Equation of Continuity II

Summary of Equations of Change

molecular stresses = pressure + viscous stresses

Summary of Equations of Change The energy molecular flux

Summary of Equations of Change Recall: the combined energy flux vector e

Combined Energy Flux Vector Convective Energy Flux Heat Rate from Molecular Motion Work Rate from Molecular Motion Combined Energy Flux Vector: We introduce something new to replace q:

Combined Energy Flux Vector Combined Energy Flux Vector: We introduce something new to replace q: Recall the molecular stress tensor: When dotted with v: Substituting into e:

Summary of Equations of Change Recall: Substituting the equation for q into e

Summary of Equations of Change Recall: Substituting the equation for q into e partial molar per unit mass

Summary of Equations of Change Recall: Substituting the equation for q into e

Summary of Equations of Change

Simultaneous Heat and Mass Transfer

Assumptions: 1.Steady-state 2.Ideal gas behavior 3.Total c is constant 4.Uniform pressure 5.Physical properties are constant, evaluated at mean T and x. 6.Neglect radiative heat transfer

Simultaneous Heat and Mass Transfer Equations of Change: Continuity (A)

Simultaneous Heat and Mass Transfer Equations of Change: Energy * Both N Ay and e y are constant throughout the film

Simultaneous Heat and Mass Transfer To determine the mole fraction profile: Recall: The molar flux for diffusion of A through stagnant B

Concentration Profiles I. Diffusion Through a Stagnant Gas Film Since B is stagnant,

Simultaneous Heat and Mass Transfer To determine the mole fraction profile: Recall: The molar flux for diffusion of A through stagnant B Recall: Integration of the above equation

Concentration Profiles I. Diffusion Through a Stagnant Gas Film Let C 1 = -ln K 1 and C 2 = -ln K 2, B.C. at z = z 1, x A = x A1 at z = z 2,x A = x A2

Simultaneous Heat and Mass Transfer To determine the mole fraction profile: Recall: The molar flux for diffusion of A through stagnant B Using the appropriate B.C.s at y = 0, x A = x A0 at y = δ,x A = x Aδ

Simultaneous Heat and Mass Transfer To determine the mole fraction profile: Evaluating N Ay from the equations above Note that:

Simultaneous Heat and Mass Transfer BUT…

Simultaneous Heat and Mass Transfer

Rearranging and combining

Simultaneous Heat and Mass y = y, x A = x A

Simultaneous Heat and Mass y = y, x A = x y = δ, x A = x Aδ Taking the ratios of the two equations

Simultaneous Heat and Mass Transfer To determine the temperature profile: Note: where the enthalpy of mixing is often neglected for gases at low to moderate pressures

Simultaneous Heat and Mass Transfer To determine the temperature profile: The general solution is

Simultaneous Heat and Mass Transfer At y = 0, T = T 0 At y = δ, T = T δ Subtracting the two equations

Simultaneous Heat and Mass Transfer Since

Simultaneous Heat and Mass Transfer

If we did not consider mass transfer

Simultaneous Heat and Mass Transfer With mass transfer

Simultaneous Heat and Mass Transfer Comparison of the energy flux with & without the presence of mass transfer: Rate of heat transfer is directly affected by simultaneous mass transfer BUT mass flux is not directly affected by simultaneous heat transfer