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Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras

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Advanced Transport Phenomena

Module 9 Lecture 38

Student Exercises: True/ False Questions

Dr. R. Nagarajan

Professor

Dept of Chemical Engineering

IIT Madras

The individuality of substances shows up in their constitutive laws; in contrast, the conservation (balance) laws apply to all substances, irrespective of their state, chemical composition, etc.

The success of the continuum approximation is a consequence of the fact that characteristic flow times and diffusion times are always much larger than the characteristic times between “successful” (chemically reactive) molecular encounters.

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The fundamental conservation laws applied to the fluid within an Eulerian control volume necessarily lead to partial differential equations (PDEs)

A continuum formulation cannot be used to predict the behavior of flow fields that contain local “discontinuities” such as shock waves, detonation waves, or deflagration waves

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A detailed local “field description” is now needed to solve all transport problems of engineering interest.

While the partial differential equations and boundary/initial conditions governing all coupled fields can always be written, they cannot be solved, even numerically, in any case of practical interest.

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“Jump” conditions can be derived only across discontinuities that are so thin that they preclude a continuum analysis of their structure (e.g., strong detonations, shock waves, phase boundaries, etc.)

An empirical approach, based on the use of extensive probe measurements, circumvents the need to understand and apply the principles of transport processes.

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The final answer one gets in solving an engineering transport problem should be independent of the particular control volume(s) used in the analysis, but some choices of control volume(s) will inevitably be much more convenient than others.

Control volumes that are neither fixed in space (Eulerian) nor moving with the fluid (material, or Lagrangian) are not useful in the analysis of chemically reacting fluid mixtures

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The conservation equations expressed in vector form have a physical meaning that is the same no matter what the choice of coordinate system used to define the positions of points in space.

Complete specification of the local convective flux of linear momentum requires six independent scalar quantities.

Linear momentum is not conserved in systems described by using accelerating coordinate frames (systems).

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The specific enthalpy, ,

is a particularly convenient dependent variable for treating energy transfer in time-dependent, non flow ("batch") systems.

While it is possible to derive useful equations governing the total (thermal, chemical, and mechanical) energy, it is not possible to derive useful equations governing only the "mechanical" portion of the mixture energy.

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In a steady flow, nothing short of a nuclear transformation (e.g., fission) can change the mass fraction of each chemical element along a streamline.

In an N-component reacting mixture, all N-species conservation equations are independent of the equation governing total mixture mass conservation.

Whereas each mass-balance equation is a scalar equation, the mixture linear-momentum equation is a vector equation, equivalent to three scalar equations (in any coordinate system).

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"Viscous dissipation" constitutes a local "sink" for mechanical energy, but a "source" for thermal energy and enthalpy.

Even though the transient continuum equations are still directly applicable, time-averaging and volume-averaging procedures are often used in the treatment of turbulent and multiphase flows to circumvent the need for impractically fine temporal and spatial resolution.

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If the body forces gi are the same for each species i present in an N-component mixture, then the net body-force term necessarily drops out of the mixture momentum equation.

When the only operative body force is that due to gravity, then it is useful to introduce the notion of gravitational potential energy in the energy equation, to take into account the work done by the gravitational body force on the flowing mixture.

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For a chemically reacting mixture in the absence of momentum diffusion, energy diffusion, and species mass diffusion, the local rate of entropy production, ,would necessarily be zero.

Even for the same temperature and pressure (e.g., 298.15 K, 1 atm) all gases do not have the same molar enthalpy.

The Second Law of Thermodynamics provides a qualitatively useful inequality (Clausius') but does not yield a quantitatively useful balance (conservation) equation.

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J. C. Maxwell showed that the dynamic viscosity of a perfect gas depends on the pressure level and directly on the square root of the molecular mass.

The near-equality of the molecular diffusivities for momentum, heat, and mass transfer in low-density gases indicates that the microscopic mechanisms of momentum, heat, and mass transfer are the same in such “fluids”

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Information on the nature of individual molecular encounters can be derived from careful measurements of the temperature dependence of gas viscosity.

The presence of velocity gradients ensures the simultaneous presence of momentum diffusion (i.e., shear stresses) in a continuum.

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According to Stokes, the local viscous stress in a Newtonian fluid is proportional to the local deformation of the continuum (both angular and volumetric).

All liquids have Prandtl numbers not very different from unity.

Electrons play an important role in liquid-metal heat diffusion, but not in liquid-metal momentum diffusion.

Radiation makes no contribution to the apparent thermal conductivity of partially transparent materials.

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All substances of engineering interest are “isotropic” in their thermal properties

Polyatomic gases with low (near unity) values of the equilibrium specific heat ratio, usually have higher Prandtl numbers than those characterizing monatomic gases (such as He, Ar, etc.)

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The local fluid velocity vector, v, can also be viewed as the local linear momentum per unit mass of fluid.

The "no-slip" condition is an immediate consequence of the principle of conservation of tangential momentum at fluid/solid interfaces.

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The velocity profile for steady viscous flow of a non-Newtonian fluid in a straight circular pipe is parabolic, provided the flow is laminar.

"Reynolds' analogy" is a quantitative relation between the dimensionless skin-friction coefficient and the corresponding heat or mass transfer coefficients for the same fluid/flow conditions.

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The surface roughness of a conduit has greater effect on fluid motion in the turbulent regime than in the laminar flow regime.

The terminal settling velocity of an isolated solid sphere of known mass can be used to infer the fluid viscosity, provided the Reynold’s number is small enough to be in the Stokes’ regime.

Chemically reacting gas flows can always be treated as incompressible provided the square of the prevailing Mach number is sufficiently small.

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Linear momentum is not conserved in swirling flows; only angular momentum is conserved in such flows

The “buoyancy force” per unit volume is not an additional fundamental force of nature. It is simply the combinations which is locally nonzero in variable-density situations accompanied by a body force g per unit mass.

Natural (“free”-) convection flows do not exhibit transition to turbulence.

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Poiseuille’s law is the basis of both the capillary viscosimeter and the capillary flowmeter

If the drag coefficient for an object is independent of Reynold’s number, then in this range the actual drag force will increase as the cube of the velocity.

The drag force on an object is necessarily directly proportional to its “frontal area”.

In a duct of increasing cross-sectional area the velocity of a steady-flow must necessarily decrease (as a consequence of total mass conservation)

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In engineering applications the photon mean-free-path is usually large enough to allow radiative transfer to be uncoupled from simultaneous energy transport by Fourier diffusion and convection.

A solidification “wave” violates the Second Law of Thermodynamics, since the result of the transformation (a (poly)crystalline solid) has a lower entropy than the melt from which it was formed.

Heat diffusion plays no role in the determination of convective heat transfer coefficients.

The use of temperature difference as a “driving force” for convective heat transfer (“Newton’s law of cooling/heating”) has its origin in Fourier’s linear law of heat diffusion.

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Variable fluid properties (e.g., the viscosity-temperature dependence) are more likely to influence convective heat-transfer coefficients for Newtonian liquids than for (Newtonian) gas mixtures.

Solids are incapable of “convecting” energy

“Fins” are more often placed on the liquid side of gas/liquid heat exchangers because that is the side of maximum heat “conductance”.

The emitted radiation from all real surfaces increases with the fourth power of the absolute surface temperature.

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Increasing the thickness of the air gap between two panes of glass will inevitably increase the effective thermal resistance of a composite “window”.

Entropy can be convected, but it cannot diffuse.

Localized boiling can dramatically augment heat- transfer coefficients as a result of both latent heat transport and the “stirring” action of the vapor bubbles produced.

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If energy is to be conserved across an interface, the temperature on either side of the interface must be the same — i.e., the temperature must be continuous across the interface.

For a propagating phase boundary, the normal component of the energy diffusion flux vector must be the same on both sides of the boundary.

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In a system undergoing chemical reaction and/or phase change, there are often important contributions to the energy diffusion flux vector other than the Fourier (—k grad T) contribution.

An understanding of the heat-transfer properties of straight ducts can be used in the formulation of "economical," general correlations for packed-bed heat transfer, but actual heat-transfer coefficients in such "tortuous-duct" systems are best determined by direct experimentation.

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Natural convection does not occur in mass transfer situations since there is no temperature change to cause the necessary density differences.

When the Schmidt number, is very large, the momentum (or vorticity) boundary layer is embedded well within the mass transfer boundary layer.

For two adjacent phases in local thermochemical equilibrium, each chemical-species mass fraction must be continuous across the phase boundary.

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In ordinary chemically reacting mixtures, the equations governing chemical- element mass fractions are always simpler than those governing individual chemical species mass fraction, since ordinary chemical reactions cannot produce or destroy chemical elements.

In the absence of appreciable “phoresis” and /or homogeneous chemical reactions, there is quantitatively useful “analogy” between mass and heat-transfer coefficients, valid even in the presence of appreciable streamwise pressure gradients.

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Multiphase flows can often be treated as single-phase flows if the suspended (“dispersed”) phase can be treated as a diffusing “ species” closely coupled to the host flow (“continuous “ phase).

At sufficiently low gas pressures, even a short straight tube with axial flow will behave like a well stirred vessel due to molecular back-mixing.

There is no such thing as a steady-flow chemical reactor since, in chemically nonequilibrium systems, there is always a time-rate of change of chemical composition

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The minimum allowable bed height for a desired reactant conversion in a fixed-bed chemical reactor is set by the catalytic activity of the pellets.

“Cold-flow” composition measurements bear no useful relations to the behavior of geometrically and dynamically similar chemically reacting fluid systems.

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A fluidized bed chemical reactor operating close to the condition of minimum fluidization (mf) behaves in a manner similar to a plug-flow (somewhat “expanded”) fixed-bed chemical reactor; indeed, fixed bed interphase energy and mass transfer correlations remain approximately valid, albeit with a Re-dependent void function,

WSRs, while a valuable teaching tool, cannot be used in practice because the most probable residence is zero, not the mean residence time

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RTDs with long "tails" usually indicate the presence of relatively "dead spaces" within a vessel.

For noninteracting series configurations of contactors, the overall RTD (and each of its complete set of moments) is invariant under an interchange of the order of vessels in the sequence.

When a chemical reaction of nonunity reaction order is carried out in a series of noninteracting contactors, the total reactant conversion is invariant under an interchange of the order of vessels in the sequence.

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If two reactors with RTDs having the same first and second moments are used to carry out the same first-order irreversible reaction, the observed reactant conversion will necessarily be indistinguishable.

Reactor appearance is an accurate indicator of whether reactor performance will more closely approximate the PFR or WSR-limit.

To approximate the WSR-limit, the feed must be mixed with the reactor contents on a time scale comparable to the mean residence (holding-) time in the reactor.

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The WSR limit cannot be approximated in the absence of mechanical propellers and baffles.

The WSR-limit ordinarily leads to a minimum-volume reactor for chemical reactions whose kinetics are of negative order, or when the reaction products (including "heat") accelerate the reaction rate ("autocatalysis").

Extinction conditions for a WSR are the same as ignition conditions. That is, there is no hysteresis in jumping between eligible distinct steady states.

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When conditions (feed, parametric settings) lead to the existence of two stable operating points straddling an intermediate unstable operating point, it is impossible to obtain and maintain such an operating point, even if a control system is added to the chemical reactor.

Nonlinear analysis of the governing ODEs, including the use of a "phase plane," can be used to determine (a) what initial states will lead to what WSR operating points, (b) whether each approach will be monotonic or exhibit (possibly damaging) temperature "overshoots," and (c) the total time needed to achieve each steady state for each possible initial state.

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When made dimensionless, the underlying equations of conservation, combined with their boundary conditions, contain no more information about a transport problem than that already contained in the Buckingham

Dimensionless groups (“eigen-ratios”, such as shape factors, Re, Ra, Pr, etc.) comprise the similarity parameters which yield “set-up-rules” for designing scale-model experiments amenable to quantitative use.

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Similitude analysis may be regarded as a procedure for discovering quantitative similarities (“co-relations”) for a class of superficially dissimilar systems having some intrinsic similarity.

There are no quantitatively useful scale-up or scale-down principles applicable to systems with chemical reaction. For this reason, scale model tests of chemical reactors are useless.

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If an equation is not “dimensionally homogeneous,” it is either wrong or valid only in a particular unit system.

Conservation (balance) laws for macroscopic control volumes cannot be used for purpose of similitude analysis; rather, differential equations are necessary.

Nondimensional groups and variables are useful even in cases amenable to complete mathematical (analytical or numerical) solution since they give the predicted results maximum generality.

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Dimensional analysis using the formal Buckingham “ -Theorem" has the merit that it can be accomplished with no understanding of the fundamentals of the problem.

While dimensional analysis and similitude analysis provide useful results in the area of "pure" fluid mechanics (momentum transfer), these techniques cannot be applied to systems with simultaneous heat and/or mass transfer.

Two phenomena are said to be mathematically analogous if they are governed by identical nondimensional field equations (PDEs).

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The relative importance of any two terms in a nondimensional PDE can be determined by simply evaluating and comparing their non dimensional coefficients (parameters).

Dimensionless parameters do not have a unique physical interpretation; rather, several alternative interpretations are common and instructive.

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