Chapter 1

1. Chapter 1 Introduction to Heat Transfer

2. Introduction Thermodynamics: • Energy can be transferred between a system and its surroundings. • A system interacts with its surroundings by exchanging work and heat • Deals with equilibrium states • Does not give information about: • Rates at which energy is transferred • Mechanisms through with energy is transferred In this chapter we will learn • What is heat transfer • How is heat transferred • Relevance and importance

3. Definitions • Heat transfer is thermal energy transfer that is induced by a temperature difference (or gradient) Modes of heat transfer • Conduction heat transfer: Occurs when a temperature gradient exists through a solid or a stationary fluid (liquid or gas). • Convection heat transfer: Occurs within a moving fluid, or between a solid surface and a moving fluid, when they are at different temperatures • Thermal radiation: Heat transfer between two surfaces (that are not in contact), often in the absence of an intervening medium.

4. Example: Design of a container A closed container filled with hot coffee is in a room whose air and walls are at a fixed temperature. Identify all heat transfer processes that contribute to cooling of the coffee. Comment on features that would contribute to a superior container design.

5. T1 T1>T2 xo qx” T2 T2 x 1. Conduction Transfer of energy from the more energetic to less energetic particles of a substance by collisions between atoms and/or molecules. • Atomic and molecular activity – random molecular motion (diffusion)

6. 1. Conduction Consider a brick wall, of thickness L=0.3 m which in a cold winter day is exposed to a constant inside temperature, T1=20°C and a constant outside temperature, T2=-20°C. • Under steady-state conditions the temperature varies linearly as a function of x. • The rate of conductive heat transfer in the x-direction depends on Wall Area, A qx” T1=20°C T T2= -20°C x L=0.3 m

7. 1. Conduction • The proportionality constant is a transport property, known as thermal conductivity k (units W/m.K) • For the brick wall, k=0.72 W/m.K (assumed constant), therefore qx”= 96 W/m2 • How would this value change if instead of the brick wall we had a piece of polyurethane insulating foam of the same dimensions? (k=0.026 W/m.K) • qx” is the heat flux (units W/m2 or (J/s)/m2), which is the heat transfer rate in the x-direction per unit area perpendicular to the direction of transfer. • The heat rate, qx (units W=J/s) through a plane wall of area A is the product of the flux and the area: qx= qx”. A

8. 1. Conduction • In the general case the rate of heat transfer in the x-directionis expressed in terms of the Fourier law: T1(high) qx” • Minus sign because heat flows from high to low T • For a linear profile T2 (low) x1 x2 x

9. 2. Convection Energy transfer by random molecular motion (as in conduction) plus bulk (macroscopic) motion of the fluid. • Convection: transport by random motion of molecules and by bulk motion of fluid. • Advection: transport due solely to bulk fluid motion. • Forced convection: Caused by external means • Natural (free) convection: flow induced by buoyancy forces, arising from density differences arising from temperature variations in the fluid The above cases involve sensible heat (internal energy) of the fluid • Latent heat exchange is associated with phase changes – boiling and condensation.

10. 2. Convection Air at 20°C blows over a hot plate, which is maintained at a temperature Ts=300°C and has dimensions 20x40 cm. Air q” The convective heat flux is proportional to

11. 2. Convection • The proportionality constant is the convection heat transfer coefficient, h (W/m2.K) Newton’s law of Cooling • For air h=25 W/m2.K, therefore the heat flux is qx”= 7,000 W/m2 • How would this value change if instead of blowing air we had still air (h=5 W/m2.K) or flowing water (h=50 W/m2.K) • The heat rate, is qx= qx”. A = qx”. (0.2 x 0.4) = 560 W. • The heat transfer coefficient depends on surface geometry, nature of the fluid motion, as well as fluid properties. For typical ranges of values, see Table 1.1 textbook. • In this solution we assumed that heat flux is positive when heat is transferred from the surface to the fluid

12. 3. Radiation • Thermal radiation is energy emitted by matter • Energy is transported by electromagnetic waves (or photons). • Can occur from solid surfaces, liquids and gases. • Dos not require presence of a medium Surroundings at Tsur • Emissive power E is the radiation emitted by the surface • Irradiation G is the rate of incident radiation per unit area of the surface, originating from its surroundings Surface at Ts

13. 3. Radiation • For an ideal radiator, or blackbody: Stefan-Boltzmann law where Ts is the absolute temperature of the surface (K) and s is the Stefan-Boltzmann constant, (s = 5.67x10-8 W/m2.K4) • For a real surface: e is the emissivity • The irradiation G, originating from the surroundings is: • is the absorptivity For a “grey” surface, a=e

14. 3. Radiation • The net radiation heat transfer from the surface, per unit area is • The net radiation heat exchange can be also expressed in the form: where

15. Example 1 Satellites and spacecrafts are exposed to extremely high radiant energy from the sun. Propose a method to dissipate the heat, so that the surface temperature of a spacecraft in orbit can be maintained to 300 K.

16. Example 2 On a hot summer day you place a black, metal disk on the ground. Assuming that the bottom surface of the disk is insulated by the ground, calculate the temperature of the plate when the heat absorbed equals the heat lost.

17. Quiz: Heat Transfer Processes Identify the heat transfer processes that determine the temperature of an asphalt pavement on a summer day

18. Quiz: Heat Transfer Processes Identify the heat transfer processes that occur on your forearm, when you are wearing a short-sleeved shirt, while you are sitting in a room. Suppose you maintain the thermostat of your home at 15°C throughout the winter months. You are able to tolerate this if the outside air temperature exceedes –10°C, but feel cold if the temperature becomes lower. Are you imagining things?

19. Conservation of Energy Surroundings, S • Energy conservation on a rate basis: -Accumulation (Storage) -Generation Control Volume (CV) Addition through inlet Loss through outlet Boundary, B (Control Surface, CS) Units W=J/s • Inflow and outflow are surface phenomena • Generation and accumulation are volumetric phenomena

20. Steady-Flow Energy Equation • For an open system mass flow provides for the transport of internal, kinetic and potential energy into and out of the system • The work term is divided in two contributions: Flow work, associated to pressure forces (=pu, where u is the specific volume) and work done by the system. Recall: Mass flow rate (kg/s) Volumetric flow rate (m3/s)

21. Example (Problem 1.36 textbook) In an orbiting space station, an electronic package is housed in a compartment having a surface area As=1 m2, which is exposed to space. Under normal operating conditions, the electronics dissipate 1kW, all of which must be transferred from the exposed surface to space. (a) If the surface emissivity is 1.0 and the surface is not exposed to the sun, what is its steady-state temperature? (b) If the surface is exposed to a solar flux of 750 W/m2 and its absorptivity to solar radiation is 0.25, what is its steady-state temperature?

22. Surface Energy Balance For a control surface: qrad” qcond” T1 qconv” T2 T x

23. Example (Problem 1.55 textbook) The roof of a car in a parking lot absorbs a solar radiant flux of 800 W/m2, while the underside is perfectly insulated. The convection coefficient between the roof and the ambient air is 12 W/m2.K. • Neglecting radiation exchange with the surroundings, calculate the temperature of the roof under steady-state conditions, if the ambient air temperature is 20°C. • For the same ambient air temperature, calculate the temperature of the roof it its surface emissivity is 0.8