THERMODYNAMICS
AND HEAT TRANSFER
MODULE – 1I
SYLLABUS
• Mechanism of different modes of heat transfer viz. Conduction,
Convection and Radiation & various applications. General heat
conduction equation in various coordinates, Formulation of
heat transfer problems using different boundary conditions
with and without heat generation. Insulation materials and Fins.
Introduction to unsteady state heat conduction- Lumped
capacity analysis. Numerical problems
INTRODUCTION
• Transfer of heat as a result of temperature difference
• Also tells us the Rate of heat transfer
• Thermodynamics – can predict the final equilibrium temperature
but not the time taken to reach equilibrium temperature
• Eg: Cooling of a hot steel bar: TD – final eqbm temp, HT – time
taken to reach the eqbm temp.
MODES OF HEAT TRANSFER
• Conduction – direct contact of particles. Eg: HT in solids
• Convection – bulk movement of fluids. Eg: HT in liquids/Gases
• Natural Convection
• Forced Convection
• Radiation – electromagnetic waves. Does not require a medium. Eg:
HT from Sun
APPLICATIONS
• Fermentation processes
• Protein purification and Enzyme Reactions
• Bioreactor temperature control
• Cryopreservation
• Heat shock in Genetic engineering
• Thermal Sterilization
• Thermal treatment of Biodegradable waste
HEAT CONDUCTION
• Fourier’s law
Q dT Drivingforce T
k Rate Q
A dx Resistance x
kA
Q Heat transferred, W States that the “rate of heat flow by
A Area,m2 conduction, Q” is proportional to the
k Thermalconductivity, W m-1K-1 “area normal to the direction of heat
dT flow, A” and to the “temperature
Temperature Gradient,K m-1
dx gradient in the direction of heat flow,
dT/dx”.
HEAT CONDUCTION
• Fourier’s law
• The constant of proportionality is called Thermal Conductivity, k (W/m-1K-1)
• The negative sign says that heat flows in the direction of decreasing
temperature.(To make the value of Q positive)
• Heat Flux – The quantity of heat transferred per unit area per unit time.
• Steady state – Temperature is a function of position only.
HEAT CONDUCTION
• Fourier’s law – Assumptions
• Steady state heat conduction
• Heat flow is unidirectional
• Temp gradient is constant/Temp profile is linear
• No internal heat generation
• The boundary surfaces are isothermal
• The material is homogeneous and isotropic
THERMAL CONDUCTIVITY, K
• Ability of the material to conduct heat. Helps to measure of the amount of heat
that can flow through a given material.
• Good thermal conductor – high thermal conductivity
• Thermal conductivity is the quantity of heat passing through a quantity of material of unit
thickness with unit heat flow area in unit time when a unit temperature difference is maintained
across the opposite faces of the material.
• Typical Values: Solids – 2.3 to 420 W/m-1K-1
• Liquids – 0.09 to 0.7 W/m-1K-1
• Gases – 0.006 to 0.6 W/m-1K-1
THERMAL CONDUCTIVITY, K
• Factors affecting thermal conductivity
• Nature of the material
• Temperature
• A material having kx=ky=kz is called an isotropic material.
STEADY STATE CONDUCTION – ONE DIMENSION
• The Plane Wall T1
k, A
• Eg: Heat flow through the wall of a stirred
Q
tank containing hot or cold fluid T2
• Assumptions
• Uniform thickness
• Constant cross-sectional Area ∆x
• k is independent of temperature
Q T T
• A>>>∆x – heat losses are negligible from the edges k 1 2
• Steady state
A x
STEADY STATE CONDUCTION – ONE DIMENSION
By Fouriers Law
Both resistance and
dT
Q - kA conductance of the material
dx
depends on the dimensions
Integratin g from x 0 to x x
of the solid as well as the
x T2
thermal conductivity of the
Qdx kAdT
0 T1 material
Q x kA (T2 T1 )
(T2 T1 ) (T1 T2 ) Driving force
Q kA
x x Resistance
kA
STEADY STATE CONDUCTION – ONE DIMENSION
• The Composite Wall
STEADY STATE CONDUCTION – ONE DIMENSION
• The Composite Wall
q A q B qC q
T1 T2 T T T T
qA ; qB 2 3 ; qC 3 4
x A xB xC
kA A kB A kC A
x x x
T1 T4 q A B C
k A A k B A kC A
Thermal Potential Difference
q
T Heat Flow
x A xB xC Thermal Resistance
k A A k B A kC A
STEADY STATE CONDUCTION – ONE DIMENSION
• Hollow Cylinder
• Composite Cylinders
• Heat transfer through spherical coordinates
• Composite spheres
• Systems with variable k - Variable thermal conductivity(in notes) Also different kinds of
problems
• General Heat conduction equation in 3 dimensions
• With and without heat generation
• Using different boundary conditions
