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Quasi-linear heat and mass transfer

I. The constitutive equations

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Summary

From the assumption that the heat flux (mass flux with respect to the mass-average velocity) vector is an isotropic function of the temperature (mass-fraction) gradient, it is shown that, wherek(D) is a function of the absolute value of the temperature (mass-fraction) gradient.

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Abbreviations

C v :

Heat capacity at constant volume per unit mass of system

D :

the diffusion coefficient

G :

another symbol for

g1,g2,g3,g4:

the principal values ofG (diagonal elements of the matrixḠ)

I :

the identity matrix,\(I_{ij} = \left\{ \begin{array}{l} 1 if i = j \\ 0 if i \ne j \\ \end{array} \right.\)

j A :

mass flux vector with respect to the mass average velocity

k :

thermal conductivity

p :

pressure

q :

heat flux vector with respect to the mass-average velocity

q1,q2,q3,q4:

Principal values ofq (diagonal elements of the matrix\(\bar q\))

\(\bar q_{ij} \) :

elements of the matrix\(\bar q\)

r A :

rate at which mass of componentA is formed in system of unit volume by chemical reaction

S :

orthogonal transformation matrix

t :

time

T :

temperature

gu :

velocity vector

ρ :

density

τ :

stress deviation tensor

ω A :

mass fraction of componentA

:

the “del” operator, in rectangular co-ordinates it equals

$$\frac{\partial }{{\partial x}}i + \frac{\partial }{{\partial y}}j + \frac{\partial }{{\partial z}}k$$
τ :v:

rate at which energy is dissipated due to viscous effects per unit volume=τ i j υ′ j i overline the corresponding diagonal matrix

References

  1. Bird, R. B., W. E. Stewart and E. N. Lightfoot, Transport Phenomena, John Wiley, New York, 1960.

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  2. Birkhoff, G. and S. MacLane, A Survey of Modern Algebra, Macmillan, New York, 1953.

    MATH  Google Scholar 

  3. McConnel, A. J., Applications of Tensor Analysis, Dover, New York, 1957.

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  4. Serrin, J., Handbuch der Physik, Band VIII/1, ed. by S. Flügge, Springer, Berlin, 1959.

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Authors and Affiliations

  1. Department of Chemical Engineering, Northwestern University, Evanston, Illinois, U.S.A.

    John C. Slattery

Authors
  1. John C. Slattery
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Slattery, J.C. Quasi-linear heat and mass transfer. Appl. sci. Res. 12, 51–56 (1964). https://doi.org/10.1007/BF03184747

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  • DOI: https://doi.org/10.1007/BF03184747

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