IGNOU MPHE 26 2026 - Using the transport equation for a non-multiplying system and homogene

Question

Using the transport equation for a non-multiplying system and homogeneous assembly, derive the integral form of transport equation using the method of characteristics. What do you understand by "Optical path length" of the medium?

19 Jan 2026

Answer :

Word Count : 287

The transport equation for a steady-state, non-multiplying, and homogeneous system without an external source is: [ \vec{\Omega} \cdot \nabla \psi(\vec{r}, \vec{\Omega}, E) + \Sigma_t \psi(\vec{r}, \vec{\Omega}, E) = \int_{4\pi} d\Omega' \int_0^\infty dE' , \Sigma_s(E' \to E, \Omega' \cdot \Omega) \psi(\vec{r}, \vec{\Omega}', E') ] For simplicity, consider monoenergetic neutrons and no scattering. The equation reduces to: [ \vec{\Omega} \cdot \nabla \psi(\vec{r}, \vec{\Omega}) + \Sigma_t \psi(\vec{r}, \vec{\Omega}) = 0 ] The method of characteristics converts the partial differential equation into an ordinary differential equation along the neutron path (characteristic line). Let (s) be the path length along

__________ ______ ____ ___ _____ ________ ________ ______ _______ ____ _____ _________.
___ _____ _____ ________ _____ ____ _______ _____ __________ _______ _____.
_______ ________ ______ _____ _____ ________ _________ ___.
________ _________ ____ _______ ____ _____ ______ ________ ______ _________ ______ ____.
____ _______ _______ __________ _______ ____ _____ _________ ________ _____ ____ __________.
__________ _________ ____ ___ _____ ______ ___ _____ ________ ______ __________.
______ ________ _____ _________ ________ ________ _________ ________ ____.
_________ _______ ____ ______ __________ ____ ___ ________ _____ __________ ___.
______ __________ ________ ______ _____ ________ _____ ___.
____ ______ _____ ______ _____ _______ ________ _________ ______.
________ _______ _________ ___ _____ ____ ___ _______ _____ ______ _______ _____.
_______ ___ ______ _________ _______ __________ _________ ____.
_______ ____ ______ _______ ____.
________ _______ ____ ___ _____ ________.
_______ __________ _______ __________ _____ _________.
______ _______ ____ ________ ___.
_________ _____ _____ __________ ___ ______ _______ _____.
____ ________ ________ ______ __________ _____.
________ _______ ____ ___ ________.
____ ____ ________ _____ _____ ________ ______ ___ _____ ____ ______.
___ ___ __________ ________ __________ ______.
__________ __________ _____ _________ __________ ____.
________ ______ _____ ________ ___.

IGNOU ACADEMY

Your IGNOU journey, made easier.

Solved Assignments
Study Notes
Guess Papers
Question Papers

Call Us WhatsApp

STUDY • PREPARE • SUCCEED

Skip in 10

IGNOU Solved Assignments Assignments Ignou Projects Project Previous Year Solved Exam Papers Notes Notes Sample Question Papers Sample Question Papers