Abebi Stafford 18.5-2 (Thermal Diffusion)

> restart; A necessary command to make the session work

the temperature gradient in the two bulb system for mass flux:

> j[AzT]:= -c^2/rho *M[A]*M[B]*D[AB]*k[T]/T*diff(T(z),z);

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the mass flux tends to cause an opposed concentration gradient:

> j[AzX]:= -c^2/rho *M[A]*M[B]*D[AB]*diff(x[A](z),z);

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it is a closed system and hence no mass flux will occur .

> twoflux:=j[AzT]+j[AzX]=0;

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> y:=simplify(twoflux);

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> twoflux2:= y/(c^2*M[A]*M[B]*D[AB]/(rho*T));

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multiply both sides by 'dz':

> newequation:=int(1,x=x[A1]...x[A2])= -int(k[T]/T,T= T[1]...T[2]);

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this is used to estimate the order of magnitude of thermal effects by diffusion

now we need the recommended mean temperature...

> Tmean:= (T[1]*T[2]/(T[2]-T[1]))*ln(T[2]/T[1]);

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let's try out 18.B to see if we have a winner...

> T[1]:=200; T[2]:=600; k[T]:=.0166;

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specs for Deuterium; if the kt isn't given you can find it in matlab's mixkt using the mole ratios of the two substances.

> simplify(newequation);

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Deuterium is .01823 lower in the hot bulb

> evalf(Tmean);

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this is the temperature at which the average kT should be evaluated.

It checks out.