Heat Transfer and Applications

Learning Outcomes

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Identify and advise the dominant heat transfer mode and qualitative estimation of its importance.
• Be able to appreciate and discuss with specialists the best heat transfer solutions.
• Be able to independently assess the relevance and impact of heat transfer process in a given engineering application/context.

Learning Outcomes

Having successfully completed this module you will be able to:

• C1/M1 Formulation and solution of fundamental problems of heat transfer using ODE and PDE are core to the teaching of the module. The underlying physics principles of energy conservation, thermodynamics, and fluid mechanics are used throughout the module for conceptual understanding and qualitative analysis/estimate of heat transfer problems. With the module content building up progressively, the complexity and the realism of problem solving also develops to include combinations of theories. The module is constantly updated to provide the state of art and evolving applications of heat transfer at cutting edge engineering, such as cooling of microelectronic components at increasing power density, the heat transfer at extreme temperatures in space and cryogenic conditions, and complex heat exchanger systems in nuclear and chemical engineering. C3/M3 Modelling and optimisation of CPU heat sink using Comsol is aimed at extending 1d analytical results to 3d problems using computational methods. The labs and related coursework provide hands-on practices for selecting appropriate model geometry/symmetry, implementing suitable meshing for accuracy and speed, the interpretation of results with emphasis on the improvements from 1d analytic calculations. C12/M12 4 computer labs for heat conduction modelling techniques and a coursework (30% overall mark) of a complex yet relatable real-life problem

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Outline engineering design for heat transfer applications
• Use the appropriate method (conceptual, analytical and numerical) to obtain the solution for a given heat transfer problem.
• Evaluate and critically assess the heat transfer analysis presented.
• Abstract and formulate the heat transfer analysis for a given engineering problem by applying the appropriate equations and/or correlations

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• The use commercial software for heat transfer analysis.
• The relevant thermal properties of materials and working fluids and the considerations for material selection according application requirements
• The mathematical underpinning of heat transfer analysis and corresponding problem solving techniques.
• The mechanisms for different heat transfer modes and their relevance to a wide range of mechanical engineering themes
• The engineering practices for enhancing heat transfer or increasing thermal insulation.

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Work as heat transfer and thermal analysis specialist as part of design teams.

This module consists of two organically integrated components: (a) a comprehensive and rigorous treatise of heat conduction, convection and radiation, the three basic modes of heat transfers; and (b) modern engineering applications of heat transfer.

Part I: Fundamentals

1.1 Introduction:

1.2 Heat conduction:

a. Simple 1d steady state: from Fourier’s law to differential equation, infinite slab and other 1d geometries (thin wire/rod, cylinder and sphere), boundary conditions and boundary value problems, nonlinear conduction and composite materials, equivalent circuits, thermal resistances including convection boundary condition, critical radius of cooling/heating;

b. Heat diffusion equation and applications: derivation, introduction to 3d and transient conduction, longitudinal and radial conduction with heat generation, extended surface and fin optimisation;

c. Transient heat conduction: qualitative behaviour and the influence (Biot number) of boundary conditions and material properties, lumped heat capacity analysis (characteristic length, criterion, time constant of cooling), analytical solution of transient heat conduction by separation of variables for general temporal solution (thermal diffusivity, Fourier number and time constant of diffusion) and specific spatial solution in 1d slab with mixed boundary conditions), extension to cylinder and sphere and approximate forms (Heisler’s charts and one-term solutions);

d. Numerical solutions: finite difference schemes for transient 1d and steady state 2d with implementation in Matlab, problem solving in Ansys.

1.3 Convection

a. Concept of boundary layer and flow over flat plate: similarity (Prandtl number) between hydraulic (part II fluid) and thermal boundary layers, Reynolds’ integration, temperature profile and heat transfer coefficient, boundary layer development over flat plate and Nusselt number correlations;

b. External flows: differences streamlined and bluff bodies, heat transfer by flow across a cylinder and sphere, correlations for various geometries and configurations;

c. Internal flow: fully developed laminar flow in a circular pipe (temperature profile, definition/calculation of bulk average temperature, heat transfer coefficient and pressure drop, Nusselt correlations), non-circular pipes and enhancement of heat transfer by narrow channels, boundary conditions (uniform heat flux or constant temperature on the tube wall), turbulent flow, entry zone;

d. Free convection: driving force and Grashof/Raleigh number, boundary layer of free convection, correlations;

e. Condensation and boiling: laminar condensation film, pool boiling characteristics (convection, nuclear and film boiling).

1.4 Radiation

a. Blackbody radiation: general characteristics (Wien’s displacement law) and Stephan-Boltzmann law;

b. Heat exchange between two bodies at different temperature: thermal equilibrium of a radiation body (radiation, reflection, transmission), solid angles and viewing factor.

Part II Applications

2.1 Heat exchangers

a. Type of heat exchangers and overall heat transfer coefficient;

b. Log-mean temperature differences: concentric tube heat exchange, parallel and counter flows and temperature profiles along the flow, correction factors for other types (multi-pass tube-shell, cross-flow);

c. Effectiveness ε of heat exchangers and the ε-NTU method: maximum possible heat transfer and effectiveness, ε-NTU relation for concentric tube heat exchangers, other types of heat exchangers, comparison of heat exchanger performances;

d. Sizing and rating problems: Independent variable and typical heat exchanger problems, methodology using forward and inverse ε-NTU relations;

2.2 Thermal management of electronic components and equipment:

a. Electronics cooling specifics: Heat transfer at different length scales from chips to system, non-uniform and non-steady heat generation, high heat flux and low temperature excursion;

b. Cooling of micro-chips: conduction and heat dispersion at micro-scales, material properties and chip design/packaging, transient heat load and thermal stress;

c. Heat flux and thermal management strategy for electronic equipment: selection of cooling method (effectiveness, cost and environment), optimal distribution of components/units and routing for forced flow;

d. Management of very high heat flux (>50 W cm–2): liquid cooling, heat pipes.

2.3 Heat transfer in energy systems:

a. Heat recovery and steam generators: Recuperation, boiler efficiency and selection of the pinch-point;

b. Combustors and turbines: Radiation from flames; film and effusion cooling technology for combustor walls and for turbine blades;

c. Cryogenic heat transfer.

The teaching method is based primarily classroom teaching, which consists of systematic development of theoretical fundamentals and problem solving through examples. Comprehensive lecture notes are provided. Problem sheets and solutions are distributed by stages to aid independent study. Some in-class demonstrations (boiling heat transfer, heat pipes etc) are used. Computer based sessions are used for the numerical modelling content.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.