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10.7: Nomenclature

  • Page ID
    53625
  • Table \(\PageIndex{1}\): Nomenclature 

    \(A\) area, \(m^2\), absorption factor
    \(\mathscr{A}\) closed surface area of the control volume \(\mathscr{V}\), \(m^2\)
    \(\mathscr{A}_a (t)\) closed surface area of an arbitrary, moving control volume \(\mathscr{V}_A(t)\), \(m^2\)
    \(A_c\) area of the entrances and exits for the control volume \(\mathscr{V}\), \(m^2\)
    \(A_c (t)\) area of the entrances and exits for the control volume \(\mathscr{V}_A(t)\), \(m^2\)
    \(\mathscr{A}_m (t)\) surface area of a body, \(m^2\)
    \(AW_J\) atomic mass of the \(J^{th}\) atomic species, g/mol
    \(\mathbf{A}\) atomic matrix, also identified as \(\begin{bmatrix} N_{JA} \end{bmatrix}\)
    \(\mathbf{A}^*\) row reduced echelon form of the atomic matrix, also identified as \(\begin{bmatrix} N_{JA} \end{bmatrix}^*\)
    \(\mathbf{B}\) Bodenstein matrix that maps \(\mathbf{r}\) onto \(\mathbf{R}_B\)
    \(c_A\) \(\rho_A / MW_A\), molar concentration of species \(A\), mol/\(m^2\)
    \(c\) \(\sum_{A=1}^{A=N} c_A\), total molar concentration, mol/\(m^3\)
    C conversion
    \(D\) diameter, m
    \(\mathbf{f}\) vector force, N
    \(f\) magnitude of the force vector, N
    \(\mathbf{g}\) gravity vector, m/\(s^2\)
    \(g\) magnitude of the gravity vector, m/\(s^2\)
    \(h\) height, m
    \(\mathbf{I}\) unit matrix
    \(K_{eq,A}\) equilibrium coefficient for species \(A\)
    \(L\) length, m
    \(m\) mass, kg
    \(\dot{m}\) mass flow rate, kg/s
    \(m_A\) mass of species \(A\), kg
    \(\dot{m}_A\) mass flow rate of species \(A\), kg/s
    \(\dot{M}_A\) molar flow rate of species \(A\), mol/s
    \(\dot{M}\) \(\sum_{A=1}^{A=N} \dot{M}_A\) total molar flow rate, mol/s
    \(MW_A\) molecular mass of species \(A\), g/mol
    \(\mathbf{M}\) mechanistic matrix that maps \(\mathbf{r}\) onto \(\mathbf{R}_M\)
    \(\mathbf{n}\) outwardly directed unit normal vector
    \(n\) \(\sum_{A=1}^{A=N} n_A\), total number of moles
    \(n_A\) number of moles of species \(A\)
    \(N\) number of molecular species in a multicomponent system
    \(N_{JA}\) number of \(J\)-type atoms associated with molecular species \(A\)
    \(\begin{bmatrix} N_{JA} \end{bmatrix}\) atomic matrix, also identified as \(\mathbf{A}\)
    \(\begin{bmatrix} N_{JA} \end{bmatrix}^*\) row reduced echelon form of the atomic matrix, also identified as \(\mathbf{A}^*\)
    \(p\) \(\sum_{A=1}^{A=N} p_A\) total pressure, N/\(m^2\)
    \(p_A\) partial pressure of species \(A\), N/\(m^2\)
    \(p_{A,vap}\) vapor pressure of species \(A\), N/\(m^2\)
    \(p_g\) \(p - p_o\), gauge pressure, N/\(m^2\)
    \(p_o\) reference pressure (usually atmospheric), N/\(m^2\)
    \(\mathbf{P}\) pivot matrix that maps \(\mathbf{R}_P\) onto \(\mathbf{R}_{NP}\)
    \(Q\) volumetric flow rate, \(m^3\)/s
    \(r\) radial position, m
    \(R\) universal gas constant, see Table 5-1 for units
    \(r_A\) net mass rate of production of species \(A\) per unit volume, kg/\(m^3\)s
    \(R_A\) \(r_A/ MW_A \), net molar rate of production of species \(A\) per unit volume, mol/\(m^3\)s
    \(\mathbf{R}_M\) column matrix of all net rates of production, mol/\(m^3\)s
    \(\mathbf{R}\) column matrix of net rates of production of stable species, mol/\(m^3\)s
    \(\mathbf{r}\) column matrix of elementary reaction rates, mol/\(m^3\)s
    \(\mathbf{R}_B\) Bodenstein column matrix of net rates of production of Bodenstein products, mol/\(m^3\)s
    \(\mathbf{R}_P\) column matrix of net molar rates of production of the pivot species, mol/\(m^3\)s
    \(\mathbf{R}_{NP}\) column matrix of net molar rates of production of the non-pivot species, mol/\(m^3\)s
    \(\mathscr{R}_A\) net global molar rate of production of species \(A\), mol/s
    \(\mathbf{S}\) stoichiometric matrix that maps \(\mathbf{r}\) onto \(\mathbf{R}\)
    S selectivity
    \(T\) temperature, K
    \(t\) time, s
    \(\mathbf{u}_A\) \(\mathbf{v}_A - \mathbf{v}\), mass diffusion velocity of species \(A\), m/s
    \(\mathbf{u}_A^*\) \(\mathbf{v}_A - \mathbf{v}^*\), molar diffusion velocity of species \(A\), m/s
    \(\mathbf{v}_A\) species \(A\) velocity, m/s
    \(\mathbf{v}\) \(\sum_{A=1}^{A=N} \omega_A v_A\), mass average velocity, m/s
    \(\mathbf{v}^*\) \(\sum_{A=1}^{A=N}  x_A v_A\), molar average velocity, m/s
    \(v\) magnitude of velocity vector, m/s
    \(\mathbf{v}_r\) relative velocity, m/
    \(V_A\) partial molar volume of species \(A\), \(m^3\)
    \(V\) volume, \(m^3\)
    \(\mathscr{V}_a (t)\) volume of an arbitrary moving control volume, \(m^3\)
    \(\mathscr{V} (t)\) volume of a specific moving control volume, \(m^3\)
    \(\mathscr{V}_m (t)\) volume of a body which is referred to as a material volume, \(m^3\)
    \(\mathscr{V}\) volume of a fixed control volume, \(m^3\)
    \(v_x, v_y, v_x\) components of the velocity vector, \(\mathbf{v} = \mathbf{i}v_x + \mathbf{j}v_y + \mathbf{k}v_z\), m/s
    \(\mathbf{w}\) velocity of the surface of the arbitrary moving control volume \(\mathscr{V}_a (t)\), m/s
    \(x_A\) \(c_A/c\), mole fraction of species \(A\) in the liquid phase
    \(y_A\) \(c_A/c\), mole fraction of species \(A\) in the gas phase
    \(x,y,z\) rectangular Cartesian coordinates, m
    \(\mathbf{Y}\) yield
       
    Greek Letters  
    \(\lambda\) unit tangent vector.
    \(\gamma\) \(\rho / \rho_{\ce{H2O}}\), specific gravity
    \(\theta\) angle, radians
    \(\nu\) \(\mu / \rho\), kinematic viscosity, \(m^2\)/s
    \(\nu_{A\alpha}\) stoichiometric coefficient for species \(A\) in the \(\alpha\)-reaction
    \(\rho_A\) mass density of species \(A\), kg/\(m^3\)
    \(\rho\) \(\sum_{A=1}^{A=N} \rho_A\), total mass density, kg/\(m^3\)
    \(\omega_A\) \(\rho_A / \rho\), mass fraction of species \(A\)
    \(\varepsilon\) void fraction, volume of void space per unit volume
    \(\mu\) viscosity, \(\mathbf{P}\)
    \(\boldsymbol{\mu}\) specific growth rate, \((m^3 \ s)^{-1}\)
    \(\sigma\) surface tension, N/m
    \(\tau\) residence time, s

     

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