Applied Engineering Math, Physics and Chemistry for Fluid Dynamics, Heat and Mass Transfer Modeling
Live-Supervised Online Course, April 02 to May 21, Tuesdays and Thursdays, 18:00-19:30 Berlin Time, Registration Deadline: March 30 (can be closed earlier by reaching to course capacity 20 students, for Early Registration Discount March 20).
This is a new course for all students and engineers who want to rebuild own Math and Physics foundation, starting from High School level and upgrade it towards the University level for Fluid Dynamics Engineering, Heat and Mass Transport Phenomena, and Material & Energy Process Modeling for different applications in mechanical and process engineering, petrochemical, aerospace, civil, biotechnology, biomedical, food and pharmaceutical, environmental technologies, etc. Novel modeling approach presented in this course can empower you for interdisciplinary projects and technology developments.
Introduction to the Course:
The entire world, all natural phenomena and industrial processes are governed by material and energy conservation laws, and can be described as movement of the particles in 3D space via certain energy exchange. The material particles can be defined as the form of atoms & molecules, nano-micro particles, colloids or interconnected differential small elements of the bulk of gas, liquid or solid. Therefore, all knowledge that we are looking for in many research works, engineering and industrial projects, can be considered as two main following categories:
1-The distribution of the material particles (mass) in 3D space at a time reference, and the related properties at each location (Velocity, Temperature, Pressure, Concentration, etc)? This is indeed the initial conditions or steady state equilibrium conditions of the process.
2- And how the material particles move and their properties changes within the time?
For the first category, we need to define material forms (atoms, molecules, nano-micro particles, bulk elements) and properties (U, T, P, C, etc) and related unites (kg, s, m, kg/m3, m/s, N, centigrade, pascal, joule, etc) and develop certain characteristic parameters, indicators, calculations and measuring tools.
And for the 2nd category, we need certain model and equations that describe material particle movements and properties evolutions. The most important model and equation for this purpose is Newton 2nd Law F=m*a which is indeed part of the energy conservation (kinetics energy), within the framework of the mass and energy conservation.
Teaching Approach
Via this course, you can learn essential math and physics, material & energy balance, and practice momentum shell balance, step-by-step towards derivation of the Navier Stokes Equations which are the most important key formulations describing all natural phenomena and industrial processes.
Essential chemical concepts, parameters and units for calculations of molecular based material and solution properties required for transport phenomena of the mixed systems, and reactive flows also will be discussed.
First you will learn, how you can start from a practical natural phenomena, industrial unit or engineering problem, describe it as a physical system with a certain body and boundary, thermodynamic state and transport mechanisms that governs properties distribution in the body of system. Then we develop the mathematical formulations of mass and energy conservation for the lumped and distributed systems for steady and transient (time dependent) conditions, including transport mechanisms and related partial differential equations.
Next step will be modeling and analytical solutions for selected examples in material and energy process, fluid dynamics, heat and mass transfer, mechanical and thermal engineering, unit operation technologies, petrochemical processes, biomedical and drug delivery systems, and environmental technology.
As for most of the practical cases, analytical solutions can be challenging or impossible, Computational Fluid Dynamics (CFD) approach will be introduce for selected examples and general form of the Navier Stokes transport equations. Classification of the partial differential equations will be discussed physically and mathematically for understanding discretization methods in CFD, applied numerical methods and stability analysis for basic CFD Code Programming and simulations by CFD Software.
By completing this course, you will be able to apply the required math, physics and chemical formulations for the related research works, engineering projects and industrial units modeling and simulations.
Course Content and Lectures:
1-Mathematics Language to Describe Physics of the World, Nature and Industry:
-The key roles of “Analytical Geometry” in science and technology development
-Initial distribution of the materials and properties in 3 D space
-Dynamics of movements and properties evolutions by time
-Lagrangian and Eulerian Motion Approaches
-Physical and mathematical concept of the Conservation Law: General logical form vs physical specific engineering form
– Physical concept and mathematical formulations of a typical engineering modeling: System, boundary, volume, surface, density, material and energy properties, input, output, mass and energy flux, flow rate, accumulation, etc.
2-Material Forms and Properties: Molecules, nano-micro particles and fluid-solid bulk
-Material quantifications, characterizations, measurements and calculations, basic factors and units
– Molecular weight, density, concentration, pressure, temperature, viscosity, heat capacity, etc, for pure systems, solutions and mixtures.
-Mass conservation for pure and multi-component systems without and with chemical reactions (continuity equation)
-Energy conservation for multi-energy types systems
3-Diffusion Transport Mechanism: Physical concept and mathematical formulation
-Brownian Motion
-Newton’s law of viscosity (stress–strain rate), viscosity meaning
-Fourier’s law (heat conduction), thermal conductivity
-Fick’s law (diffusion), diffusivity
-Typical examples of diffusion transport of mass, momentum and heat in nature and industry
4-Convection Transport Mechanism:
-Physical concept and mathematical formulations
-Convection mechanism concept: Correct formulation?
-Examples in fluid dynamics, heat and mass transfer in nature and industrial unit operations.
5- Mathematical Formulation of Conservation Laws: Material and Energy balance system and subsystems
-Control Volume Integral form vs. Differential Element Analysis
-Gauss’ Theorem converting integral on control volume into the net of exchange across the boundary of the system
-Transport Phenomena Equations
6- Boundary Conditions
-Logical and physical concepts of the boundary conditions for engineering process modeling
-Mathematical concepts of the boundary conditions for solving differential equations
7- Ordinary Differential Equations (ODEs) in Transport Phenomena
-First-order linear ODEs (integrating factor), separable ODEs
-Second-order linear ODEs (constant coefficients)
-Typical engineering examples: Lumped heat transfer, shell and tube heat exchangers, 1D Fluid flow velocity profiles (Hagen–Poiseuille equation in tubes, Couette Flow between two plates).
8- Partial Differential Equations (PDEs) in Transport Phenomena
-Why PDEs are important in Life Science and Engineering
-Gradient of Gradient: Dynamics form of conservation laws
-1D unsteady diffusion examples in fluid dynamics, thermal engineering and mass transfer operations
-2D and 3D steady state diffusion examples in Heat and mass transfer
9-Navier Stokes Equations
-Momentum shell balance:
– iso-velocity concept as the heart of fluid dynamics modeling
-Thin liquid films and fluid flow in tube engineering modeling examples
-Full Navier-Stokes Equations, physical concepts and mathematical formulations in cartezian, cylindrical and spherical coordinates
10- Combination and Separation Variables Techniques for Solving PDEs
-2D Steady Heat Conduction
-1D Unsteady Diffusion Problems
-Laminar flow CVD Reactors (Chemical vapor deposition)
11- Boundary Layer concept and modeling
-Viscose flow boundary layer
-Developing region in fluid dynamics
-Heat and mass transfer boundary layers
12-Dimensional Analysis and Similarity:
-Why the size matters?
-Characteristic scales
-Scale-Up: From the Lab and Pilot Scales towards Industrial Scales
-Key dimensionless groups: Reynolds, Froude, Prandtl, Schmidt, Peclet, Grashof, Nussel, Sherwood, Schmidt, etc
13- Canonical analytical solutions in fluid mechanics
-Hydrostatics: pressure variation, manometers
-Fully developed laminar pipe flow (Hagen–Poiseuille)
-Plane Poiseuille/Couette flow (between plates)
-Shear stress and velocity profiles; connection to pressure drop
14- Canonical analytical solutions in heat and mass transfer
-1D steady conduction (plane wall/cylinder) with/without generation
-Lumped capacitance (Biot number meaning)
-1D transient diffusion basics (concept + one classic solution form)
15- Introduction to Computational Fluid Dynamics (CFD) Simulations
-Basic CFD Concepts
-From physical domain to computational domain: Transport Equations in CFD
-Computational cells as differential elements subsystems
-Finite Difference vs Finite Volume: Mathematical and physical approaches
-Discretization Methods
-CFD methods stability analysis and CFL Conditions
-Boundary conditions in CFD, verification vs validation
-Workflow: geometry → mesh → physics → solver → post processing
Registration Form
Related Article:
Science in Simple Words: What is Where? Why is There? and When Moves Where?
This is the main scientific approach for understanding position, properties and movement of everything to explore nature, model industrial process, and develop technology (as I discussed in other means recently: https://lnkd.in/eNvnrBg4).
1-What is Where? = Initial Conditions, positions and properties of everything at t=0 for a system, which can be a small particle, a droplet, human body, industrial unit or entire Earth Planet.
2- Why is There? = Distribution Mechanism of mass and energy in a system
This is governed by “Boundary Conditions + Transport Phenomena Mechanisms (Diffusion, Convection and Radiation)” within input and output terms of “Mass & Energy Conservation Law”:
Input – Output + Generation -Consumption = Accumulation
3- When Moves Where? = How everything moves towards certain direction with which velocity and acceleration?
The answerer is: Newton 2nd Law “F=m*a” by which we could understand the principle of the world structure and movements, distribution of the planets, stars, moving an apple, particles, droplets, cars or airplanes, etc.
However Newton 2nd law is applicable on a solid body, under net of forces “F” applied on its external surfaces in certain direction.
4- Navier Stokes Equations:
To use Newton 2nd laws for everything, we should divide our system, to small subsystems, which can be either small solid particles, or small elements of fluids (gas/liquid) that moves together, having isovelocity, which can be assumed solid-like body, and then considering all different forces (1-body force gravity, electric or magnetic fields, 2-pressure, 3-friction/viscos 4-momentum) applied on the external surface of each element which has interaction with other surrounding elements via friction/momentum/pressure exchange. This resulting Navier-Stokes Equations which is applicable for modeling all natural phenomena and industrial, medical, biological and environmental processes (https://lnkd.in/eGxXSUt2).
5- Links to Thermodynamics, Fluid Dynamics, Heat and Mass Transport Phenomena Sciences?
Thermodynamics law 1 is indeed energy conservation. 2nd Thermodynamic law describes heat-work conversion, which links microscopic-macroscopic movements. Fluid dynamics, heat and mass transfer also mostly explain particular laws such as “Newton Viscosity Law”, “Fourier Heat Conduction Law” and “Fick Diffusion Law”, needed for input-output mechanisms.
Newton 2nd law is indeed, conservation of macroscopic mechanical energy (momentum).
Therefore all of these sciences try to describe: What is Where? Why is There? and When Moves Where?
Relater Contents: WAC Transport Phenomena Academy https://lnkd.in/ePErpz8R
#Universemodeling #Newtonlaw #Thermodynamics #TransportPhenomena #ProcessEngineering #MechanicalEngineering #Modeling #FluidDynamics #HeatTransfer #CFD #Energy #ScienceEducation #CivilEngineering #PetroleumEngineering #BiomedicalEngineering
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