Entropy, Absolute Temperature and Coldness in by Ingo Mueller PDF

By Ingo Mueller

ISBN-10: 3211811265

ISBN-13: 9783211811269

ISBN-10: 3709129656

ISBN-13: 9783709129654

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Extra resources for Entropy, Absolute Temperature and Coldness in Thermodynamics: Boundary Conditions in Porous Materials

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MULLER, A Macroscopic Model for the Flow of a Fluid through a Porous Solid, submitted to ZAMP. (++) For generality I have employed the principle of equipresence here, according to which all constitutive quantities may depend on the variables. 01.. ~ and 41 lt as solutions of a well posed boundary and initial value problem. 3. Some Special Cases. It is easily appreciated from the above arguments that the field equations just derived are far from general and yet they are much too general to be of direct use to people ~ terested in soil mechanics or hydrology.

Indices in square brackets indicate antisymrnetriza tion. Symmetry of the tensor of heat conductivity etc. 33 Hence it follows that xr"~'(Jt(){f) -A11(-& att) "\:'cJt The left hand side of· this equation does not depend on "':'~ the right hand side must not depend on therefore that Cf>L•jl + A Kr•tl = 0 ~~ so either. It follows so that the relation holds just as in an isotropic rigid solid. If cp;, = A qi. e. the tensor of heat conductivity is symmetric. We may notice that this result is critically de- 34 Part II - On heat conduction in a rigid body pendent on the fact that I have included ~ among the variables in the constitutive relations and that is also true for the pr~ diction of finite speeds for temperature waves.

I propose to calculate the velocity of propagation of a wave in the second derivatives of temperature in an isotropic rigid solid. The jwnps ["'J, [ ~~ ] and [ "':~] across the wave vanish and therefore the constitutive quantities e and q~ are also continuous across the wave. Of course, the balance of energy holds on either side so that we obtain {)e. (/ CJ fJ' [D"{J] (,; iJ e. ~i] = 0• = 0 we know from the theory of moving' singular surfaces that the jwnps of the second derivatives of~ are all determined by two parameters of which one is the normal speed (~eee) of the sur(ace • We have and ei, is the wave normal.

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Entropy, Absolute Temperature and Coldness in Thermodynamics: Boundary Conditions in Porous Materials by Ingo Mueller


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