HeatTransfer: Radiation Heat Transfer
Objectives Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 2 • Understandthe basics of radiation heat transfer. • Examine surface properties linked to radiation heat exchange. • Study radiation exchange between two bodies. • Understand radiation heat transfer to ambient. • Identify the considerations for numerically solving radiation heat transfer problems. • Study two examples: • Radiation heat loss from a sphere inside an enclosure • Radiation heat loss to the night sky
Understanding Radiation Heat Transfer Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 3 • Does not require the presence of matter. • All matter emits radiation. • Radiation may be considered propagation of electromagnetic waves, photons or quanta. • Thermal radiation is that portion of electromagnetic radiation that is generated by the thermal motion of charged particles in matter. • In contrast to conduction and convection, radiation reaches its maximum efficiency in the absence of matter. • Radiation may be considered a surface phenomenon where the wavelength of radiation can be given by: Where: c = phase speed / Speed of light f = frequency of the wave
Understanding Radiation Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 4 Image: Courtesy NASA
Surface Properties Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 5 • Emissivity (Є) represents the efficiency of a body for emitting radiation. • Absorptivity (α), Reflectivity (ρ) and Transmissivity (τ) respectively represent the portion of radiation that is absorbed, reflected and transmitted by an object.α+ ρ+ t =1 Glass Cover Glass cover: High transmissivity, low reflectivity Absorber plate: high absorptivity, low reflectivity Absorber Plate Solar Collector
Radiation Exchange between Two Bodies Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 6 • Net Radiation exchange between two bodies depends upon two factors: • Temperatures of the bodies • View Factor • The View Factor for simple shapes can be found analytically. • Complex shapes require numerical analysis. In the example at right, body B sees all of body A,but body A cannot see all of body B. If body A is very close to body B: • The view factor from A to B is almost 1 • The view factor from B to A is <1 B A
Example of View Factors Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 7 figure 2 figure 1 View factors for perpendicular rectangles with a common edge (figure 1) and coaxial parallel disks (figure2). Images courtesy of Fundamentals of Heat Transfer, F.P. Incropera and D.P. DeWitt, John Wiley and Sons.
Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 8 Radiation Heat Transfer to Ambient • Radiation heat loss to ambient (at absolute zero) occurs when a second body is not present in proximity to the body radiating heat. For example, the dark side of the earth radiating heat to space. • Radiation heat lost to ambient is easier to calculate as it is assumed that heat is being lost through radiation but not being received. • Radiation heat lost to ambient can be calculated through the Stefan Boltzman Law: • The heat “Q” transmitted from an area can be given as
Consideration for Numerically Solving Radiation Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 9 • For radiation problems using FEA, large numbers of mesh cells are extremely difficult to solve and in some cases unfeasible. • The reason is cell to cell shape factor calculations that are memory intensive and computationally expensive (see bottom figure). • Radiation surfaces, or those surfaces that take part in radiation heat exchange, should be pre-defined by the user. Any surfaces that have negligible parts to play can be ignored. • In general, larger nonlinear effects, like radiation, require smaller relaxation parameters to avoid divergence. C To estimate the radiation heat loss from surface “A” in a 2D box, view factors from A to B, A to C, and A to D would have to be calculated. Similarly to find the net heat exchange, view factors for all combinations e.g C-B, B-D would have to be calculated. D B A
Example: Radiation Heat Loss from a Sphere Inside an Enclosure Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 10 Spherical object made of ceramic contained inside a ceramic box. Sphere is at 60ºC Heat source face is 150ºC Ambient is at -80ºC A video presentation is available for this module that covers setting up, solving and viewing results for this example.
Additional Example: Radiation Loss to Night Sky Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 11 • Radiation heat loss to the night sky on a clear night is much higher than on cloudy nights. • Frost on a windshield indicates radiation heat loss to the night sky. Notice that as radiation heat is being lost to space at temperature of absolute zero, the above expression is the simplified version of the one observed earlier in the slide “Radiation Heat Transfer to Ambient”.
Summary Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 12 • Radiation heat transfer is usually neglected at small temperatures; however, it becomes the major mode of heat transfer at high temperatures. • For instance, molten metal loses more heat through radiation than convection and conduction combined. • Radiation heat exchange can be calculated between two bodies or between the body and ambient. • The former is complex because of the involvement of view factors. • The view factors indicate how much two radiating bodies “see” one another.
Summary Section 6 – Thermal Analysis Module6: Radiation Heat Transfer Page 13 • Thus the more surfaces participating in heat exchange, the more complex the problem becomes as view factor calculations increase the computation time. • The calculation of heat loss to ambient is relatively straight forward. • Surface properties such as emissivity play a major role in determining radiation heat loss. • Similarly, properties such as absorptivity, reflectivity and transmissivity are also important for calculations.