<jupyter_start><jupyter_text>Bread burning point is about 87 degrees Celcius, so we want the cheese to reach half its melting point of about 66 degrees Celcius just before the bread reaches its burning point.<jupyter_code>state = State(tbread = 23,      #C
              tcheese = 23)     #C
system = System(kpan = 0.529, #avg cast iron @100 - avg cast iron @200, * 0.35, - from avg cast iron @100  W/cmC
                kbread = 0.062, #W/cmC
                tpan = 135,     #C, 125-145 when swept
                area = 184,     #cm sq, std. area of a piece of wonder bread
                t0 = 0,         #sec
                t_end = 600,    #sec
                thickness = 0.2,#cm, one slice of cheese
                init = state)   #sec
def coook(state, t, system):
    b, c = state
    
    unpack(system)
    
    dbdt = kpan*area*(tpan-b)/1.4 #conduction equation, pan to bread
    dcdt = kbread*area*(b-c)/thickness  #conduction equation, bread to cheese
    
    return dbdt/1900*0.1, dcdt/1900*0.33 #joule to degree C conversion, 1/10 and 1/3 efficiency respectively
coook(state, 0, system)
results, details = run_ode_solver(system, coook)
results.plot()
details
system.thickness = 0.4 #two slices
results, details = run_ode_solver(system, coook)
results.plot()
details

system.thickness = 0.6 #three slices
results, details = run_ode_solver(system, coook)
results.plot()
details
system.thickness = 0.8 #four slices
results, details = run_ode_solver(system, coook)
results.plot()
details
system.thickness = 1 #five slices
results, details = run_ode_solver(system, coook)
results.plot()
details
system.thickness = 1.2 #six slices
results, details = run_ode_solver(system, coook)
results.plot()
details
system.thickness = 2 #ten slices
results, details = run_ode_solver(system, coook)
results.plot()
details<jupyter_output><empty_output>
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