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At this point we are confronted with Truesdell’s comment “So far, everything is crystal clear’, and indeed this is a key result which allows us to simplify Eq. 85 to the form

Figure 16 At this point we are confronted with Truesdell’s comment “So far, everything is crystal clear’, and indeed this is a key result which allows us to simplify Eq. 85 to the form

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The rates of chemical reaction are constrained by the supplemental axiom for mass that takes the form
The rates of chemical reaction are constrained by the supplemental axiom for mass that takes the form
We can sum the species A thermal energy equation over all species to obtain
We can sum the species A thermal energy equation over all species to obtain
On the basis of Axiom IIA (see Eq. 3) and Axiom IVB (see Eq. 20) this result can be simplified to
On the basis of Axiom IIA (see Eq. 3) and Axiom IVB (see Eq. 20) this result can be simplified to
This form of the thermal energy equation is different than DeGroot and Mazur (1962, page 18, Eq. 34); Slattery (1999, Sec. 8.3.4); Deen (1998, Eqs. 11.2- among ot! 3 and 11.2-6); Rosner (2000, page 53, Eq. 2.5-17), thermal energy equation do not contain the term marked by an next step 1 Truesdell Sec. 243). n this note is to compare Eq. 48 with the thermal en the equations presented by Bird et al. (2002, page 589) hers. Of special importance is the fact that these other representations of the asterisk (*) in Eq. 48. Our ergy equation developed by (1969, Chapter 5) and presented earlier by Tru esdell and Toupin (1960,
This form of the thermal energy equation is different than DeGroot and Mazur (1962, page 18, Eq. 34); Slattery (1999, Sec. 8.3.4); Deen (1998, Eqs. 11.2- among ot! 3 and 11.2-6); Rosner (2000, page 53, Eq. 2.5-17), thermal energy equation do not contain the term marked by an next step 1 Truesdell Sec. 243). n this note is to compare Eq. 48 with the thermal en the equations presented by Bird et al. (2002, page 589) hers. Of special importance is the fact that these other representations of the asterisk (*) in Eq. 48. Our ergy equation developed by (1969, Chapter 5) and presented earlier by Tru esdell and Toupin (1960,
Eq. 35 leads to the two heat flux relations given by
Eq. 35 leads to the two heat flux relations given by
It is important to note that the three supplemental axioms imposed by Truesdell (Eqs. 51, 55 and 62) are less restrictive than the six supplemental axioms imposed by Whitaker (Eqs. 3, 19, 20, 36, 37 and 38). In addition, one needs to remember that the sixth supplemental axiom, Axiom IVC, plays no role in the derivation of the thermal energy equation given by Eq. 48.
It is important to note that the three supplemental axioms imposed by Truesdell (Eqs. 51, 55 and 62) are less restrictive than the six supplemental axioms imposed by Whitaker (Eqs. 3, 19, 20, 36, 37 and 38). In addition, one needs to remember that the sixth supplemental axiom, Axiom IVC, plays no role in the derivation of the thermal energy equation given by Eq. 48.
We begin our study of Eq. 63 with the representation for €,; which is given by
We begin our study of Eq. 63 with the representation for €,; which is given by
heating flux as —q, so that the divergence of h takes the form
heating flux as —q, so that the divergence of h takes the form
The route forward from this point is not clear; however, Truesdell (1969) suggests that . “general equation of transport” is “not difficult to prove”, and this leads to the translatio: given by (Whitaker, 2012, Eq. B.13 and Appendix D1) and presented here as
The route forward from this point is not clear; however, Truesdell (1969) suggests that . “general equation of transport” is “not difficult to prove”, and this leads to the translatio: given by (Whitaker, 2012, Eq. B.13 and Appendix D1) and presented here as
This form of the thermal energy equation is identical to Eq. 48 except for the presence of the last term. This difference can be attributed to the difference in the supplemental axioms used by Truesdell (1969) and those used by Whitaker (2012). It is important to note that the fundamental axioms for mass, momentum and energy are identical; however, the supplemental axioms listed on the following page are not.
This form of the thermal energy equation is identical to Eq. 48 except for the presence of the last term. This difference can be attributed to the difference in the supplemental axioms used by Truesdell (1969) and those used by Whitaker (2012). It is important to note that the fundamental axioms for mass, momentum and energy are identical; however, the supplemental axioms listed on the following page are not.
and we apply it to the species A body illustrated in Figure A-1. This procedure is base on the Eulerian concept that the linear momentum equation can be applied to any distinc body and to any arbitrary body that is “cut out of” a distinct body (Truesdell, 1968 pade 193). In this development, we begin with the linear momentum equation for species A
and we apply it to the species A body illustrated in Figure A-1. This procedure is base on the Eulerian concept that the linear momentum equation can be applied to any distinc body and to any arbitrary body that is “cut out of” a distinct body (Truesdell, 1968 pade 193). In this development, we begin with the linear momentum equation for species A
and in terms of these averages, the linear momentum equation forspecies A takes the form
and in terms of these averages, the linear momentum equation forspecies A takes the form
We have learned something very important about the stress vector by applying the species momentum equation to the slab illustrated in Figure A-1, and we can learn more with an application to the tetrahedron shown in Figure A-2. One should think of the tetrahedron as a body cut out of a distinct body according to the Euler cut principle.
We have learned something very important about the stress vector by applying the species momentum equation to the slab illustrated in Figure A-1, and we can learn more with an application to the tetrahedron shown in Figure A-2. One should think of the tetrahedron as a body cut out of a distinct body according to the Euler cut principle.
We can apply Eq. A-1 to the tetrahedron shown in Figure A-2 and express the result as
We can apply Eq. A-1 to the tetrahedron shown in Figure A-2 and express the result as
Use of these results in Eq. A-13 leads to
Use of these results in Eq. A-13 leads to
in which T, is the species A stress tensor defined as
in which T, is the species A stress tensor defined as
and we want to extract the point equation associated with this concept. Our analysis of the first term in Eq. A-23 requires the use of the general transport equation, and for this special case that theorem takes the form
and we want to extract the point equation associated with this concept. Our analysis of the first term in Eq. A-23 requires the use of the general transport equation, and for this special case that theorem takes the form
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