Fundamentals of transport phenomena balances in homogeneous fluids. The Cauchy and the Navier-Stokes equations. Rheological constitutive equations. Momentum transport in turbulent flows. Mechanical energy equation. The Fourier-Kirchhoff equation. Conduction heat transfer. Forced and natural convection heat transfer. Multicomponent systems. Mass transfer by molecular diffusion, convection.

+ Course introduction. Physical quantities used for description of flow fluid, and heat transfer and their categorization - scalar, vector, tensor. Fundamentals of Cartesian tensor calculus.
+ Fundamental balance equation, i.e. GBE (General Balance Equation) of physical property, accumulation, convection, other mechanism (molecular transport), source/sink, flux, material derivative, conservative and non-conservative form.
+ Fluid flow and continuity equation, momentum balance equation, and angular momentum balance equation. Convective momentum flux vs total stress (tensor), isotropic pressure, and dynamic stress tensor. Cauchy motion equation. Integral balance equations - continuity, momentum, and angular momentum.
+ Kinematics of fluid flow (the rate of deformation tensor and the vorticity tensor). Newtonian fluid and Newton's law for fluid, dynamic viscosity.
+ The Navier-Stokes equation. Basic inspection analysis of the Navier-Stokes equation (limiting cases). Engineering Bernoulli equation.
+ Analytical solution of basic task (one/two dimensional) for basic simple geometries of laminar Newtonian flow. Viscometry, rheology, flow curve/rheogram.
+ Rheological constitutive equations. Non-Newtonian models in comparison with Newtonian model, i.e. GNF model (Generalized Newtonian Fluid model), and apparent viscosity description. Rheological models of pure viscous non-Newtonian time independent liquids (Bingham plastic, power-law). Analytical solution of flow of non-Newtonian liquid in simple selected geometry/ies.
+ Turbulent flow (introduction). Navier-Stokes equation and turbulent flow. Viscous/inertial forces, stability, deterministic chaos, time dependent flow, three dimensional, existence of eddies. Eddy/energy cascade. Kolmogorov scale, Re^{3/4}. RANS (Reynolds Averaged Navier Stokes), instantaneous velocity, time averaged value, continuity and Navier-Stokes equation, Reynolds stress tensor, Boussinesq hypothesis, eddy viscosity, kinetic energy of turbulent eddies k, rate of dissipation of the kinetic energy.
+ Mechanical energy balance. Internal energy balance, enthalpy balance and heat transfer. Fourier's law of heat conduction. Fourier-Kirchhoff's equation. Initial and boundary conditions.
+ Steady-state heat conduction. Thermal resistance. Overall heat transfer coefficient.
+ Heat conduction with internal sources or sinks.
+ Unsteady heat conduction in solids in 1D (infinite slab, cylinder, sphere), and more dimensions, based on inspection analysis and Fourier method of separation variables.
+ Forced and natural convection. Inspection analysis of Fourier-Kirchhoff equation. Momentum and heat transfer analogy.
+ Fundamental concepts and equations of mass transfer. Analogy between momentum, heat and mass transfer. Fick's law. Molecular mass transfer. Unsteady mass transfer. Convective mass transfer. Interphase mass transfer.

Practicing theoretical knowledge related to the lecture material, i.e. analytical solutions to flow, heat and mass transfer cases in simple geometries. Small experiments and demonstrations.

Study materials are available in IS Moodle CTU at https://moodle-vyuka.cvut.cz/course/view.php?id=9457&section=0.