1. SUBJECT : HEAT & MASS TRANSFER Date : 15/02/2013
Lecture 5
SUBJECT : HEAT & MASS TRANSFER
Date : 15/02/2013

2. Methodology of a Conduction Analysis
Specify appropriate form of the heat equation.
Solve for the temperature distribution.
Apply Fourier’s Law to determine the heat flux.
Simplest Case: One-Dimensional, Steady-State Conduction with No
Thermal Energy Generation.
Common Geometries:
The Plane Wall: Described in rectangular (x) coordinate. Area perpendicular to direction of heat transfer is constant (independent of x).
The Tube Wall: Radial conduction through tube wall.
The Spherical Shell: Radial conduction through shell wall.

3. Plane Wall
The Plane Wall
Consider a plane wall between two fluids of different temperature:
Heat Equation:
(3.1)
Implications:
Boundary Conditions:
Temperature Distribution for Constant :
(3.3)

4. Heat Flux and Heat Rate:
Plane Wall (cont.)
Heat Flux and Heat Rate:
(3.5)
(3.4)
Thermal Resistances and Thermal Circuits:
Conduction in a plane wall:
(3.6)
Thermal circuit for plane wall with adjoining fluids:
(3.12)
(3.11)

5. Composite Wall with Negligible Contact Resistance:
Plane Wall (cont.)
Composite Wall with Negligible
Contact Resistance:
i.e. wall of different material layers
E.g. wall of house where paint..plaster..brick..plaster..paint
Wall of HX
Tightly fitted
Let L – thickness of different material
K – thermal conductivity of wall material
T – temperature variation in wall
For series connection Q must be same
Assumptions Made:
Perfect contact between two layers
No fall of temperature at interface

6. Plane Wall (cont.)
Thermal Resistance for Unit Surface Area:
Heat conduction through composite wall be considering Thermal contact Resistance
Contact Resistance: No perfect contact between two layers of composite wall
Presence of air or gas in voids offer very high value of resistance
Leads to large drop of temperature of interface
Values depend on: Materials A and B, surface finishes, interstitial conditions, and contact pressure (Tables 3.1 and 3.2)

7. Series – Parallel Composite Wall:
Plane Wall (cont.)
Series – Parallel Composite Wall:

8. Series – Parallel Composite Wall:
Plane Wall (cont.)
Series – Parallel Composite Wall:
Parallel Composite Wall:
For series connection :

9. In actual practice surrounded to wall/slab layer of fluid is available
Fluid is present on both side of wall
One may be hot and another may be cold on both sides.
In this case HT by convection is predominant i.e. hot fluid will give heat to wall. Wall will transfer to cold fluid.
Convection:

10. Plane Wall (cont.)

11. Composite Wall with Negligible Contact Resistance:
Plane Wall (cont.)
Composite Wall with Negligible
Contact Resistance:
i.e. wall of different material layers
E.g. wall of house where paint..plaster..brick..plaster..paint
Wall of HX
Tightly fitted

12. The Tube Wall Heat Equation:
(3.23)
What does the form of the heat equation tell us about the variation of with
in the wall?
Is the foregoing conclusion consistent with the energy conservation requirement?
How does vary with ?
Temperature Distribution for Constant :
(3.26)

13. Heat Flux and Heat Rate:
Tube Wall (Cont.)
Heat Flux and Heat Rate:
(3.27)
Conduction Resistance:
(3.28)
Why is it inappropriate to base the thermal resistance on a unit
surface area?

14. But, U itself is tied to specification of an interface.
Tube Wall (Cont.)
Composite Wall with
Negligible Contact
Resistance
(3.30)
But, U itself is tied to specification of an interface.
(3.32)

15. Spherical Shell Heat Equation
What does the form of the heat equation tell us about the variation of
with ? Is this result consistent with conservation of energy?
How does vary with ?
Temperature Distribution for Constant :

16. Spherical Shell (cont.)
Heat flux, Heat Rate and Thermal Resistance:
(3.35)
(3.36)
Composite Shell:

17. Problem: Thermal Barrier Coating
Problem 3.23: Assessment of thermal barrier coating (TBC) for protection
of turbine blades. Determine maximum blade temperature
with and without TBC.
Schematic:

18. Problem: Thermal Barrier (Cont.)
ANALYSIS: For a unit area, the total thermal resistance with the TBC is
With a heat flux of
the inner and outer surface temperatures of the Inconel are

19. Problem: Thermal Barrier (Cont.)

20. Problem: Radioactive Waste Decay
Problem 3.62: Suitability of a composite spherical shell for storing
radioactive wastes in oceanic waters.

21. Problem: Radioactive Waste Decay (Cont.)