Assignment 6 Due on 11 Sep 2014, 11am
Remarks: This assignment concerns Hookes relation, Superposition, thermal effects, and definition of plane
stress/strain. Consider the standard basis e for E for
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 26
10 Nov 2014
Practice Problem 26.1 Consider a cylindrical bar of unstrec
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 10
Practice Problem 10.1 (a) Prove that if the given displacement u and sa
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 13
Practice Problem 13.1 Consider a hanging bar fixed at upper end as show
B. L. Sharma
ME321: Advanced Mechanics of Solids: 2013
Home work Solution 1.1.
Checking Linear Independence of Vectors: Let C1 , C2 , C3 be real numbers. Since b is a basis for
R3 , its elements are l
Assignment 8 Solution
Solution 8.1 The displacement components in the Cartesian Coordinates and Polar Coordinates are related
as
u1 (x1 , x2 ) = ur (r, ) cos u (r, ) sin ,
u2 (x1 , x2 ) = ur (r, ) sin
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 11
Practice Problem 11.1 (a) Derive Hookes relation from a quadratic strai
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 7
Practice Problem 7.1 Consider a body and suppose that an arbitrary point
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 16
25 Sep 2014
e3
!
R
e2
e1
Figure 16.1: Problem 1.
Practice Problem 16.1
B. L. Sharma
Practice Problem 1.1. Let
1 , e
2 , e
3 ,
e
form a right handed orthonormal basis for E. Let x E be represented by its components x1 , x2 , x3 along the
three axes. Consider the vector va
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 17
29 Sep 2014
Practice Problem 17.1 Given the stress function : (x1 , x2
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 4
Practice Problem 4.1 The state of stress throughout a body B, with respe
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 18
9 Oct 2014
Practice Problem 18.1 Consider the axisymmetric problem of a
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 12
Practice Problem 12.1 A simply connected body B has total strain under
Assignment 9 Solution
c < x2
. Assume body forces are zero and only
)=
0 r
< x1
. Assume body forces are zero and only
ace example, consider the case of a concentrated force system acting at the origi
ME321: Advanced Mechanics of Solids
2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 3
Problem 1. There is a disk of mass m and radius R as shown in Fig. 1. Als
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 9
Practice Problem 9.1 A small strain deformation is specified by the disp
B. L. Sharma
ME321: Advanced Mechanics of Solids: 2013
Assignment 1
Due on 7 Aug 2014, 11am
Remarks: This assignment concerns linear spaces and linear transformations. Inner-product is not needed
to s
Assignment 10 Solution
Solution 10.1
(ii)
(i) = (,ii ) = (,ii ),j = (,j ),ii =
.
k = (lkm ijk uj,il ) e
m ,
( u) = (ijk uj,i ) e
m = (li mj lj mi ) uj,il e
m ,
= (klm ijk uj,il ) e
m um,ll e
m = ( u)
Assignment 3 Due on 21 Aug 2014, 11am
Remarks: This assignment concerns Cauchy stress and local equilibrium. Assume that e is the standard basis
e
for E for all problems in this assignment. The supers
ME321: Advanced Mechanics of Solids: 2014-15 1st Semester
Practice Problems prepared by Teaching Assistants, based on lecture 5
Practice Problem 5.1 Suppose e is the standard basis for E. Ignore the s
Natural Convection:
Correlations and slides
General Considerations (cont)
Pertinent Dimensionless Parameters
Grashof Number:
g Ts T L3
GrL
2
Buoyancy Force
Viscous Force
L characteristic length of
Internal Flow:
Forced Convection
Entrance Conditions
Entrance Conditions
Must distinguish between entrance and fully developed regions.
Hydrodynamic Effects: Assume laminar flow with uniform velocit
Transient Conduction:
Spatial Effects
Heat Transfer, Autumn 2016
IIT Kharagpur
Plane Wall
Solution to the Heat Equation for a Plane Wall with
Symmetrical Convection Conditions
If the lumped capacitan
Conduction: Theory of Extended
Surfaces
Why extended surface?
h, T
q
q hA(Ts T )
Increasing h
Increasing A
2
Fins as extended surfaces
A fin is a thin component or appendage attached to a
larger body
Condensation Heat
Transfer
Condensation on a Vertical Surface
Heat transfer to a surface occurs by condensation when the
surface temperature is less than the saturation temperature of an
adjoining vap
CORRELATIONS FOR CONVECTIVE HEAT TRANSFER
I. CORRELATIONS FOR FORECD CONVECTION
1. Forced convection from flat plate
Flow regime
Laminar, local
Range of application
Tw const , Re x 5 105 ,
Correlation