617-3022/01 – Transport Phenomena (PJ)
| Gurantor department | Department of Chemistry | Credits | 6 |
| Subject guarantor | prof. Ing. Marek Večeř, Ph.D. | Subject version guarantor | prof. Ing. Marek Večeř, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FMT | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
Student:
- get the essence of unsteady processes and relations between them and structure of matter.
- knows derivation principles of transport equation and is able to apply it to the simple case problems.
- is able to explore possibilities of solutions of differential equations
- is able to formulate problem for possible numerical solution
- is able to choose substantial parameters with practical application form characterization of velocity field, temperature field and concentration field.
Teaching methods
Lectures
Tutorials
Summary
Viscosity heat conductivity and diffusivity in continuum. Relation of transport coefficients to the structure of matter. Application of balance equations for momentum, mass and heat transfer. Steady and unsteady processes. Application of simple problem solutions to the 3D space. Boundary and initial conditions for transport processes. Relation between exact and empirical solutions, engineering applications.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Written and oral exam.
E-learning
Other requirements
Passing of two tests with score higher than 50%.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
Lecture topics
1. Continuum. Nature as continuum environment. Applicability of mathematic analysis and differential calculus for process description. Transport of properties. Transport by static molecular movement. Momentum, heat, matter. Similitudes of processes. System definition: simple system between two parallel plates. Driving force, flow density, factor of proportionality. Viscosity, Heat conductivity and Diffusivity. Newton’s viscosity law, Fourier’s law, Fick law.
2. Conductive heat transfer in stationary body. Heat, heat flux, differential balance of heat. Specific heat capacity. Application of Fourier’s law, expression of differential heat balance in the terms of temperatures. Vector form of heat balance. Boundary conditions in context of reality.
3. One dimensional heat transfer. Solution in heat flux densities and temperatures. Cartesian, cylindrical and spherical coordinates. Boundary conditions, overestimation. Solution of heat transfer for two independent variables. Unsteady heat transfer to the semi-infinite space. Solution by separation of variables. Dimensional analysis. Term of infinity, unsteady heat transfer to the finite slab. Two dimensional steady state heat transfer, three dimensional steady state heat transfer. Laplace equation and its solution. Principles of method finite differenced. Relaxation method and principles of solution stability. Monte Carlo methods and commercial solvers.
4. Mechanical equilibrium in fluids. Stress tensor. Sign convention, Stress tensor symmetry. Pressure. Shear stress. Simple shear flow. Tensor formulation. Kinematic tensor. Shear rate. General definition of viscosity. Mass balance in differential volume – continuity equation.
5. Momentum balance. Volume forces, surface forces. Equation of motion. Solution of equation of motion. Evaluation of inertia and viscous forces, Reynold’s number. Boundary conditions. Velocity on the interphase, no slip boundary condition. Creep flow equation. Viscometric flows. Simple flow configurations soluble by ordinary differential equations. Application to the viscosity measurements. Flow symmetry. Two dimensional creep flows. Stoke’s law, Stoke’s paradox.
6. Ideal liquid. Euler equation, Bernoulli equation. Applicability. Stream function. Analogy with heat transfer. Space distribution. Boundary layer theory. Friction factor. Solution by integral balance. Flow past immersed bodies – hydrodynamic boundary layer. Relation to the Reynolds number.
7. Prandtl’s equation of hydrodynamic boundary layer. Flow past immersed slab. Solution by similarity. Approximate solution of momentum balance. Hydrodynamic and aerodynamic applications. Aerodynamic tunnel measurements. Measurements of local properties, velocity, pressure, and shear stress. Particle Image Velocimetry PIV. Laser-Doppler anemometry. Flowmeters.
8. Flow past immersed body. Critical point. Pressure distribution. Hydrodynamic boundary layer separation point. Wake. Vortex street. Flow past immersed body and particle of low viscous liquid. Surface and interface tension. Curved interface. Drops and bubbles. Interface stability. Breakup and coalescence. Surface viscosity.
9. Turbulence. Average velocity. Turbulent velocity profile. Fluctuation. Isotropic turbulence. Turbulent viscosity and diffusivity. Static approach. Radiation. Principles and differences from conductive heat transfer. Reflection, Emission, Absorbance. Thermal screen, barrier, greenhouse effect.
10. Convective heat transfer. Heat transfer equation in moving liquid. Possible solutions. Plug flow. Negligibility of longitudinal conduction. Linear velocity profile. Heat transfer with laminar flows in pipes. Nusselt number. Péclet number. Heat transfer during flow past immersed slab. Comparison of hydrodynamic and thermal boundary layers. Concept of film and penetration theory.
11. Film condensation on vertical plate. Condensate layer. Heat transfer coefficient during condensation. Boiling nearby wall. Effect of surface tension, hydrostatic pressure, heat conduction and heat convection. Conditions for bubble and film boiling.
12. Methods for measurement of temperatures and thermal flows. Principles of flow field description by the transport processes. Hot wire. Electro-diffusional diagnostics.
13. Diffusion. Fick’s law. One component and multicomponent diffusion. Molecular models for diffusion in gases liquids and solids. Measurements of diffusivity. Typical boundary conditions for mass transfer problems. Interface equilibrium. Floating boundary conditions.
14. Concurrent heat and mass transfer. Wet bulb thermometer. Heat tube. Thermo-diffusion. Pressure transport. Dynamics of compressed gases, pressure waves.
Practical tutorials:
1.) Introduction to programing in Matlab. Scalars, vectors: creations by operators. Matrix, element access, new values for selected elements. Special types of matrix. Linear algebra. Solving system of sets of linear equations. Logical operations. Code programing, functions, If-else, switch-case, loop, for, while, break and continue in loops, 2D a 3D plots, Numerical methods for solving differential and integral equations.
2.) Stationary heat conduction. Heat conduction by multicomponent planar wall. 1st order boundary condition. Insulation thickness calculation. Heat conduction by multicomponent cylindrical wall with 3rd order boundary condition. Heat conduction in cylinder with electrical source of heat. Solving problems of heat conduction by shell energy balance.
3. Unsteady convective heat transfer. Heating of solid body (various geometry) in contact temperature field. Biot number, external and internal heat resistance. Heat conduction in bodies with negligible internal heat resistance, heating of semi-infinite slab – method of combination variables. Heat conduction at concurrent effect of internal and external heat resistance, temperature distribution in the finite slab – method of separation variables, boundary conditions of 2nd and 3rd order. Dimensionless time, temperature and position. Fourier number, application in to engineering correlations of dimensionless quantities T* = f(x*, Fo, Bi).
4.) Momentum balance. Body forces, surface forces. Equation of motion. Viscosity and mechanism of momentum transfer, Newton’s law of viscosity. Velocity distribution during laminar flow. Shell balance of momentum. Newtonian and non-Newtonian liquid, flow curves. Methods for flow curves measurements. Types of viscometers and theory of its application.
5.) Ideal liquid. Euler’s equation. Bernoulli equation. Real liquid. Application of eq. to the common problems of hydrodynamics. Hydrostatics, pressures in liquids and gases.
6.) Flow of falling liquid film by inclined solid surface. Flow by circular tube. Momentum balance for isothermal systems, equation of continuity and equation of motion. Stationary flow analysis by balance equations. Tangential flows of Newtonian liquid between two coaxial cylinders. Shape of liquid level rotating in cylindrical vessel.
7.) Test I
8.) Creeping flow past immersed solid sphere. Stoke’s law. Viscosity determination from speed of falling sphere. Friction factor as a function of Reynolds number. Determination of radius of falling sphere in liquids, rising spherical particles from melts. Resistance of bodies to the flow, drag coefficient. Flows in tubes, pressure drop calculations.
9.) Hydrodynamic boundary layer. Integral balance of hydrodynamic boundary layer. Laminar flow past plane with assumption of approximation linear velocity distribution, 2nd and 3rd order polynomial velocity distribution. Dimensionless expression of boundary layer thickness, normal stress, drag coefficient as a function of Reynolds number.
10.) Thermal boundary layer. Convective heat transfer during flow past immersed planar slab. Thickness of thermal boundary layer. Prandtl number. Relation between hydrodynamic and thermal boundary layers. Nusselt number, derivation by Prandtl and Reynolds number.
11.) Natural and forced heat convection. Grashof number. Determination of heat transfer coefficient for cooling of glass sheet, for heat transport during forced and natural cooling of aluminum plate, for heating of steel rod in heating bath. Condensation. Heat transfer coefficients for condensation of pure components on solid surface. Condensation of steam on vertical solid surface.
12.) Diffusivity of components in binary mixtures. Collision integral, method for assumption diffusivity for multicomponent mixtures and non-ideal conditions. Diffusion in dilute and concentrate systems.
13.) One dimensional diffusion of component A in stationary component B. Preparation of well-defined mixture of hydrocarbon saturated vapors and air. Pseudo stationary one dimensional diffusion, determination of mass transfer coefficient for diffusion of water saturated vapor in to the air. Evaporation, solution, and sublimation of spherical particles. Concurrent heat and mass transfer, Sherwood number, Lewis number, temperature of wet bulb thermometer.
14.) Test II
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction