The document outlines essential concepts of steady state heat conduction, including heat conduction equations in various coordinates, boundary and initial conditions, and thermal resistance. It further explores heat conduction in plane walls, cylinders, and spheres while discussing the effects of thermal contact resistance and thermal resistance networks. Additionally, it addresses critical radius of insulation for different geometries.

1. HEAT TRANSFER :
STEADY STATE HEAT CONDUCTION
Prof. Pramod Maurya AP, SCOE, KHARGHAR 1
1. GENERAL HEAT CONDUCTION EQUATION : Rectangular Coordinates
2. GENERAL HEAT CONDUCTION EQUATION : Cylindrical and
Spherical Coordinates
3. BOUNDARY AND INITIAL CONDITIONS
4. STEADY HEAT CONDUCTION IN PLANE WALLS
5. The Thermal Resistance Concept
6. THERMAL CONTACT RESISTANCE
7. GENERALIZED THERMAL RESISTANCE NETWORKS
8. HEAT CONDUCTION IN CYLINDERS & SPHERES
9. CRITICAL RADIUS OF INSULATION

2. Prof. Pramod Maurya AP, SCOE, KHARGHAR 2
1. GENERAL HEAT CONDUCTION EQUATION : Rectangular Coordinates

3. Prof. Pramod Maurya AP, SCOE, KHARGHAR 3
Contd….

4. Prof. Pramod Maurya AP, SCOE, KHARGHAR 4
---------- Fourier-Biot equation
Contd….

5. Prof. Pramod Maurya AP, SCOE, KHARGHAR 5
2. GENERAL HEAT CONDUCTION EQUATION : Cylindrical Coordinates
GENERAL HEAT CONDUCTION EQUATION : Spherical Coordinates

6. Prof. Pramod Maurya AP, SCOE, KHARGHAR
3. BOUNDARY AND INITIAL CONDITIONS
6
• The mathematical expressions of the thermal conditions at the boundaries are called
the boundary conditions.
• The temperature at any
point on the wall at a
specified time also depends
on the condition of the wall
at the beginning of the heat
conduction process. Such a
condition, which is usually
specified at time t = 0, is
called the initial condition.

7. Prof. Pramod Maurya AP, SCOE, KHARGHAR
4. STEADY HEAT CONDUCTION IN PLANE WALLS
7
The energy balance for the wall can be
expressed as
Separating the variables in the above equation
and integrating
from x = 0, where T(0) = T1,
to x = L, where T(L) = T2, we get

8. Prof. Pramod Maurya AP, SCOE, KHARGHAR
5. The Thermal Resistance Concept
8
The heat conduction through a plane wall
can be rearranged as
a. Thermal circuit diagram for Conduction only b. Thermal circuit diagram for Convection only

9. Prof. Pramod Maurya AP, SCOE, KHARGHAR 9
c. The thermal resistance network for heat transfer through a plane wall subjected to
convection on both sides
where U is the overall heat transfer coefficient

10. Prof. Pramod Maurya AP, SCOE, KHARGHAR 10
d. Multilayer Plane Walls

11. Prof. Pramod Maurya AP, SCOE, KHARGHAR
6. THERMAL CONTACT RESISTANCE
11
• In reality, a surface is microscopically rough
no matter how smooth it appears to be.
• An interface contain numerous air gaps of
varying sizes that act as insulation because of
the low thermal conductivity of air
• Thus, an interface offers some resistance to
heat transfer, and this resistance per unit
interface area is called the thermal contact
resistance, Rc

12. Prof. Pramod Maurya AP, SCOE, KHARGHAR
7. GENERALIZED THERMAL RESISTANCE NETWORKS
12
a) Thermal resistance network for two
parallel layers
b) Thermal resistance network for combined
series-parallel arrangement

13. Prof. Pramod Maurya AP, SCOE, KHARGHAR
8. HEAT CONDUCTION IN CYLINDERS & SPHERES
13
A. cylindrical layer
Where, A = 2πrL
integrating
from r = r1, where T(r1) = T1,
to r = r2, where T(r2) = T2,
gives
Where
B. Spherical layer
Where
C. Cylindrical (or Spherical) shell subjected to
convection

14. Prof. Pramod Maurya AP, SCOE, KHARGHAR
CONTD…
14
C. Cylindrical (or Spherical) shell subjected to convection
for a cylindrical layer
for a spherical layer

15. Prof. Pramod Maurya AP, SCOE, KHARGHAR
CONTD…
15
D. Multilayered Cylinders and Spheres
The interface temperature T2 between the first and
second cylindrical layers can be determined from

16. Prof. Pramod Maurya AP, SCOE, KHARGHAR
8. CRITICAL RADIUS OF INSULATION
16
From thermal network, the
heat transfer rate :
differentiating above equation
with respect to r2 and equating
it to zero
A. For Cylinder
A. For Sphere

17. Prof. Pramod Maurya AP, SCOE, KHARGHAR 17