Solving the heat equation with enthalpy method

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gasper7

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I have a problem that I truly hope won't be much of a burden to you. It may be straightforward for some of you, but it's not for me. It's been troubling me for days.
I have an ice cube of lenght L, with initial temperature of Tm-10K. After that, I increase the temperature on left side on Tm+10K, whereas it remains the same on right side at Tm, since it's insulated. What I would like to do is to calculate the temperature distribution from x=0 to x=Lwith an enthalpy method.
Now, what is an enthalpy method? One of the best examples that i found on the web is this one -LINK, pages 4-6. What troubles me is 2 unknowns in 1 equation, since i am looking at T(x,t), where the later depends on enthalpy E(x,t) - and this is defined by T(x,t), looking at the equations. It's highly likely that I overcomplicated the example, since it can probably easily be solved by solving initial and boundary conditions, but i don't know how.
I sincerly hope some of your will be able to help me.
Regards,
 
gasper7 said:
I have a problem that I truly hope won't be much of a burden to you. It may be straightforward for some of you, but it's not for me. It's been troubling me for days.
I have an ice cube of lenght L, with initial temperature of Tm-10K. After that, I increase the temperature on left side on Tm+10K, whereas it remains the same on right side at Tm, since it's insulated. What I would like to do is to calculate the temperature distribution from x=0 to x=Lwith an enthalpy method.
Now, what is an enthalpy method? One of the best examples that i found on the web is this one -LINK, pages 4-6. What troubles me is 2 unknowns in 1 equation, since i am looking at T(x,t), where the later depends on enthalpy E(x,t) - and this is defined by T(x,t), looking at the equations. It's highly likely that I overcomplicated the example, since it can probably easily be solved by solving initial and boundary conditions, but i don't know how.
I sincerly hope some of your will be able to help me.
Regards,
Click to expand...

Why don't you try it as a steady state conduction problem? conductivity of water = 0.609 W/(m*K) ref. http://www.engineeringtoolbox.com/thermal-conductivity-liquids-d_1260.html
 
I have to solve it with an enthalpy method, and later on compare it with other methods. I have all the data, the calculation of E troubles me here.
 
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