = 0

B_{3}(T_{a}- x_{5}) - B_{2}(x_{5}- T_{r2}) = 0

I don't really know how to find the values of x_{0}and u_{0}from here.

I would highly appreciate some help!

Thanks in advance,

Andreas

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# Steady-state HELP

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