


Politecnico di Torino  
Academic Year 2012/13  
01MURMK Thermalhydraulics and thermofluiddynamics 

1st degree and Bachelorlevel of the Bologna process in Energy Engineering  Torino 





Subject fundamentals
The course is in the second year of energy engineering and improves the fundamental knowledge involved in the thermalhydraulic analysis of the power and process thermal plants. Mass, energy and momentum phenomena and modelling methods are presented to extend the previous study on the heat transfer phenomena and single phase fluid flow; the analysis of the fluid flow is extended to porous media and twophase flow; the most used convective heat transfer models are discussed and also some elements of the twophase heat transfer are presented. The conduction in the solids is extended from the monodimensional case to more complex cases both in steady state and transient conditions; also the radiation heat transfer elements and the heat exchangers analysis are improved and the heat pipes are examined. The theoretical topics are presented in the lessons, with several examples; exercises lessons are devoted to the practical application of the theory. In laboratory sessions the experimental study of the single phase and twophase flow in tubes and fittings is proposed.

Expected learning outcomes
At the end of the course students will be able:
to understand the main phenomena involved in the heat transfer and fluid flow typical of the energy conversion processes and related plants; to formulate the mass, momentum and energy balances applied to solid body and flowing fluids; to apply the calculation methods and correlations in the design and analysis of systems and components operating with singlephase fluids to transfer mass and energy; to understand the main phenomena of the mass and energy transfer in components and systems operating with twophase fluids; to perform the thermalhydraulic design and analysis of the heat exchangers; to improve the calculation of the radiation heat transfer. 
Prerequisites / Assumed knowledge
Knowledge of Mathematical analysis, Physics, Thermodynamics and of the basics of heat transfer and fluid flow.

Contents
THERMALHYDRAULICS
1) Thermodynamic and transport physical properties; heat transfer laws; conservation equations; dimensional analysis and fluid mechanics Fluid flow and heat transfer mechanisms; phenomenological laws; thermodynamic and transport physical properties of gas, liquid and solid. Fluid statics: the pressure field in a static fluid; calculation of the force acting on wall and immersed body. Conservation equation of mass, energy and momentum in differential form; NavierStokes and Euler equations. Conservation equations in integral form. Application of the dimensional analysis to fluid flow and heat transfer; formulation of dimensionless groups from the differential conservation equations; physical interpretation of the dimensionless groups; similitude. Ideal fluid flow, potential flow and streamlines; Bernoulli's equation for incompressible fluid in frictionless flow. Bernoulli's equation for viscous fluids. Laminar and turbulent boundary layer; Prandtl's equations for the boundary layer along a flat wall; evaluation of the boundary layer thickness. Viscous fluid flow in conduits: velocity profile and fiction factor in laminar flow; turbulent flow in conduits, Reynolds equations, Prandtl mixing length theory; velocity profiles and friction factor in turbulent flow in conduits; pressure drops in flow across tube banks. Pressure drop in fittings. Mass transfer; Fick's law; mass transfer dimensionless numbers and the analogy with heat and momentum transfer. 2) Conduction heat transfer in solids Thermal conductivity; steadystate one dimensional conduction without heat sources; conduction with internal heat generation; extended surfaces with convective boundaries; steadystate heat conduction, examples of two dimensional analytical solutions; unsteadystate heat conduction: lumped heat capacity system; examples of analytical solution and graphical analysis. steady and unsteady conduction with numerical methods. THERMOFLUIDDYNAMICS 1) 'Fluid mechanics' Fluid flow in porous media; permeability and Darcy law. Flow in open channels. Basic elements of twophase flow: typical flow parameters; flow patterns; basic elements for the calculation of the void fraction and the pressure drop in conduits. 2) 'Heat transfer in fluids' Revision on the heat transfer mechanisms in fluids; singlephase convective heat transfer. Dimensionless groups and empirical correlations for the calculation of the heat transfer coefficient: free convection; forced convection in laminar and turbulent flow in conduit and in cross flow. Examples of theoretical models for the heat transfer calculation in laminar flow. Heat transfer in turbulent flow by means of the analogy between the heat and momentum transfer. Heat transfer in free convection and mixed convention. Basic elements on the twophase heat transfer: heat transfer phenomena and correlations in boiling and condensation. 3) 'Heat exchangers and heat pipes' Heat exchangers: a revision of the different configurations; design calculations and analysis by means of the logarithmic mean temperature difference and the NTU methods. Heat pipes: typologies and basic elements for the calculation. 4) 'Radiation heat transfer' A revision of the fundamental laws of radiation heat transfer, radiation properties of the surfaces, black body and gray body, electric analogy, radiation function, radiation heat transfer in gas and vapours. 
Delivery modes
THERMALHYDRAULICS
Experimental tests concerning pressure drops in tube and fittings, analysis of experimental data and comparison with data and theoretical prediction. Resolution of problems of fluid statics; applications of the conservation equations; dimensional analysis and similitude; ideal and viscous fluid flow in conduit and study of the circulation in adiabatic loop. Steadystate heat conduction in solids; calculation of extended surfaces, multidimensional conduction in steady state and in transient regime by means of analytical and numerical methods. THERMOFLUIDDYNAMICS Laboratory: Visualization of the flow patterns and void fraction measurement in airwater twophase flow. Exercises: Calculation of the flow in open channels; calculation of the void fraction and pressure drop by means of the homogeneous model. Calculation of the heat transfer coefficient in laminar and turbulent flow in conduits and in cross flow; calculation in free and mixed convection. Heat exchangers and heat pipes calculations. Radiation heat transfer between gray bodies in presence of non absorbent and absorbent media. 
Texts, readings, handouts and other learning resources
Notes for the lessons of heat transfer and fluid flow (C. Bertani, B. Panella, M.Malandrone).
J.P. Holman, Heat Transfer, 1986. J.D. Parker, J.H. Boggs, E.F. Blic, Introduction to fluid mechanics and heat transfer, 1969. F.H. White, Fluid mechanics, 1986. P.B. Whalley, 'Boiling, Condensation and Gasliquid Flow', Clarendon, Oxford, 1986. 
Assessment and grading criteria
The evaluation will be made by means of a single written examination on both parts of the course; the examination will contain numerical exercises to be solved and open questions on theory topics; also the reports of the laboratory sessions will be evaluated. People with a mark >= 27/30 from the written exam may, optionally, go also through an oral examination.

