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CN5040 Advanced Transport Phenomena Homework Assignment 1

This document provides the homework assignment for an advanced transport phenomena course. It includes two problems with multiple parts each to solve. Problem 1 involves using Einstein notation to prove vector identities, while Problem 2 involves calculating gradient and divergence operations and volume integrals over a sphere. Students are instructed to turn in their work for the problems marked with an asterisk at the next lecture.

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115 views1 page

CN5040 Advanced Transport Phenomena Homework Assignment 1

This document provides the homework assignment for an advanced transport phenomena course. It includes two problems with multiple parts each to solve. Problem 1 involves using Einstein notation to prove vector identities, while Problem 2 involves calculating gradient and divergence operations and volume integrals over a sphere. Students are instructed to turn in their work for the problems marked with an asterisk at the next lecture.

Uploaded by

bala sai
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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CN5040 Advanced Transport Phenomena

Homework Assignment 1

Turn in the completed assignment (the problems with *) at the end of forthcoming
lecture.

1. Use the Einstein notation to prove the following:


(a) a × ( b × c ) = (a ⋅ c )b − (a ⋅ b)c
(b) ∇ × ∇f = 0
(c) ∇ ⋅ ∇ × a = 0

2. Determine the following:


1
*(a) ∇∇
r
*(b) Volume integral of rr over a sphere of radius R.

(c) Volume integral of rrrr over a sphere of radius R (hint: the resulting 4th-rank
tensor is a combination of δij).

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