By Dennis B. Weis

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Example text

That could well not be the case; for a reversible reaction, the equilibrium value w* could well be different from unity. 6 The extent of reaction w is what is called an internal state variable in thermodynamics. The state depends on w, but we cannot impose the value of w arbitrarily and independently of the values of the external state variables (such as volume and temperature) which we choose to impose. Hence the possibility of defining an equilibrium value of w, w*, which is the one corresponding to the situation where ∂w/∂t = 0 if things like volume and temperature are held constant.

1 Γ/JΦ which it is all too natural to call the Stefan number, St (both Γ and J are negative, so St is nicely positive). 7) We now wish to make t and X dimensionless, but we are short one parameter, and thus we find out that a similarity solution is sure to come out. The Neuman variable z = X/2 ( Dt) is going to work again. 8) S = 2K ( Dt) with K a constant to be determined. 4 Notice that the fact that S is proportional to without finding the solution of the problem. 11) This is a second order differential equation subject to three BCs, and hence the value of K can be extracted.

The XY tangential stress. With the assumed kinematics, this is indeed the only nonzero component of the stress in excess of pressure. 1), since C = ΦU. 3) which is indeed in the form of Eq. 1) when the ratio of the viscosity µ to the density Φ is interpreted as the diffusivity of momentum, D = µ/Φ. U can be regarded (more about this later) as the “potential” for momentum transfer. 4) 28 Introduction to Methodology Ch. 1 which by itself does not negate the possibility that velocity may suffer a discontinuity.

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