ME-605
HEAT & MASS TRANSFER
(BY: SAUMENDRA SHARMA, Asst. PROF. DEPARTMENT OF MECHANICAL ENGINEERING, G.I.I.T. )
Syllabus (According to R.G.P.V.)
UNIT 1 : Basic Concepts: Models of heat transfer, Fourier’s law, Newton’s
law, Stefan Boltzmann law, Thermal resistance and conductance, Analogy
between flow of heat and electricity, Combined heat transfer process.
Conduction: Fourier heat conduction equation, Its form in rectangular,
cylindrical and spherical coordinates, Thermal diffusivity, Linear one
dimensional steady state conduction through a slab, tubes, spherical shells
and composite structures, Electrical analogy, Critical insulation, Thickness
for pipes, Effect of variable thermal conductivity.
Introduction: When we starts study of heat transfer the first question arise in
our mind is that what is the difference between heat and temperature and why we
study heat transfer? Because in earlier classes we studied thermodynamics, so what
is the need of heat and mass transfer?
Difference between heat and temperature:
Temperature is a measure of the amount of energy possessed by the molecules of a
substance. It is a relative measure of how hot or cold a substance is and can be
used to predict the direction of heat transfer. The usual symbol for temperature is
T. The scales for measuring temperature in SI units are the Celsius and Kelvin
temperature scales.
On the other hand, heat is energy in transit due to temperature
difference. The transfer of energy as heat occurs at the molecular level as a result
of a temperature difference. The usual symbol for heat is Q. Common units for
measuring heat are the Joule and calorie in the SI system.
Difference between thermodynamics and heat transfer:
When we talking about thermodynamics then we defined it as follows:
“ Thermodynamics is an axiomatic science which deals with the relations among
heat, work, and properties of system which are in equilibrium (Thermal, Chemical,
mechanical). It describes state and changes in state of physical system.”
It means Thermodynamics tells us:
1. how much heat is transferred
2. how much work is done
3. final state of the system
For example consider the cooling of a hot steel bar which is placed in under water
spray. Thermodynamics may be used to predict the final equilibrium temperature
of the steel bar water combination. Thermodynamics will not tell us how long it
takes to reach this equilibrium condition or what the temperature of the bar will be
after a certain length of time before the equilibrium condition is attained.
While heat transfer may be used to predict the temperature of both bar and
water as a function of time. Hence heat transfer may be defined as follows:
“ The transmission of energy from one region to another region as result of
temperature difference between them.”
It means Heat transfer tells us:
• How (with what modes) heat is transferred
• At what rate heat is transferred.
• Temperature distribution inside the body
Importance of heat transfer:
In field of Electrical engineering for the design of cooling systems for
motor, generator, transformer. In field of Chemical engineering
evaporation, condensation, heating and cooling of fluids. In field of Civil
engineering designing of buildings, construction of dams. In field of
Mechanical engineering cooling of I. C. engine, heat exchanger, steam
generation, refrigeration.
Modes of Heat Transfer:
There are three different modes of heat transfer:
1. Conduction
2. Convection
3. Radiation
Conduction:
An energy transfer across a system boundary due to a
temperature difference by the mechanism of inter-molecular interactions.
Conduction needs matter and does not require any bulk motion of matter.
Conduction rate equation is described by the Fourier Law:
q =−kA∇T
where: q = heat flow vector, (W)
k = thermal conductivity, a thermodynamic property of the
material.
(W/m K)
A = Cross sectional area in direction of heat
flow. (m2) ∇T = Gradient of temperature (K/m)
= ∂T/∂x i + ∂T/∂y j + ∂T/∂z k
Note: Since this is a vector equation, it is often convenient to work
with one component of the vector. For example, in the x direction:
qx = - k Ax dT/dx
In circular coordinates it may convenient to work in the radial
direction: qr = - k Ar dT/dr
Convection:
An energy transfer across a system boundary due to a temperature
difference by the combined mechanisms of intermolecular interactions and
bulk transport. Convection needs fluid matter.
Newton’s Law of Cooling:
where:
q = h As ∆T
= heat flow from surface, a scalar,
q (W)
= heat transfer coefficient (which is not a thermodynamic
h property of
the material, but may depend on geometry of surface,
flow
characteristics, thermodynamic properties of the fluid,
etc. (W/m2 K)
As = Surface area from which convection is occurring (m2)
Radiation:
Radiation heat transfer involves the transfer of heat by electromagnetic
radiation that arises due to the temperature of the body. Radiation does not need
matter.
Emissive power of a surface:
E=σεTs4 (W/ m2)
where: ε= emissivity, which is a surface property (ε= 1 is black
body)
σ= Steffan Boltzman constant = 5.67 x 10-8 W/m2 K4.
Ts = Absolute temperature of the surface (K)
ONE DIMENSIONAL STEADY STATE HEAT CONDUCTION:
The plane wall:
The differential equation governing heat diffusion is:
k 0 dx dx
With constant k, the above equation may be integrated twice to obtain the general
solution:
T (x) = C1 x +C2
where C1 and C2 are constants of integration. To obtain the constants of
integration, we apply the boundary conditions at x = 0 and x = L, in which case
T (0) = Ts,1
and
T (L) =Ts,2
Once the constants of integration are substituted into the general equation, the
temperature distribution is obtained:
−T
T (x) =(T
s,2
The heat flow rate across the wall is
given by:
dT/kA
s,1
x
) +T
L s,1
Ts,1 −Ts,2
qx =−kA dx =L (Ts ,1 −Ts,2 ) = L / kA