This document discusses inverse heat conduction problems. It begins by explaining that inverse heat transfer techniques are used to determine boundary conditions and heat fluxes based on measured temperature fields, since measuring these directly can be difficult. It notes that these problems are ill-posed and require optimization techniques to solve. The document then contrasts direct and inverse heat transfer problems. It provides several examples of applications for inverse heat transfer. Finally, it discusses objective functions and optimization techniques commonly used to solve inverse heat conduction problems, including the conjugate gradient method.

1. INVERSE HEAT CONDUCTION
PREPARED BY
SOUVIK GHOSH
BRANCH- THERMAL ENGINEERING
ROLL NO- 1757004

2. INTRODUCTION
 Inverse heat transfer technique is used to find the
heat flux,boundary conditions of a wall or duct from
the measured temperature field. There are many
situations in heat transfer problem where direct
measurement of boundary conditions and the inlet
conditions are difficult,in that case we use inverse
heat transfer method to retrieve the problem.
 Inverse heat conduction problems are ill-posed
problems i.e. the solutions may not be unique or it
may change with slight variation in the input
variable. These types of problems are solved by the
use of optimization technique.

3. DIRECT HEAT TRANSFER
PROBLEM
 The cause (boundary
conditions,heat flux or
source temperature) is
given and the effect
(temperature field in the
body) is determined.
INVERSE HEAT TRANSFER
PROBLEM
 The effect is known and the
cause has to be
determined. The
temperature field is
determined by some
measuring instrument and
from that measured
temperature field we have
to determine the initial
boundary conditions and
heat flux.

4. APPLICATIONS
 When a space vehicle enters into the atmosphere the
surface temperature of the thermal shield is very high so
the heat flux can’t be measured directly. In this case we
use inverse heat transfer technique. Temperature sensors
are placed beneath the heated surface.From the
measured temperature we can evaluate heat flux.

5.  In many applications of the heat transfers the surfaces are
directly subjected to fire so the direct measurements of
heat flux at that surface is very difficult.
 But it can readily be estimated by an inverse analysis
utilizing transient temperature recordings taken at a
specified location beneath the surface.

6. MORE APPLICATIONS
 Estimation of thermophysical properties of materials.
Ex:-estimation of temperature dependency of thermal
conductivity of a cool ingot during steel tempering.
 Estimation of inlet condition and boundary heat flux in
forced convection inside ducts.
 Estimation of bulk radiation properties and boundary
conditions in absorbing,emitting and scattering semi-
transparent materials.
 Monitoring radiation properties of reflecting surfaces of
heaters and cryogenic panels.
 Estimation of timewise varying unknown interface
conductance between metal solidification and metal
mould during casting.

7. OBJECTIVE FUNCTION
Heat flux
Qх
θm
inlet
It is a rectangular duct the bottom
plate is insulated and the top plate
is subjected to some heat flux Qх.
Now applying the heat transfer
concept the governing equation can
be written as
insulated
𝜕²θ
𝜕𝑦²
= (1 α)
𝜕θ
𝜕𝑡
Where θm= inlet temperature
α= thermal diffusuvity
Boundary conditions:- At y=0,
𝜕θ
𝜕𝑦
= 0 i. e. the plate is insulated
At y=b , there is heat flux Qх
At inlet condition θ=θm and at initial time θ=0

8. If we know the value of θm and heat flux Qx then we can solve the temperature
Inside the duct.
If suppose Qx and θm are unknown then we can’t solve the problem
These values can be determined by the inverse technique.We place the sensors
Inside the domain and we take the readings.By this temperature readings we apply
The optimization technique.The optimization technique must contain some
objective functions.The objective function is nothing but the difference between
square of the two temperatures.One is the measured temperature at the sensor and
Other is the calculated temperature.
J(Qx)- 1<𝑡<𝐷
1<𝑚<𝑀
[θ𝑐(Xm,Ym,t)-θm(Xm,Ym,t)]²
m= no of mounted sensors
θc(Xm,Ym,t)= calculated temperature
at the measurement locations, θm(Xm,Ym,t)= measured temperature taken at D
discrete time intervals. Our basic aim is to minimized the objective function by
applying some optimization techniques.

9. OPTIMIZATION TECHNIQUES
 DETERMINISTIC METHODS
 Newton- gauss method
 Levenberg – marquardt’s
method
 Conjugate gradient
method
 Newton’s method
 Quasi-newton method
 Steepest descent methode
 STOCHASTIC METHODS
 Generic algorithms
 Differential evolution
algorithms
 Particle swarm
optimization
 Simulated annealing
Conjugate gradient method is used extensively for solving inverse heat conduction
Problem.

10. SOURCE PHYSICAL
SITUATION
METHODOLOGY ESTIMATION
Huang and
Ozisik,NIIT,1992
Laminar forced
convection in parallel
plate channel
CGM Boundary heat flux
Li and Yan, JHT, 2000 Laminar forced
convection in an annular
duct
CGM Space and time
dependent inner wall
heat flux
Lin et al,IJHMT,2007 Laminar forced
convection in parallel
plate channel with wall
conduction effect
CGM Space and time
dependent boundary
heat flux
Colaco and
Orlandc,NIIT,2001
Laminar forced
convection in 2-D
irregularly shaped
channel
CGM Space and time
dependent boundary
heat flux
Huang and
chen,IJHMT,2000
Laminar forced
convection in 3-D channel
CGM Space and time
dependent boundary
LITERATURE REVIEW

11. THANK YOU