Heat Transfer

1. Heat Transfer

2. Definition • Heat transfer is energy transfer due to a temperature difference in a medium or between two or more media • Different types of heat transfer processes are called different modes of heat transfer • Conduction heat transfer is due to a temperature gradient in a stationary medium or media • Convection heat transfer occurs between a surface and a moving fluid at different temperatures • Radiation heat transfer occurs due to emission of energy in the form of electromagnetic waves by all bodies above absolute zero temperature • Net radiation heat transfer occurs when there exists a temperature difference between two or more surfaces emitting radiation energy

3. Heat Transfer Applications • Heat transfer is important to Industrial and Environmental problems and processes • All Energy production and conversion processes involve heat transfer • US businesses and institutions spend $175 billion/year on energy • In Canada, Energy makes up • 6% of GDP, • 200 000 jobs, • $54 billion in exports (~$1,800 per capita), and • $20-30 billion in investments • In electric power generation, heat transfer problems must be solved • In some applications, heat transfer rate is maximized (heating) while in other cases it is minimized (cooling)

4. Relationship of Heat Transfer to Thermodynamics • We learnt in thermodynamics that energy can be transferred by interactions between a system and its surroundings • Heat and work are the only form of interactions between a system and its surroundings • Thermodynamics is concerned with equilibrium end states and processes • But does not provide information on the nature of the process or the rate at which energy is transferred • Energy transfer rates are important in engineering process design and development

5. Introductory Heat Transfer Concepts • Relationship of heat transfer to thermodynamics Heat transfer = work + rate of change of internal energy • For a thermodynamic reversible process, where: T = temperature S = entropy P = pressure V = volume U = internal energy t = time

6. Since all heat transfer processes are irreversible and S cannot be defined as a function of T, the rate of heat transfer Q, cannot be predicted by the above thermodynamic equation. • We must therefore use transport laws, i.e. • Fourier’s Law • Newton’s law of cooling, and • Stefan Boltzmann law for radiation. • Heat transfer is indeed applied thermodynamics • Heat transfer is energy transfer as a result of a temperature difference

7. Modes of Heat Transfer • There are three basic modes of heat transfer • Conduction • Convection • Radiation • We will first examine all three modes briefly and then examine them in more detail later

8. Conduction • Conduction heat transfer is due to random molecular and atomic vibrational, rotational and translational motions • High temperature and more energetic molecules vibrate more and transfer energy to less energetic particles as a result of molecular collisions or interactions • The heat flux (a vector) qx´´ (W / m2) is characterized by a transport property know as the • Thermal Conductivity, k (W / m · K) • W = watts m = Meters K = temperature in Kelvin

9. L T1 T2 X=0 X=L T1 qx´´ T2 x 0 L Consider the heat flux through a slab of thickness, L • For the one-dimensional plane, the heat flux or heat transfer rate is Fourier’s Law: • The total heat transfer through a given cross-sectional area, A, is given by: where

10. Conduction example

11. T∞ q’’ Moving fluid Ts Ts > T∞ Convection • Convection heat transfer involves both energy transfer due to random molecular motions and by bulk motion of the fluid • Convection heat transfer includes both forced convection and natural convection • In convection heat transfer, the transfer of heat is between a surface and a moving fluid (liquid or gas), when they are at different temperatures. The rate of transfer is given by Newton’s Law of Cooling.

12. Typical values of convection heat transfer coefficient

13. Convection example Problem 1.13, p.35, text Calculate the heat flux from your hand when it is exposed to moving air and water, assuming the surface temperature of your hand is 30°C.

14. Convection example - 2

15. Radiation • All surfaces of finite temperature emit energy in the form of electromagnetic waves • In the absence of an intervening medium, there is a heat transfer by radiation between two surfaces at different temperatures • The maximum flux, E (W / m2), at which radiation may be emitted from a blackbody surface is given by: • Stefan Boltzmann Law where Eb or E = Surface emissive power (W / m2) T = absolute temperature (K) σ = Stefan-Boltzmann constant = 5.67 x 10-8 (W / m2 ּ K4) Eb Ts

16. For a real surface: • For a surface with absorptivity α, the incident radiation (G, W/m2) or surface irradiation from the surroundings that is absorbed by the surface is given by: where G = incident radiation (W / m2) T = absolute temperature (K) ε = surface emissivity (0 ≤ ε ≤ 1) α = surface absorptivity (0 ≤ α ≤ 1) G Gabs

17. For a gray surface α = ε • When radiant energy is incident on a transparent surface, it can be absorbed, reflected, or transmitted through the material. Hence, where ρ = materials surface reflectivity  = materials transmissivity

18. Tsur qsur’’ qs’’ Ts • Consider a small gray surface at temperature Ts that is completely enclosed by the surroundings at temperature Tsur. • The net rate of radiation heat transfer from the surface is: • Where hr is the radiation heat transfer coefficient, W / m2 K

19. Representative range of radiation heat transfer coefficient values

20. Radiation ex. Problem 1.26, p.37, text An instrumentation package has a spherical outer surface of diameter D = 100 mm and emissivity  = 0.25. The package is placed in a large space simulation chamber whose walls are maintained at 77 K. If the operation of the electronic components is restricted to the temperature range of 40  T  85°C, what is the range of acceptable power dissipation for the package?

21. Conservation of Energy for a Control Volume or System • Consider a control volume (C. V.) shown here: • Energy Conservation or First Law of Thermodynamics requires that for the C.V. • The rate of energy inflow (Ein) and rate of energy generation (Eg) must be balance by the rate of energy outflow (Eout) and energy storage (Est), Hence, • For a short time interval Δt,

22. For a closed system when Eg = 0: • Where Q is the heat energy inflow, W the work done by the system or heat energy outflow, and ΔU the change in internal energy of the system • On rate basis the above equation is written as: • For an open system with mass flow rate (m) under steady state conditions, the flow work is the product of Pressure (P) and specific volume of the fluid (v). The work done by the system is W and if there is no energy generation or conversion within the system or control volume, the energy conservation equation on rate basis is:

23. Where: m = mass flow rate (kg/s) u = specific internal energy or internal energy per unit mass (J/kg) q = heat transfer rate (W) W = work done by the system per unit time (W) v = specific volume of volume per unit mass (m3/kg) Pv = specific flow work or flow work per unit mass (J/kg) V = Fluid flow velocity (m/s) P = Pressure (Pa) g = Gravity (m/s2) z = elevation (m)

24. Conservation of Energy for a Control Surface • For a surface illustrated below, there is no mass or volume, and consequently, Eg = 0, and Est = 0. • For conservation of energy for the control surface under steady state or transient conditions: Surface Surroundings qcond” qrad” T1 Fluid qconv” Tsur U T T2 T T x

25. Energy balance example (cv)

27. Energy balance example (cs)