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- 1. 1 Note to Students and Instructors on the Power Point Presentation The presentation is intended to be used along with the text. It helps minimize the instructor from writing out all the equations. Many equations need to be further elaborated by the instructor.
- 2. Chapter 1 – Introduction
- 3. 3 In this chapter, we • Define heat transfer • Show the relationship between thermodynamics and heat transfer • Define the three modes of heat transfer – conduction, convection, and radiation • Give a brief introduction to each mode of heat transfer • Briefly describe a few cases where heat transfer plays an important role • Suggest a methodology for the solution of heat transfer problems • Define some of the significant terms used in the book.
- 4. 4 Heat transfer is energy transfer resulting only from temperature differences. 1.1 Relationship between thermodynamics and heat transfer. First law of thermodynamics is a statement of conservation of energy and deals with equilibrium states. Consider a spherical copper ball initially at a uniform temperature suddenly immersed in water as shown in the figure.
- 5. 5 Applying the first law of thermodynamics we find that the final temperature of the ball and water is 36.7 oC. But the first law will not give the time required to go from the initial state to the final state. In the study of heat transfer we attempt to the additional questions of the temperature distribution and the heat transfer rate as functions of time. 1.2 Modes of Heat Transfer Heat transfer is a surface phenomenon – heat transfer occurs from (or to) a surface. Three modes of heat transfer are generally recognized. Conduction: Heat transfer in a solid or a stationary fluid Convection: Heat transfer in a in motion. Two modes of convection: In forced convection fluid motion occurs due to an external force and the motion continues with or without heat transfer In natural convection fluid motion is caused solely by temperature differences
- 6. 6 Both conduction and convection require a material medium. Radiation does not require a material medium. In conduction and convection one can determine the heat transfer rate from an elemental area by knowing the conditions of the material in the immediate vicinity of the area. In radiation one needs to know the entire field that the area sees. The heat transport in conduction and convection is much, much slower than in radiation.
- 7. 7
- 8. 8 1.3 Conduction Conduction heat transfer is heat transfer in solids and fluids without macroscopic motion. Conductive heat transfer generally occurs in solids though it may occur in fluids without macroscopic motion or with rigid body motion. The basis for analysis of conduction is the first law of thermodynamics in conjuction with Fourier’s Law of Conduction. Fourier’s law: conductive heat flux at a point in a given direction is proportional to the magnitude of the temperature gradient in that direction and is positive in the direction of decreasing temperature. '' x T q k x (1.3.1)
- 9. 9 In steady state, no part of the solid stores energy, and the heat transfer rate across every cross section perpendicular to the x-direction is uniform. As the cross sectional area is uniform, the heat flux is also uniform, Integrating Eq. (1.3.2) Figure 1.3.1 '' x T q k x (1.3.2) 2 1 '' 0 T L x T kdT q dx (1.3.3) '' 1 2 x x x x x A T T q q dA kA L (1.3.4) '' 1 2 x T T q k L
- 10. 10 Thermal conductivity k is a property of the material and is always positive. It varies from about 0.0262 W/m K for air to about 2300 W/m K for carbon (type IIa diamond), i.e., by a factor of 100 000. The negative sign in Fourier’s law satisfies the second law of thermodynamics. For heat transfer to be positive in the x-direction the temperature gradient in that direction should be negative i.e., heat transfer occurs in the direction of decreasing temperature.
- 11. 11 (1.3.4) Convection When there is a temperature gradient in a fluid in bulk motion heat transfer occurs by two mechanisms. Molecular motion – conduction Bulk motion of fluid packets Total heat transfer is the sum of the two. Convective heat transfer coefficient is defined by Eq. (1.4.1.) '' ( ) c c s f q h T T (1.4.1)
- 12. 12 The convective heat transfer coefficient is always positive. With uniform surface temperature Ts and Tf if the heat flux is local we obtain the local heat transfer coefficient. If the heat flux is the average over an area we get the average heat transfer coefficient. The choice of the reference temperature Tf is arbitrary. With each correlation the choice of the reference temperature for defining the convective heat transfer coefficient should be stated. However, by convention the reference temperature for external flows such of an semi-infinite fluid flow over a flat plate, cylinder, sphere and so on, the reference temperature is the temperature of the fluid far away from the surface, known as the free stream temperature usually denoted by T. In internal flows the reference temperature is usually the bulk temperature Tb. A detailed definition of the bulk temperature is given under internal flows.
- 13. 13 Convection is subdivided into forced and natural convection. In forced convection the fluid flow continues whether there is heat transfer or not. In natural convection the fluid flow is caused solely be temperature differences due to heat transfer, in the presence of a body force. Some representative values of the convective heat transfer coefficients in each mode is given in Table 1.4.1. In natural heat transfer, radiative heat transfer may form significant part of the total heat transfer.
- 14. 14 1.5 Radiation All materials emit energy by radiation in the form electro-magnetic waves or photons. The maximum radiative heat flux that can be emitted by a solid surface at a defined surface temperature, the black body emissive power is given by the Stefan-Boltzmann law, (1.5.1) A surface that emits the maximum energy flux is an ideal radiator, also known as a black surface. The emitted energy flux of any real surface is less than the maximum.
- 15. 15 Consider the radiative heat transfer from a convex surface completely enclosed by a second much larger surface as shown in Figure 1.5.1. The two surfaces are separated by medium that does not participate in radiation. No part of the inner surface can see any other part of itself – no part is concave. In this case the heat radiative transfer rate is given by: (1.5.2) (1.5.3)
- 16. 16 Analogous to the convective heat transfer coefficient we may define a radiative heat transfer coefficient employing Eq. (1.5.3) for this case. (1.5.4) From Eq. (1.5.4) it is clear that the radiative heat transfer coefficient is a function of the temperatures of the two surfaces and the emissivity of the inner surface. However, in many cases the variation of the coefficient with temperatures is such that an average value can be used. 1.6 Surface heat transfer coefficient In many cases of natural convection the radiative heat transfer rate is a significant part of the total heat rate. In such cases a surface heat transfer coefficient – the ratio of the total heat flux to a chactraristic temperature difference.
- 17. 17 In such cases the surface heat transfer coefficient is given by: h = hc + hr 1.9 Terminology Pure substance: Contains only one type of molecules. Uniform: The value of a parameter does not vary spatially. Homogeneous mixture: Contains more than one phase of a pure substance so mixed that every volumetric element contains the same proportion of molecules of different substances or phases. Examples: Air or steam and water droplets. In a uniform state, the properties of a homogeneous substance the thermodynamic (density, internal energy…) and transport properties viscosity, thermal conductivity…) are spatially independent. Isotropic substance: Properties are direction independent. One-dimensional: Variable of interest varies with only one spatial coordinate.
- 18. 18 1.9 Terminology (continued) Steady State: Variable of interest does not change with time. Transient or dynamic state: Variable is time dependent. Control Mass (also system, closed system): focus is on an identifiable mass. Control Volume (open system): A region in space. Can be moving, deformable or rigid. Uncertainty: Indicates that a value of a variable cannot be treated as exact. Causes of uncertainty: Uncertainties in the values measured with instruments. Actual measurement in an environment that is not identical to where original measurements were made. Lack of repeatability in the measured values. Two ways of indicating uncertainties.
- 19. 19 Uncertainty (continued) 1. Express the value of a variable as x y 2. Express the value of x as % 100 / x z z y x 1.10 Methodology in the solution of heat transfer problems Balance of mass Control Mass: Mass remains constant. Control Volume: Rate of change of mass within the CV + net rate of mass flow rate out = 0 Balance of linear momentum: In a specified direction Control Mass: Rate of change of momentum = sum of all the forces on the mass Control Volume: Rate of change of linear momentum of the mass in the CV + net rate of momentum flow out = sum of all the forces on the material in the CV
- 20. 20 Balance of Energy (First Law of Thermodynamics) Assumption: changes in kinetic and potential energies are negligible. Control Mass Rate of change of internal energy of the mass = net rate of heat transfer to the mass – net rate of work transfer from the mass + rate of internal energy generation. Control Volume Rate of change of internal energy of the mass in the CV + net rate of enthalpy flow out of the CV = Net rate of heat transfer to the CV – net rate of work transfer from the CV + rate of internal energy generation in the CV.
- 21. 21 1.12 Some suggestions for solving problems 1. Read the problem statement carefully and translate them into a sketch. 2. Transfer all the information in the problem statement to the sketch. 3. List all assumptions. Some assumptions may need to be made while solving the problems. 4. Find and list all the required properties. 5. Conceptualize the solution by writing all the steps. 6. Apply your analysis in symbolic form. Substitute the numerical values at the end. 7. Present your solution in a neat and orderly manner. 8. For some problems defend every step of the solution. 9. The purpose of solving problems is to ensure a good understanding of the material and the analysis.