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2 The science of how heat flows is called heat transfer. There are three ways heat transfer works: conduction, convection, and radiation. Heat flow depends on the temperature difference. innova-ve entrepreneurial global 2

3 Conduction is the transfer of heat through materials by the direct contact of matter. Dense metals like copper and aluminum are very good thermal conductors. A thermal insulator is a material that conducts heat poorly. Heat flow (watts) Thermal conductivity (watts/m o C) Q = k A (T 2 -T 1 ) L Area of cross section (m 2 ) Length (m) Temperature difference ( o C) innova-ve entrepreneurial global 3

4 Heat conduction in solids and liquids works by transferring energy through bonds between atoms or molecules. innova-ve entrepreneurial global 4

5 When the flow of gas or liquid comes from differences in density and temperature, it is called free convection. When the flow of gas or liquid is circulated by pumps or fans it is called forced convection. Heat transfer coefficient (watts/m 2o C) Heat flow (watts) Q = h A (T 2 -T 1 ) Area contacting fluids (m 2 ) Temperature difference ( o C) innova-ve entrepreneurial global 5

6 Suppose we have two surfaces at temperature T 1 and T 2, both are finite in area, and neither surface is completely enclosed by the other (e.g. the floor and ceiling of a room where only a fraction of the energy leaving the ceiling strikes the floor and vice versa. A portion of heat is transferred from surface A1 to Surface A2 innova-ve entrepreneurial global 6

7 For a body totally enclosed by its surroundings, the net rate of heat transfer by thermal radiation is given by : Q = εσ AF 12 (T 1 4 T 2 4 ) Emissivity ε = W W Black Body Steffan-Boltzman Constant Btu σ = x 10 8 = x 10 8 W hr ft 2 4 R m 2 K 4 At thermal equilibrium emissivity = absorptivity A is surface area of the receiving body F 12 is view factor, F 12 = fraction of energy leaving A 1 reaching A 2 T1 is surface temperature of the source, T2 is surface temperature of the receiver innova-ve entrepreneurial global 7

8 1. The energy is absorbed 2. The energy is transmitted 3. The energy is reflected absorptivity (a) transmissivity (t) reflectivity (z) The energy may be split by the three process such that : a + t + z = 1 innova-ve entrepreneurial global 8

9 If all of the energy is either reflected or absorbed (no transmitted radiation), we define the body as Opaque a + z = 1 If all of the energy striking a surface is absorbed, we define the body as Black body a = 1 For heat transfer calculations, we often assume that the properties a, t, and z are independent of wavelength. When this assumption is made we say that we have gray surfaces. innova-ve entrepreneurial global 9

10 The calculation of view factors is a straightforward exercise in calculus as shown in the figure on the preceding page. For each point on the surface A 1, we consider rays of thermal energy emanating out equally in all directions. The fraction of these rays (actually, the total solid angle) which strikes A 2 gives the fraction of energy reaching that surface. Integrating over all points on surface A 1 and averaging gives the view factor F 12. The following relationship is true: A 1 F 12 = A 2 F 21 innova-ve entrepreneurial global 10

11 q 1->2 = σ A 1 F 12 T 1 4 q 2->1 = σ A 2 F 21 T innova-ve entrepreneurial global 11

12 Case 1: Differential surface parallel to a finite rectangular surface L 1 D L 2 F 12 = 1 2π X Y 1 + X 2 tan X + Y X Y 2 tan Y 2 where X=L 1 /D and Y=L 2 /D innova-ve entrepreneurial global 12

13 b a c Case 2: Plane circular surface with common central normal 1 + B2 + C 3 ( 1 + B 2 + C 3 ) 4B 2 C 2 F = 12 2B 2 where B = b/a and C = c/a innova-ve entrepreneurial global 13

14 Case 3: Plane element A 1 to sphere of radius r 2 ; normal to centre of element passes through centre of sphere F = r 2 12 h 2 h r 2 A 2 da 1 innova-ve entrepreneurial global 14

15 Case 4: Spherical point source to a sphere of radius r 2 da 1 h F ( ) 2 r 1 1 where R h = = R 2 r 2 da 2 innova-ve entrepreneurial global 15

16 Q 12 = F 12 σ A 1 ( T 4 1 T 4 2 ) q 12 = F 12 σ ( T 4 1 T 4 2 ) Q is the energy transferred in W, q is flux in W/m 2 T is in Kelvin F 12 is the view factor which is dependent on the geometry of the system A is area in m 2 innova-ve entrepreneurial global 16

17 Q is the energy transferred in W, q is flux in W/m 2 Using these values, we can estimate the impact of the incident (damage/fatalities/ losses) innova-ve entrepreneurial global 17

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