Advanced Transport Phenomena Module 5 Lecture 23. Energy Transport: Radiation & Illustrative Problems. Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras. RADIATION. Plays an important role in: e.g., furnace energy transfer (kilns, boilers, etc.), combustion
Module 5 Lecture 23
Energy Transport: Radiation& Illustrative Problems
Dr. R. Nagarajan
Dept of Chemical Engineering
(Stefan-Boltzmann “black-body” radiation law)
(Wein “displacement law”)
Approximate temperature dependencea of Total Radiant-Energy Flux from Heated Solid surfaces
e w (T w) = fraction of
Dependence of total “hemispheric emittance” on surface temperature of several
refractory material (log-log scale)
to unit area centered at its base, where
Total emissivity of gas mixture eg(X1, X2, …, Tg)
(for special case of one dominant emitting species i)
Tg (q, f, Xi) temperature in gas at position defined by
q angle measured from normal, andf
∫0dXi optical depth
(piLrad)eff effective optical depth
Leff equivalent dome radius for particular gas configuration seen by surface area element
A manufacturer/supplier of fibrous 90% Al2O3- 10% SiO2 insulation board (0.5 inches thick, 70% open porosity) does not provide direct information about its thermal conductivity, but does report hot- and cold-face temperatures when it is placed in a vertical position in 800F still air, heated from one side and “clad” with a thermocouple-carrying thin stainless steel plate (of total hemispheric emittance 0.90) on the “cold” side.
The manufacturer of the insulation reports Th , Tw –combinations for the configuration shown in Figure. What is the k and the “R” –value (thermal resistance) of their insulation?
We consider here the intermediate case:
and carry out all calculations in metric units.
Natural Convection Flux: Vertical Flat Plate
and, for a perfect gas:
This is in the laminar BL range
Therefore, for the thermal “resistance,” R:
(one of the common English units) at
1. Calculate for the other pairs of is the resulting dependence of reasonable?
2. How does compare to the value for “rock-wool” insulation?
3. Would this insulation behave differently under vacuum conditions?