Radiation Exchange

EGR 4345

Heat Transfer

Blackbody Radiation Exchange

Blackbody Radiation Exchange

Rate at which radiation leaves surface i and is intercepted by surface j

For a black surface, Ji = Ebi

Net radiative exchange

Blackbody Radiation Exchange

Therefore

Or

Net radiation transfer from any surface in an enclosure of black surfaces

Net Radiation Exchange at a Surface in an Enclosure

Net Radiation Exchange at a Surface in an Enclosure

Assumptions– Isothermal surfaces, Ti is known

– Uniform radiosity– Uniform irradiation– Opaque– Diffuse– Gray surface– Medium in enclosure is nonparticipating

Net Radiation Exchange at a Surface in an Enclosure

Determine the net rate at which radiation leaves surface i

Where

In terms of emissive power and absorbed radiation

Net Radiation Exchange at a Surface in an Enclosure

For an opaque, diffuse, gray surface

Solve for Gi and substitute into qi

Or Driving Potential

Surface Radiative Resistance

Net Radiation Exchange Between Surfaces in an Enclosure

Net Radiation Exchange Between Surfaces in an Enclosure

Total rate at which radiation reaches surface i from all surfaces, including i

Reciprocity

Substituting in for Gi

Net Radiation Exchange Between Surfaces in an Enclosure

Summation rule

Therefore

Or

Use matrix operations to solve

Space or Geometric Resistance

Net Radiation Exchange in a Two-Surface Enclosure

Two diffuse, gray surfacesthat form an enclosure

Net Radiation Exchange in a Two-Surface Enclosure

General Equation

Special equations

Radiation Shields

General Equation

Low emissivityincrease resistance

Reradiating Surface

Zero net radiation, qi = 0

Reradiating Surface