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AEE331 HEAT TRANSFER

Course Objectives

The main objective of this course is to familiarize the students with the basic 3 heat transfer modes, namely conduction, convection and radiation, which are common in aerospace systems. The students are also equipped with the ability to identify the existing heat transfer mode(s) on a given problem, and then to analyze the problem by determining the involved heat transfer rates or temperature distributions. The relevant system of equations or differential equations is formed simply by the conservation of energy principle applied to a control volume of finite size or differential size. Following the introduction of Fourier's law for heat conduction, and derivation of the general heat diffusion equation in three dimensions, equations are simplified for one-dimensional problems. Applications to plane walls, with and without thermal energy generation (heat sources), extended bodies (fins), and non-uniform cross sections with quasi one-dimensional approach are made. The concept of equivalent thermal circuit and thermal resistance to conduction heat transfer is introduced. While solving one-dimensional conduction problems with convection over a surface and/or radiation, Newton's law of cooling for convection heat transfer that develops across the thermal boundary layer and/or the black body radiation formula are used for providing the necessary boundary condition at the surface. Following one-dimensional problems, an analytical solution method is taught for treating two-dimensional linear conduction problems without volumetric heat generation. Fundamental knowledge for drawing constant temperature lines (isotherms) and heat flow lines (adiabats) is also provided to appreciate heat transfer phenomena across 2-D bodies. Transient conduction is treated analytically for complex shapes using the lumped capacitance method, and for simple shapes with 1-D conduction solving the full diffusion equation. The use of the non-dimensional Biot number is explained in transient conduction problems. The convection heat transfer mode is observed extensively in aerospace applications. Regarding this heat transfer mode, the fundamental physics pertaining to it is discussed first. For this velocity and thermal boundary layer equations are derived, and then non-dimensionalized, leading to the definitions of the Reynolds number, Prandtl number. By equating the conduction heat transfer at the surface but on the fluid side to convection heat transfer definition the so-called Nusselt number is obtained and this is shown to equal nothing but the fluid's dimensionless temperature gradient at the surface. Both analytical and experimental functions are given for the Nusselt number for various flow configurations. Internal flow convection problems are also treated. Free convection is shown to exist when gravitational effects are important. Relevant dimensionless parameters are discussed and Nusselt number correlations are given for some simple configurations, such as flat plate and horizontal infinite cylinder.  Fundamental concepts of radiation heat transfer are taught. 

Course Content

Basic concepts. One-dimensional steady-state conduction, extended surfaces, two-dimensional steady-state conduction, shape factors, transient conduction. Forced convection, Reynolds analogy, convection for external and internal flows. Free convection, boiling and condensation, heat exchangers. Radiation heat transfer between surfaces.

Course Learning Outcomes

By this course the students will be able to

• Identify the relevant heat transfer modes involved in a problem.

• Perform conduction heat transfer analysis analytically through one-dimensional single layer or composite wall systems, with and without volumetric thermal energy generation as well as convection and radiation heat transfer modes over the walls of the system.

• Calculate the relevant dimensionless Biot number that plays a critical role in transient conduction analysis, and carry out analytical solutions to time-dependent conduction problems for complex shapes with low Biot numbers, and simplified shapes (1-D) with high Biot numbers.

• Develop an understanding of the physics of convection heat transfer and important dimensionless numbers, namely the Reynolds and Prandtl numbers that play a critical role in flow physics.

• Apply Newton's law of cooling for determining the convection heat transfer over a surface and more importantly determine the convection heat transfer coefficient required by this law using the flow conditions over the surface and appropriate correlating Nusselt number relation for the given surface geometry and flow condition, both in forced flow and buoyancy-driven flow situations.

• Learn the differences between internal and external flow fields. Develop an understanding of the effects of the boundary layer development on heat transfer. For internal flows, determine the hydrodynamic entry length and thermal entry length.

• Develop an understanding of the use of Grashof and Rayleigh numbers in a buoyancy-driven flow situation, which is known as free convection.

• Become familiarized with fundamental concepts of radiation heat transfer.

Program Outcomes Matrix