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Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT MadrasPowerPoint Presentation

Dr. R. Nagarajan Professor Dept of Chemical Engineering IIT Madras

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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
- Primary sources in combustion
- Hot solid confining surfaces
- Suspended particulate matter (soot, fly-ash)
- Polyatomic gaseous molecules
- Excited molecular fragments

RADIATION EMISSION FROM & EXCHANGE BETWEEN OPAQUE SOLID SURFACES

- Maximum possible rate of radiation emission from each unit area of opaque surface at temperature Tw (in K):
(Stefan-Boltzmann “black-body” radiation law)

- Radiation distributed over all directions & wavelengths (Planck distribution function)
- Maximum occurs at wavelength
(Wein “displacement law”)

RADIATION EMISSION FROM & EXCHANGE BETWEEN OPAQUE SOLID SURFACES

Approximate temperature dependencea of Total Radiant-Energy Flux from Heated Solid surfaces

a

RADIATION EMISSION FROM & EXCHANGE BETWEEN OPAQUE SOLID SURFACES

e w (T w) = fraction of

Dependence of total “hemispheric emittance” on surface temperature of several

refractory material (log-log scale)

RADIATION EMISSION FROM & EXCHANGE BETWEEN OPAQUE SOLID SURFACES

- Two surfaces of area Ai & Aj separated by an IR-transparent gas exchange radiation at a net rate given by:
- Fij grey-body view factor
- Accounts for
- area j seeing only a portion of radiation from i, and vice versa
- neither emitting at maximum (black-body) rate
- area j reflecting some incident energy back to i, and vice versa

- Accounts for

RADIATION EMISSION FROM & EXCHANGE BETWEEN OPAQUE SOLID SURFACES

- Isothermal emitter of area Aw in a partial enclosure of temperature Tenclosure filled with IR-transparent moving gas:
- Surface loses energy by convection at average flux:
- Total net average heat flux from surface = algebraic sum of these

RADIATION EMISSION FROM & EXCHANGE BETWEEN OPAQUE SOLID SURFACES

- Thus, radiation contributes the following additive term to convective htc:
- In general:
- Radiation contribution important in high-temperature systems, and in low-convection (e.g., natural) systems

RADIATION EMISSION & TRANSMISSION BY DISPERSED PARTICULATE MATTER

- Laws of emission from dense clouds of small particles complicated by particles usually being:
- Small compared to lmax
- Not opaque
- At temperatures different from local host gas

- When cloud is so dense that the photon mean-free-path, lphoton << macroscopic lengths of interest:
- Radiation can be approximated as diffusion process (Roesseland optically-thick limit)

RADIATION EMISSION & TRANSMISSION BY DISPERSED PARTICULATE MATTER

- For pseudo-homogeneous system, this leads to an additive (photon) contribution to thermal conductivity:
- neff effective refractive index of medium
- Physical situation similar to augmentation in a high-temperature packed bed

RADIATION EMISSION & TRANSMISSION BY IR-ACTIVE VAPORS MATTER

- Isothermal, hemispherical gas-filled dome of radius Lrad contributes incident flux (irradiation):
to unit area centered at its base, where

Total emissivity of gas mixture eg(X1, X2, …, Tg)

- Can be determined from direct overall energy-transfer experiments

RADIATION EMISSION & TRANSMISSION BY IR-ACTIVE VAPORS MATTER

- More generally (when gas viewed by surface element is neither hemispherical nor isothermal):
(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

RADIATION EMISSION & TRANSMISSION BY IR-ACTIVE VAPORS MATTER

- Integrating over solid angles :
(piLrad)eff effective optical depth

Leff equivalent dome radius for particular gas configuration seen by surface area element

- Equals cylinder diameter for very long cylinders containing isothermal, radiating gas

RADIATION IN HIGH-TEMPERATURE CHEMICAL REACTORS MATTER

- Coupled radiation- convection- conduction energy transport modeled by 3 approaches:
- Net interchange via action-at-a-distance method
- Yields integro-differential equations, numerically cumbersome

- Six-flux (differential) model of net radiation transfer
- Leads to system of PDEs, hence preferred

- Monte-Carlo calculations of photon-bundle histories
- PDE solved by finite-difference methods

- Net interchange via action-at-a-distance method

RADIATION IN HIGH-TEMPERATURE CHEMICAL REACTORS MATTER

- Net interchange via action-at-a-distance method:
- Net radiant interchange considered between distant Eulerian control volumes of gas
- Each volume interacts with all other volumes
- Extent depends on absorption & scattering of radiation along relevant intervening paths

RADIATION IN HIGH-TEMPERATURE CHEMICAL REACTORS MATTER

- Six-flux (differential) model of net radiation transfer method:
- Radiation field represented by six fluxes at each point in space:

RADIATION IN HIGH-TEMPERATURE CHEMICAL REACTORS MATTER (five similar first-order PDEs for remaining fluxes)

- In each direction, flux assumed to change according to local emission (coefficient ) and absorption () plus scattering ():

- Six PDEs solved, subject to BC’s at combustor walls

RADIATION IN HIGH-TEMPERATURE CHEMICAL REACTORS MATTER

- Monte-Carlo calculations of photon-bundle histories:
- Histories generated on basis of known statistical laws of photon interaction (absorption, scattering, etc.) with gases & surfaces
- Progress computed of large numbers of “photon bundles”
- Each contains same amount of energy

- Wall-energy fluxes inferred by counting photon-bundle arrivals in areas of interest
- Computations terminated when convergence is achieved

PROBLEM 1 MATTER

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.

PROBLEM 1 MATTER

- a. Given the following table of hot- and cold-face temperatures for an 18’’ high specimen, estimate its thermal conductivity (when the pores are filled with air at 1 atm). (Express your result in (BTU/ft2-s)/(0F/in) and (W/m.K) and itemize your basic assumptions.)
- b. Estimate the “R” value of this insulation at a nominal temperature of 10000F in air at 1 atm.
- If this insulation were used under vacuum conditions, would its thermal resistance increase, decrease, or remain the same? (Discuss)

PROBLEM 1 MATTER

SOLUTION 1 MATTER

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.

SOLUTION 1 MATTER

Natural Convection Flux: Vertical Flat Plate

But:

and, for a perfect gas:

Therefore

SOLUTION 1 MATTER

Therefore

SOLUTION 1 MATTER

Student Exercises

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?

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