Damped Wave Transport and Relaxation
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Table of contents
- Cover
- Table of Contentsxiii
- Prefacevii
- Acknowledgementsxi
- About the Authorxii
- 1. The Damped Wave Conduction and Relaxation Equation1
- Origin2
- Wave Dominant and Fourier Regimes6
- Worked Example 1.1 - Temperature Variation of Thermal Conductivity8
- Worked Example 1.2- Wave and Fourier Regimes during Convection, Conduction and Relaxation9
- Boundary Layer in Time and Scaling of the Governing Equation10
- Poor Convergence of Fourier Series11
- Light Speed Barrier and Finite Speed of Heat Propagation15
- Hyperbolic, Parabolic and Elliptic PDE16
- Non-Fourier Equations for Heat Conduction17
- Third Order PDE to describe Non-Fourier Heat Conduction29
- Finite Speed Conduction, Diffusion and Momentum Transfer32
- Experimental Measurement of Relaxation Times33
- Case of Infinite Relaxation Time and D'Alambert's Solution35
- Summary36
- Exercises38
- 2. Transient Heat Conduction and Relaxation46
- The Ballistic Term48
- Semi-Infinite Medium Subject to Constant Wall Temperature49
- Relativistic Transformation of Coordinates49
- Regimes of Heat Flux at a Interior Point inside the Medium52
- Approximate Solution54
- Extension to 3-Dimensions57
- Worked Example 2.1- Can c in w=c I 0 (sqrt(tau^2 - X^2))/ 2) be a function of time ?58
- Worked Example 2.2 - Verification of w = c I (sqrt(tau^2 - X^2))/ 2) as solution59
- Worked Example 2.3 - Verification of w = cSin(κX - ωτ) + dCos(κX - ωtau) is a solution to Hyper60
- Worked Example 2.4 - Transformation, η = sqrt(tau^2 - X^2), to convert hyperbolic PDE into Bessel e61
- Worked Example 2.5 - Examine g in g(tau) I 0(tau/2) = exp(tau/2)62
- Worked Example 2.6 - Method of Laplace Transform Solution to Hyperbolic PDE Without the Damping Term63
- Relativistic Transformation of Cylindrical Coordinates in Infinite Medium64
- Worked Example 2.7-Governing Equation of Heat flux in Cylindrical Coordinates67
- Relativistic Transformation of Spherical Coordinates in a Infinite Medium69
- Worked Example 2.8 - Transient Temperature in a Semi-infinite Cone at Constant Apex Temperature73
- Worked Example 2.9 - Governing Equation of Heat flux in Spherical C75
- Finite Slab at Constant Wall Temperature76
- On the Use of Storage Coefficient81
- Hyperbolic PDE as Governing Equation81
- Parabolic PDE as Governing Equation83
- The Dual Phase Lag Model84
- Transient Temperature in a Sphere at CWT88
- Pulse Injection in an Infinite Medium90
- Temperature Overshoot92
- Convective Boundary Condition93
- Plane of Null Transfer95
- Temperature Dependent Heat Source98
- Critical Point of Zero Transfer101
- Worked Example 2.10 - Convective Heating in a Rod105
- Method of Laplace Transforms107
- Problem of Semi-infinite Medium in Cartesian Coordinates given a Step Change in Temperature at one o109
- Constant Wall Flux in a Semi-infinite Medium111
- Worked Example 2.11 - Transient Heat Conduction and Relaxation in a Ice Cube with Phase Change112
- Convective Heating in a Semi-infinite Medium114
- Average Temperature in a Finite Slab with Convective Boundary Condition117
- Worked Example 2.12 - Generalized Fourier Expression with up to the Second Derivative in Heat Flux a121
- Parabolic Solution123
- Worked Example 2.13 - Dual Phase Lag Model and Temperature in a Finite Slab124
- Worked Example 2.14 - Magnesium Oxychloride Sorrel Cement Coating and Subcritical Damped Oscillation127
- Summary130
- Exercises133
- 3. Transient Mass Diffusion and Relaxation146
- Introduction147
- Worked Example 3.1 - Depletion of Molecules at the Surface and non-Fick Equation152
- Finite Speed Diffusion with Fast Chemical Reaction in a Semi-Infinite Catalyst154
- Worked Example 3.2 - Spatiotemporal Concentration when k* = 1159
- Worked Example 3.3 - Solution of Spatiotemporal Concentration by Method of Laplace Transforms159
- Worked Example 3.4 - Mass Diffusion and Relaxation and Simultaneous Zeroth Order Chemical Reaction160
- Finite Speed Diffusion with Fast Chemical Reaction in Infinite Catalyst in Cylindrical Coordinates162
- Finite Speed Diffusion with Fast Chemical Reaction in Infinite Catalyst in Spherical Coordinates167
- Finite Slab at Constant Wall Concentration173
- Finite Cylinder at Constant Wall Concentration175
- Finite Sphere with Constant Wall Concentration177
- Critical Radii of Nuclear Fuel Rod Neither Less than the Cycling Limit Nor Greater than the Shape Li179
- Zone of Zero Transfer in a Ziegler Natta Polymerization Catalyst183
- Worked Example 3.5 - Zone of Zero Transfer in a Zeigler Natta Catalyst when the Bulk Reaction Rate i186
- Worked Example 3.6 - Mass Diffusion and Relaxation from a Dissolving Drop189
- Worked Example 3.7 - Method of Laplace Transform Solution in a Finite Slab During Simultaneous Diffu191
- Worked Example 3.8 - Spatiotemporal Concentration from a Perfume Container at the Shopping Mall in S193
- Worked Example 3.9 - Spatiotemporal Concentration from a Perfume Container at the Shopping Mall in S195
- Worked Example 3.10 - Diffusion and Relaxation from a Dissolving Pill in Spherical Coordinates in 1197
- Worked Example 3.11 - Chemisorption of Organic Sulfides in Automobile Gasoline onto Palladium200
- Worked Example 3.12 - Diffusion and Relaxation from a Dissolving Pill in Spherical Coordinates in 3201
- Diffusion, Relaxation and Convection204
- Worked Example 3.13206
- Worked Example 3.14211
- Summary214
- Exercises217
- 4. Transient Momentum Transfer and Relaxation222
- 34 Different Flow Types224
- Damped Wave Momentum Transfer and Relaxation227
- Worked Example 4.1 - Emptying of a Filled Pipe using the Extended Euler Equation232
- Worked Example 4.2 - Emptying of a Filled Pipe with Multiple Ports234
- Flow Near a Horizontal Wall Suddenly Set in Motion236
- Worked Example 4.3 - General Substitution =Z+ (1 - )^(1/2) to Transform Hyperbolic PDE to Parabolic242
- Worked Example 4.4 - Emptying of a Filled Pipe using the Extended Euler Equation with Porous Packing244
- Worked Example 4.5 - Emptying of a Filled Pipe using the Extended Euler Equation with Porous Packing245
- Shear Flow Between Two Plates Moving in Opposite Direction at Constant Velocity with Separation Dist247
- Worked Example 4.6 - Shear Flow Between Two Vertical Plates Moving In Opposite Direction at Constant252
- Transient Laminar Flow in a Circular Conduit255
- Worked Example 4.7 - Oscillations in a U Tube Manometer from the Extended Euler Equation including t259
- Flow of Blood in Capillaries260
- Tangential Flow Induced by a Rotating Cylinder265
- Worked Example 4.8 - Tangential Flow Induced by a Rotating Cylinder at Short Distances268
- Worked Example 4.9 - Tangential Flow Induced by a Rotating Cylinder from Shell Balance270
- Transient Flow Past a Sphere272
- Worked Example 4.10 - Radial Flow between Two Concentric Spheres274
- Worked Example 4.11 - Room Cooled by a Ceiling Fan277
- Worked Example 4.12 - Outward Radial Squeeze Flow between Two Circular Disks281
- Worked Example 4.13 - Conversion of Hyperbolic PDE into a PDE with Similarity Transformation Variabl284
- Worked Example 4.14 - Response to a Oscillating Pressure Gradient in a Circular Tube286
- Friction Factors290
- Summary293
- Exercises295
- 5. Applications304
- Convective and Conductive Contributions in Circulating Fluidized Bed Heat Transfer307
- CPU Overheating and the Storage Coefficient313
- Cosinuous Concentration Profile during Scale-up of Grafting in Helical Ribbon Agitated CSTR315
- Thermal Barrier Coating318
- Asymptotic Analysis of Governing Equation320
- Average Temperature (UL 1709 Test)322
- Exact Solution323
- Infinite Order PDE and Solution by Method of Laplace Transforms325
- Maxwellian Basis for Secondary Pressure Fluctuations in Gas-Solid Bubbling Fine Particle Fluidized B329
- Delivery of Drugs and Finite Speed Diffusion334
- Response to a Pulse in Mass Flux335
- Cylindrical Coordinates337
- Spherical Coordinates340
- Solute Binding and Elimination345
- Worked Example 5.7.1 - Effective Diffusivity and Binding Constant348
- Maternal Effect Genes352
- Drug Penetration in the Tissue353
- Neurotransmission across the Synaptic Cleft354
- Enzymatic Reactions355
- Transdermal Delivery Systems359
- Diffusion Through Cylindrical Membranes364
- Matrix Delivery System367
- Krogh Tissue Cylinder370
- Worked Example 5.7.2 - Anaroxic Regions in Cartesian Coordinates372
- Summary374
- Exercises376
- Sources, References and Further Reading386
- Appendix A413
- Appendix B420
- Appendix C424
- Answers to Exercises431
- Subject Index435
Transient problems in transport phenomena have a variety of applications, ranging from drug delivery systems in chemotherapy in bioengineering to heat transfer to surfaces in fluidized bed combustion (FBC) boilers in mechanical engineering. However, the attention given to transient problems is disproportionate with its occurrence in the industry. Damped Wave Transport and Relaxation looks at transient problems in heat, mass and momentum transfer: including non-Fourier effects of conduction and relaxation; non-Fick effects of mass diffusion and relaxation; and non-Newtonian effects of viscous momentum transfer and relaxation. The author also reviews applications to current problems of interest and uses worked examples and illustrations to describe the manifestations of using generalized transport equations. This book is intended for graduate students in transport phenomena and is an ideal reference source for industrial engineers.
* Provides a connection with molecular phenomena
* Separate sections are devoted to heat, mass and momentum transfer
* Includes exercises and examples of applications
* Provides a connection with molecular phenomena
* Separate sections are devoted to heat, mass and momentum transfer
* Includes exercises and examples of applications