RADIATION MODELING FOR

BIO-MEDICAL APPLICATIONS

A THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

Bachelor of Technology

In

Mechanical Engineering

By

SAMIR CHOUDHURY

Department of Mechanical Engineering

National Institute of Technology

Rourkela, Orissa

2009

RADIATION MODELING FOR

BIO-MEDICAL APPLICATIONS

A THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

Bachelor of Technology

In

Mechanical Engineering

By

SAMIR CHOUDHURY

Under the Guidance of

Prof. S. K. Mahapatra

Department of Mechanical Engineering

National Institute of Technology

Rourkela, Orissa

2009

National Institute of Technology

Rourkela

CERTIFICATE

This is to certify that the thesis entitled, “RADATION MODELING FOR BIO-MEDICAL

APPLICATIONS” submitted by Sri Samir Choudhury in partial fulfillment of the requirements for

the award of Bachelor of Technology Degree in Mechanical Engineering at the National Institute of

Technology, Rourkela (Deemed University) is an authentic work carried out by him under my

supervision and guidance.

To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other

University / Institute for the award of any Degree.

Date:………………… Prof. S. K. Mahapatra

Mechanical Engineering

NIT ROURKELA

ACKNOWLEDGEMENT

The satisfaction and euphoria on the successful completion of any task would be

incomplete without the mention of the people who made it possible whose constant

guidance an encouragement crowned out effort with success.

I am grateful to the Dept. of Mechanical Engineering, NIT ROURKELA, for giving

me the opportunity to execute this project, which is an integral part of the curriculum in

B.Tech programme at the National Institute of Technology, Rourkela.

I would also like to take this opportunity to express heartfelt gratitude for my project

guide Prof. S.K. Mahapatra, who provided me with valuable inputs at the critical stages

of this project execution.

I would like to acknowledge the support of every individual who assisted me in making

this project a success and I would like to thank Mr. B. N. Padhi (a research scholar), for

his help whenever it was required.

Date:……………. SAMIR CHOUDHURY

B.Tech (10503066)

Dept. of Mechanical Engg.

CONTENTS

1. ABSTRACT……………………………………………………………………….........i

2. LIST OF FIGURES…………………………………………………………………….ii

3. INTRODUCTION……………………………………………………………………...1

4. EQUATION OF RADIATIVE HEAT TRANSFER IN PARTICIPATING

MEDIUM…………………………………………………………………………….........5

4.1 Absorption

4.2 Out-scattering

4.3 Emission

4.4 In-scattering

5. OVERALL ENERGY CONSERVATION EQUATION………………………………8

6. FINITE VOLUME METHOD…………………………………………………….........9

7. FORMULATION OF THE DISCRETIZATION EQUATIONS

7.1 Steady state RTE…………………………………………………………………..10

7.2 Solution procedure………………………………………………………………...13

7.3 Transient state RTE………………………………………………………………..14

7.4 Solution procedure………………………………………………………………...16

7.5 Linear anisotropic phase function…………………………………………………17

8. RESULTS AND DISCUSSIONS……………………………………………………..19

9. CONCLUSION………………………………………………………………………..35

10. FUTURE SCOPE OF RESEARCH……………………………………………........36

11. REFERENCES…………………………………………………………………........37

ABSTRACT

Thermal radiation is important in many applications, and its analysis is difficult in the

presence of a participating medium. In traditional engineering studies, the transient term

of the radiative transfer equation (RTE) can be neglected. The assumption does not lead

to important errors since the temporal variations of the observables e.g. temperature are

slow as compared to the time of light of a photon. However in many new applications in

different fields the transient effect must be considered in the RTE, like it has a great

usability in the field of Bio-medical (applications like optical tomography, detection of

scar tissues and many more all of which is interaction of LASER with the participating

medium, tissue). In the transient phase, the reflected and the transmitted signals have

temporal signatures that persist for a time period greater than the duration of the source

pulse. This could be a source of information about the properties inside the medium.

Hence sufficiently accurate solution methods are required.

In the last few years, the finite volume method (FVM) and discrete transfer method has

emerged as one of the most attractive methods for modeling steady and transient state

radiative transfer.

The present research work deals with the analysis of steady and transient radiative

transfer in two dimensional square enclosure using FVM and analysis of steady and

transient RTE with one boundary subjected to single short pulse irradiation.

iii

LIST OF FIGURES

Fig. I….A typical control volume

Fig. II….Control angle discretization in Finite Volume method

Fig.III….Different orientation of angles in a discretized control angle

Fig. IV….Step Scheme for a control volume

Fig.1…. Variation of dimensionless heat flux at the bottom wall for absorbing and

emitting square enclosure.

Fig.2…. Variation of dimensionless heat flux at the bottom wall for purely scattering

square enclosure.

Fig.3…. Variation of dimensionless heat flux along centerline in y-direction for

isotropic scattering.

Fig.4…. Variation of dimensionless heat flux along centerline in y-direction for linear

backward scattering.

Fig.5….Variation of dimensionless heat flux along centerline in y-direction for linear

forward scattering.

Fig.(i)….Geometry subjected to normal collimated incidence

Fig.(ii)….Transmittance and Reflectance of a square enclosure

Fig.6….Variation of transmittance and reflectance with distance in x-direction

Fig.7…. Variation of transmittance with distance in x-direction for different wall

emissivity

Fig.8…. Variation of reflectance with distance in x-direction for different wall

emissivity

Fig.9…. Variation of transmittance with distance in x-direction for different

anisotropic factor

Fig.10…. Variation of reflectance with distance in x-direction for different anisotropic

factor

Fig.11…. Variation of transmittance with distance in x-direction for different angle of

incidence

iii

Fig.12…. Variation of reflectance with distance in x-direction for different angle of

incidence

Fig.(a)….2-D square enclosure subjected to pulsed collimated incidence

Fig.(b)….Unit Step pulse used to irradiate the bottom wall

Fig.13….Variation of transmittance with non-dimensional time

Fig.14….Variation of reflectance with non-dimensional time

Fig.15….Variation of transmittance with non-dimensional time for different optical

thickness

Fig.16….Variation of reflectance with non-dimensional time for different optical

thickness

Fig.17….Variation of transmittance with non-dimensional time for different pulse-

width

Fig.18….Variation of reflectance with non-dimensional time for different pulse-width

Fig.19….Variation of transmittance with non-dimensional time for different scattering

albedo

Fig.20….Variation of reflectance with non-dimensional time for different scattering

albedo

Fig.21….Variation of transmittance with non-dimensional time for different

anisotropic factor

Fig.22….Variation of reflectance with non-dimensional time for different anisotropic

factor

Fig.23….Variation of transmittance with non-dimensional time for different angle of

incidence

Fig.24….Variation of reflectance with non-dimensional time for different angle of

incidence

iii

INTRODUCTIONFor the last few decades, there is an exponential growth in the research area of transient

radiative heat transfer in participating media. Traditional analysis of radiation transfer

neglects the transient effect of light propagation due to the large speed of light compared

to the local time and length scales [2].

As the technology advanced and the short pulsed laser applications developed, the steady

state assumption was no longer valid as the temporal width of the input pulse was similar

to the order of Pico and Femto-seconds. Ultra-short pulsed lasers are used in a wide

variety of applications such as thin film property measurements, micro-machining,

removal of contamination particles, ablation of polymers, remote sensing of the

atmosphere, combustion chambers and other environments which involve interaction of

the laser beam with scattering and absorbing particles of different sizes [3]. Another

interesting application of short-pulsed lasers is in optical tomography where their use can

potentially provide physiological and morphological information about the interior of

living tissues and organs in a non-intrusive manner. All these applications need models to

predict transient radiation transport in participating media. In the past, various analytical

studies and numerical models of transient radiative transfer have been reviewed by Mitra

and Kumar [4]. The normal-mode-expansion technique is used in [1] to obtain a semi-

analytical solution for the angular distribution of radiation at any optical distance within a

linearly anisotropic scattering, absorbing, emitting, non-isothermal, gray medium

between two parallel reflecting boundaries. From the literature it is evident that many

researchers adopted different methods to deal with the problem. The commonly used

methods to solve the transient radiative transfer equation are the Monte Carlo method, the

integral equation solution, the finite volume method (FVM), the radiation element

method (REM), discrete transfer method (DTM) and the discrete ordinates method

(DOM).

The Monte Carlo method is used to simulate problems involving radiative heat

transfer because of its simplicity, the ease by which it can be applied to arbitrary

configurations and its ability to capture actual and often complex physical conditions [5].

The Monte Carlo technique has been used by Guo et al. [5] to simulate short-pulsed laser

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transport in anisotropically scattering and absorbing media. The authors examined the

effects of pulse width, medium properties, and the effects of Fresnel reflection on the

transmissivity and reflectivity of the medium. However, the method has inherent

statistical errors due to its stochastic nature [2]. It also demands a lot of computational

time and computer memory as the histories of the photons have to be stored at every

instant of time [5]. Thus, the Monte-Carlo method is ruled out in practical utilizations

such as real-time clinical diagnostics where computational efficiency and accuracy are

major concerns [6]. Guo and Maruyama [7] evaluated the isotropic law in three

dimensional inhomogeneous and linear anisotropic scattering media. The discrete

ordinates method has been used by various researchers to solve the transient radiative

transfer equation (RTE). Sakami et al. [8] used the DOM to analyze the ultra-short light

pulse propagation in an anisotropically scattering two dimensional medium. Mitra et al

[9] used a P1 approximation to model transient radiative transfer in a rectangular

enclosure.

Hsu [10] considered the Monte Carlo simulations for transient radiative transfer

process within the participating media inside the one-dimensional geometry with the

multiple scattering and reflective boundaries. Various effects, including the scattering

albedo, pulse shape and width, surface reflectivity and optical thickness, are examined

and concluded that if the boundary surface is reflective, then the temporal spread is

influenced by multiple reflections and partial transmissions at the surfaces. The backward

or reverse Monte Carlo method was successfully applied by Lu and Hsu [11] to simulate

transient radiative transport in a non-emitting, absorbing, and anisotropically scattering

one-dimensional slab subjected to ultra-short light pulse irradiation. Wu and Coworkers

[12] and Tan and Hsu [13] have used the integral equation formulation to solve the

transient radiative transfer problem analytically. Tan and Hsu [13] used the integral

equation formulation and the radiation element method by Guo and Kumar [14] to

simulate radiative transport in the same problem with black boundaries exposed to diffuse

or collimated irradiation.

Y.Hasegawa, et al., [15] used Monte Carlo method to simulate the transient light

transmission through the living tissue which was characterized by strong forward

scattering phase function. Brewster and Yamada [16] later conducted the transient study

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using the same MC algorithm used by Hasegawa, et al. They examined various effects

i.e., albedo, optical thickness, anisotropic scattering, and the detector size, on the

reflected and transmitted temporal signals. Finite volume methods developed by Chai et

al., [17] to solve the steady-state RTE have also been employed to solve the transient

RTE by Chai [18,19]. The finite volume technique is used with the step and curved line

advection method (CLAM) [20] spatial discretization schemes to model transient radiative

transfer in 1-D and 2-D geometries. The author found that the CLAM scheme captures

the penetration depths of radiation more accurately than the step scheme for the same

grid.

Rath et al., [21] extended the DTM, to solve transient radiative transport problems

in a one-dimensional planar absorbing and scattering medium, one boundary of which is

subjected to a short-pulse laser and the other boundary is cold. Effects of optical

thickness, scattering albedo, and anisotropy factor on transmittance and reflectance are

analyzed. Sarma et al., [22] analyzed the radiative heat transfer problem in 1-D planar

absorbing, emitting and anisotropically scattering gray medium in radiative equilibrium

subjected to collimated radiation by the discrete transfer method. The Galerkin method is

extended by T. Okutucu; Y. Yener [23] for the solution of the transient radiative transfer

problem in a one-dimensional participating plane-parallel grey medium with a collimated

short-pulse Gaussian irradiation on one of its boundaries. The transient transmittance and

reflectance of the medium are evaluated for various optical thicknesses, scattering

albedos and pulse durations. Muthukumaran and Mishra [24] used the finite volume

method for solving transient radiative heat transfer problem in a planar participating

medium subjected to a short-pulse diffuse or collimated radiation. For a train of pulses,

effects of the extinction coefficient and the scattering albedo on transmittance and

reflectance signals are studied.

A finite element model, which is based on the discrete ordinates method and least-

squares variational principle, is developed by W.An et al., [25] to simulate the transient

radiative transfer in absorbing and scattering media in one dimensional and two-

dimensional enclosure and W.An et al., [26] extended the same method to simulate short-

pulse light radiative transfer in homogeneous and nonhomogeneous media. Their results

indicated that the reflected signals can imply the break of optical properties profile and

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their location. Most recently Yilmazer A, Kocar C [27] discussed the radiative transfer

problem in plane-parallel, participating medium with linearly anisotropic scattering using

the ultraspherical-polynomials approximation method. Effects of the order of

approximation, optical thickness, specular reflection, anisotropic scattering, and change

of the source term on results are investigated different order of approximation.

Majority of the findings are based on the most simplified assumption of black wall,

whereas the reflective wall assumption resembles more to the practical application [4].

The multiple scattering and reflective boundaries, influences considerably the radiation

transport in a participating medium. When the boundary surface becomes reflective, then

the temporal spread changes significantly by the multiple reflections and partial

transmissions at the surfaces [10]. Therefore, the present article focuses on the problem

of a participating medium bounded by diffusely emitting boundaries, under the condition

of radiative equilibrium. The total intensity is directly solved using FVM without

splitting into the collimated part and diffusive part as cited in existing formulation [21,

22, 24, 28].

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EQUATION OF RADIATIVE HEAT

TRANSFER IN A PARTICIPATING MEDIUM

When the medium through which the radiative energy is traveling is participating then

any incident beam will undergo

Absorption

Scattering

Emission

Scattering away from the direction under consideration is known as out-scattering and

scattering from the other directions into the direction under consideration is known as in-

scattering.

Absorption:

The absolute amount of absorption is directly proportional to the magnitude of incident

energy as well as the distance the beam travels through the medium.

where k(r) is the linear absorption coefficient

Out-scattering:

It is same as absorption but only difference is that absorbed energy is converted into

internal energy while scattered energy is simply redirected along another direction.

where is known as the linear scattering coefficient

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Emission:

The rate of emission from a volume element is proportional to the magnitude of the

volume. So the emitted intensity is proportional to the length of the path and local energy

content in the medium. At the thermodynamic equilibrium intensity everywhere will be

equal to blackbody intensity.

where k(r) is the emission constant same as for absorption

In-scattering:

It has contribution from all the directions and hence must be calculated by integration

over all solid angles, considering the radiative heat flux impinging on a volume element

from an infinitesimal pencil of rays in a specified direction.

Scattering phase function:

The scattering phase function in the RTE describes how radiation energy is scattered

by a participating medium. Scattering can be classified into two categories. These are

isotropic and anisotropic scattering. Isotropic scattering indicates energy scattered equally

into all direction whereas anisotropic scattering can be forward and backward scattering.

Scattering phase function satisfies the following relation:

where is the direction from which intensity is scattered into a direction .

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Hence finally we have that energy flux scattered into a direction from all incoming

directions is:

Making an energy balance on the radiative energy traveling in the direction we have

change in the intensity found by summing all contribution from emission, absorption,

out-scattering and in-scattering

Expanding the left side of the above equation using Taylor’s Series and truncating after

the first term we would the following equation as

The above equation is known as the Radiative Heat Transfer equation in a participating

medium.

OVERALL ENERGY CONSERVATION

EQUATION7 | P a g e

Thermal radiation is one of the modes of hest transfer and must compete with conduction

and convection. So the temperature field depends on all the three modes of heat transfer.

The general form of the energy equation is:

where u = internal energy

v =velocity vector

p = radiation pressure tensor

q = total heat flux vector

= heat generated within the medium

= dissipation function

= density of the medium

As the medium is radiatively participating through emission, absorption and scattering so

the second and third effect is negligible. Assuming U=CvdT and Fourier’s law of

conduction to hold

q = qr + qc

In the absence of the heat generation

where = density of the medium

Cv = specific heat

K = thermal conductivity

T = temperature

qr = radiative heat flux

FINITE VOLUME METHOD

The basic idea of the control volume formulation is dividing the calculation domain into a

number of non-overlapping control volumes such that there is one control volume

surrounding each grid point. The differential equation is integrated over each control

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volume. Piecewise profiles expressing the variation between the grid points are used to

evaluate the required integrals. The result is the discretization equation for a group of grid

points.

The discretization equation obtained expresses the conservation principle for the finite

control volume as the differential equation expresses it for an infinitesimal control

volume.

(Fig.I)

There are four basic rules which should be kept in mind during the formulation of the

discretization equations are:

1. Consistency at the control-volume faces

2. All coefficients must always be positive

3. Negative slope linearization of the source term

4. Sum of the neighbour coefficients equal to the coefficients of the grid point under

focus.

FORMULATION OF DISCRETIZATION

EQUATION

STEADY STATE RTE:

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A scattering, absorbing and emitting medium in a square enclosure with black wall is

considered for the analysis. Discretizing the computational domain in both spatially and

angular direction, then integrating the RTE over a control volume dV and control angle

and neglecting the effect of transient term

(Fig.II)

(Fig.III)

After applying divergence theorem on LHS and intensity is assumed constant within a

control volume and a control angle the above equation can be written as

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On further simplification, for a control volume and a control angle the equation becomes

Using Step spatial differencing scheme (which sets the downstream boundary intensities

equal to the upstream nodal intensities)

(Fig.IV)

The discretized equation can be written in the following form

where

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SOLUTION PROCEDURE:

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TRANSIENT STATE RTE:

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A scattering, absorbing and emitting medium in a square enclosure with black wall is

considered for the analysis. Discretizing the computational domain in both spatially and

angular direction, then integrating the RTE over a control volume dV, control angle

and a small time interval taking into account the effect of transient term

Applying divergence theorem to the 2nd term and the magnitude of intensity is assumed to

be constant over the control volume and a control angle. Under these assumptions and

using the fully implicit scheme the above equation can be written as

where and

are the nodal intensities at the start and at the end of the time step respectively. On

further simplification, for a control volume and a control angle the equation becomes

where

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After applying the STEP scheme the final discretized equation looks like this,

In case the radiation intensity leaving a surface that is not black (i.e. gray) emits and

reflects energy diffusely, then the change in the boundary intensity would be as

following:

where the 1st term is emissivity and the 2nd

term is the reflectance of the surface.

SOLUTION PROCEDURE:

The finite volume discretization results in a set of algebraic equations with the radiation

intensities as the unknowns. An iterative method is used to solve the resulting set of

algebraic equations within each time step. The solution process adopts a marching

procedure to solve the set of equations.

The algorithm for the solution procedure is as follows:

1. Start with a suitable intensity distribution for the entire domain.

15 | P a g e

2. Proceed to the next time step.

3. Set the initial or the most current nodal intensities as the guessed values.

4. Update the upstream boundary intensities.

5. Following the marching order, calculate the nodal intensities for all internal

control volumes.

6. Calculate the radiation arriving and living the opposite walls.

7. Return to step 4 and repeat the calculation until convergence.

8. Stop when the desired time is reached or go to step 2 to advance to a new time

step.

Linear Anisotropic phase function:In the previously formulated discretized equations the participating medium was taken to

be isotropically emitting, absorbing and scattering. But in reality it doesn’t happens. The

participating medium has some anisotropicity involved in it. So in the following

formulation the linear anisotropic condition is derived and used in the code to make it

more accurate and precise to have a proper understanding of the behavior of the medium.

As seen earlier the scattering phase function is obeying the following condition

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In the finite volume method this is approximated as

where = average energy scattered from control angle l’ to the control angle l.

The scattering phase function can be represented in the form of a series

For isotropic condition M=0

For linear anisotropic condition M=1

Hence for linear anisotropy with M=1 we have

where Pm is the Legendre’s Polynomial

= Sinθ’ (cosφ’ + sinφ’ ĵ) + cosθ’

= Sinθ’ (cosφ + sinφ ĵ) + cosθ

So,

Average scattering phase function can be evaluated by

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Hence

RESULTS AND DISCUSSIONS

1.Isothermal Absorbing-Emitting Medium

The medium is maintained at a constant temperature T. The black, square enclosure is

having cold walls at 0 Kelvin. The calculation domain is discretized into 20x20 uniform

control volumes in the X and Y directions. Finer angular discretizations is used that of

2x12 control angles with uniform and in the and directions respectively.

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0.6

0.7

0.8

0.9

1

1.1

0 0.1 0.2 0.3 0.4 0.5

X

q*

PresentJohn Chai

(Fig.1)

The above figure shows dimensionless heat flux at the bottom wall which is in good

agreement with the published results.

2.Purely scattering medium

A square enclosure is considered with black walls and the medium scatters energy

isotropically with the scattering albedo ( = /) as unity. The bottom wall is hot

maintained at a temperature Th with the remaining walls maintained at 0 Kelvin.

19 | P a g e

(Fig.2)

The above figure shows dimensionless heat flux at the bottom wall which is in good

agreement with the published results.

3.Linear Anisotropically Scattering Medium

A square enclosure is considered with black walls and the medium scatters energy

anisotropically with the scattering albedo ( = /) as unity. The bottom wall is hot

maintained at a temperature Th with the remaining walls maintained at 0 Kelvin. The

phase functions are studied using 25x25 control volumes and 6x24 control angles.

20 | P a g e

(Fig.3)

The above figure shows dimensionless heat flux at the centerline in y-direction which

is in good agreement with the published results.

The figure below shows dimensionless heat flux at the centerline in y-direction. It is in

good agreement with the published results for backward scattering B2 series as both have

same number of terms in its expansion.

21 | P a g e

(Fig.4)

(Fig.5)

The above figure shows dimensionless heat flux at the centerline in y-direction. The

F1 series has more number of terms than linear forward scattering hence they do not

agree but the trend is same which assures the correctness of simulation.

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4.Collimated Incidence

The top wall of the black, square enclosure is subjected to a normal collimated incidence

(as shown in figure). The other walls are maintained at 0 Kelvin and the medium scatters

energy isotropically with a scattering albedo of unity. The domain is divided into 25 x 25

control volumes and 3 x 24 control angles in the and directions. Step scheme is used

in the present problem. The control angles are adjusted to capture the collimated

incidence.

Fig. (i) Square Enclosure with

collimated irradiation

Fig. (ii) Reflectance & Transmittance for

an enclosure with collimated beam

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(Fig.6)

Variation of wall emissivity:

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(Fig.7)

(Fig.8)

Variation of anisotropic factor:

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ε=1

ε=0.4

ε=0.8

ε=1

ε=0.8ε=0.4

(Fig.9)

(Fig.10)

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a=1

a=-1a=0

a=-1

a=0

a=1

Variation of angle of incidence:

(Fig.11)

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𝜭=90° 𝜭=45

°

𝜭=30°

𝜭=90°

𝜭=30°

𝜭=45°

(Fig.12)

5. Temporal variations of the optical signals

The bottom wall of the black, square enclosure is subjected to a normal collimated

incidence (as shown in figure). The other walls are maintained at 0 Kelvin and the

medium scatters energy isotropically with a scattering albedo of unity. A unit step pulse

as shown of a non-dimensional pulse width is used to irradiate the wall and

the different flux variation with non-dimensional time is observed.

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Fig.(a) collimated irradiation at the bottom wall.

Fig.(b) Time of arrival of the collimated square pulse at different locations.

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(Fig.13)

(Fig.14)

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Variation of Optical thickness:

(Fig.15)

(Fig.16)

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=0.5

=1

=2

=1

=2

=0.5

Variation of pulse-width:

(Fig.17)

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tp*=3

tp*=2

tp*=1

tp*=3tp*=1

tp*=2

(Fig.18)

Variation of scattering albedo:

(Fig.19)

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=1 =0.75

=0.5=0

(Fig.20)

Variation of the anisotropic factor:

(Fig.21)

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=1

=0.75

=0.5

=0

a=1

a=-1

a=0

(Fig.22)

Variation of angle of incidence:

(Fig.23)

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a=-1

a=0

a=1

=90

=45

=30

(Fig.24)

CONCLUSION Finite volume method found to be a suitable method for the simulation of

collimated incidence problem with Steady and Transient RTE.

Transmitted flux decreases considerably with the increase in optical thickness

whereas reflectance increases.

Reflected flux increases with the pulse width (nearly twice) whereas there is not much

considerable change in transmitted flux.

In the fully scattering medium both transmitted flux and reflected flux increases and

reach their maximum.

Linear forward scattering has more transmittance and less reflectance than the

isotropic condition and vice-versa for the linear backward scattering.

Transmittance decreases with the increase in the collimated angle whereas the reverse

happens in the case of reflectance.

Present study helps us to create a database for the healthy tissues.

36 | P a g e

=30

=45

=90

By comparing with the available information from the experiments, it will help

to indentify the turbid tissues (damaged) if present.

This created database will help to simulate through the inverse radiation to

obtain the unknown tissue properties.

FUTURE SCOPE OF RESEARCH

Study of the effect during the interaction of short-pulse collimated radiation in

participating medium on the transmittance and the reflectance signals for:

The different type of scheme like the CLAM scheme

The different type of pulse profile like time varying Gaussian profile

Combined conduction and radiation

Multi-dimensional enclosures

Cylindrical co-ordinates

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REFERENCES

[1] Beach H. L., Ozisik M. N. and Siewert C. E., Radiative transfer in linearly anisotropic-scattering, conservative and non-conservative slabs with reflective boundaries, Int. Jl. Heat and Mass Transfer, 14(1971)1551-1565. [2] Modest M.F., “Radiative heat transfer”. McGraw Hill International Edition, 1996

[3] Mitra K, Kumar S, Microscale aspects of thermal radiation transport and laser application, Adv Heat Transfer, 33(1999)187–294.

[4] Mitra K, Kumar S, Development and Comparison of models for light-pulse transport through scattering–absorbing media, Applied Optics, 38(1999)188-196.

[5] Guo Z., Kumar S., San K-C., “Multidimensional Monte Carlo simulation of short pulse transport in scattering media”. Jl. Of Thermophysics Heat Transfer, 14, 4(2000)504-511.

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[6] Guo Z., Kumar S., “Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media”. Appl. Opt 40(19) (2001)3156–63.

[7] Guo Z., Maruyama S., “Radiative heat transfer in inhomogeneous, non-gray and anisotropically scattering media”. International Journal of Heat and Mass Transfer 43(2000) 2325-2336.

[8] Sakami M, Mitra K, Hsu P F., “Analysis of light-pulse transport through two-dimensional scattering and absorbing media”. Journal of Quantitative Spectroscopy & Radiative Transfer 73 (2002) 169–179.

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