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Dimensionless model equations

The model mass and energy balance equations will have consistent units, throughout, i.e., kg/s, kmol/s or kj/s, and corresponding dimensions of mass/ time or energy/time. The major system variables, normally concentration or [Pg.31]

1 Case A. Continuous Stirred-Tank Reactor (CSTR) [Pg.47]

The mass balance for a continuous-flow, stirred-tank reactor with first-order reaction is [Pg.47]

Dividing the balance equation by the volume of reactor, V, leads to the equation in the form [Pg.47]

This equation has two parameters t, the mean residence time (z = V/F) with dimensions of time and k, the reaction rate constant with dimensions of reciprocal time, applying for a first-order reaction. The concentration of reactant A in the reactor cannot, under normal circumstances, exceed the inlet feed value, Cao and thus a new dimensionless concentration, Cai, can be defined as [Pg.48]

The other variable time, t, can vary from zero to some undetermined value, but the system is also represented by the characteristic time, x. Note that the value of 1/k also represents a characteristic time for the process. [Pg.48]


Program TANK solves the normal dimensional model equation for the problem, whereas TANKD is formulated in terms of the dimensionless model equations. [Pg.324]

The dimensionless model equations are programmed into the ISIM simulation program HOMPOLY, where the variables, M, I, X and TEMP are zero. The values of the dimensionless constant terms in the program are realistic values chosen for this type of polymerisation reaction. The program starts off at steady state, but can then be subjected to fractional changes in the reactor inlet conditions, Mq, Iq, Tq and F of between 2 and 5 per cent, using the ISIM interactive facility. The value of T in the program, of course, refers to dimensionless time. [Pg.369]

Defining Z = z/L, t=T/T0, C=CA/CA0> =Dt/L2, the model equations can be recast into dimensionless terms to give the following dimensionless model equations ... [Pg.340]

The dimensionless model equations are used in the program. Since only two boundary conditions are known, i.e., S at X = l and dS /dX at X = 0, the problem is of a split-boundary type and therefore requires a trial and error method of solution. Since the gradients are symmetrical, as shown in Fig. 1, only one-half of the slab must be considered. Integration begins at the center, where X = 0 and dS /dX = 0, and proceeds to the outside, where X = l and S = 1. This value should be reached at the end of the integration by adjusting the value of Sguess at X=0 with a slider. [Pg.527]

The dimensionless model equations for an electrochemical reduction reaction in a PBE are in a form of a set of partial ... [Pg.288]

The last case we consider is that of a flat velocity profile with linear adsorption and desorption. In this case, the dimensionless model equations are given by... [Pg.236]

These dimensionless groups of fluid properties play important roles in dimensionless modeling equations of transport processes, and for systems where simultaneous transport processes occur. [Pg.87]

Based on the previous assumptions and decided geometry, the final dimensionless model equations, following a previous woik by Kumar et al.[5], are listed below. The definitions for the dimensionless parameters are provided at the end of this article. [Pg.393]

The solution to the dimensionless model, Equation 7.34 through Equation 7.39 are... [Pg.286]

As we have shown in the previous sections, the dynamics of the dense phase are described by nonlinear ordinary differential equations (ODEs) on time having an integral term for the mass and heat transfer between the dense and the bubble phases. The bubble phase is described by pseudosteady state linear ODEs on height. The linear ODEs of the bubble phase are solved analytically and the solution is used to evaluate the integrals in dense-phase equations. The reader should do this as practice to reach the dimensionless model equations given next. [Pg.507]

We now seek a numerical solution to the dimensionless model equations,... [Pg.150]

Under neutral condition, co is equal to 0. If the dismrbance appears in x direction, ky = 0. Substituting the disturbance expression to the dimensionless model equation and the boundary condition, we have the following ... [Pg.248]


See other pages where Dimensionless model equations is mentioned: [Pg.47]    [Pg.414]    [Pg.644]    [Pg.31]    [Pg.464]    [Pg.233]    [Pg.218]    [Pg.242]    [Pg.468]    [Pg.39]    [Pg.394]    [Pg.517]    [Pg.348]    [Pg.280]    [Pg.526]    [Pg.246]   
See also in sourсe #XX -- [ Pg.38 , Pg.585 ]

See also in sourсe #XX -- [ Pg.192 ]




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