1. STEADY HEAT CONDUCTION
AZIZUL BIN MOHAMAD
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2. Steady State 1-D Conduction
Assumptions
Temperature varies in only one coordinate directions
Energy Balance still applies but time term goes to zero
Soln’s dependent on coordinate systems
Plane Wall
Linear T
Constant heat flux and rate
Cylinder
Logarithmic T
Constant heat rate
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3. 1-D HEAT CONDUCTION
1-D heat transfer through a simple or composite body exposed to convection from both sides to mediums at temperatures Ts,1 and Ts,2 can be expressed as
Where Rtotal is the total thermal resistance between the two mediums.
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4. Thermal Resistance
Will utilize circuit analysis methods making analogy between heat flux and electric current.
Electricity
Thermal Conduction
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5. Convection Resistance
Thermal Circuit Planar Wall
Constant q throughout the circuit
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7. For a plane wall exposed to convection on both sides, the total resistance is expressed as:
This relation can be extended to plane walls that consist of two or more layers by adding an additional resistance for each additional layer.
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8. Conduction resistance (plane wall):
The elementary thermal resistance relations can be expressed as follows:
Conduction resistance (plane wall):
Conduction resistance (cylinder):
Conduction resistance (sphere):
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9. Convection resistance Interface resistance Radiation resistance
Rc = thermal contact resistance
hc = thermal contact conductance
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10. Composite Wall
Heat rate still constant across. But Temperature gradient changes
Can use to find internal temperature distributions
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11. Parallel Walls Uniform Temperature at 1 and 2
Heat flux split between sections
Thermal Resistance based on local areas
Set up system of equations based upon energy balance into nodes
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12. A 3-m-high and 5-m-wide wall consists of long 16-cm x 22-cm cross section horizontal bricks (k = 0.72 W/m.°C) separated by 3-cm thick plaster layers (k = 0.22 W/m.°C).
There are also 2-cm- thick plaster layers on each side of the brick and a 3-cm-thick rigid foam (k = W/m.°C) on the inner side of the wall.
The indoor and the outdoor temperatures are 20°C and -10°C, and the convection heat transfer coefficients on the inner and the outer sides are h1=10W/m2.°C and h2=25W/m2.°C, respectively.
Assuming one-dimensional heat transfer and disregarding radiation, determine the rate of heat transfer through the wall.
Ans: q = 4.38 W Qtotal = 263 W
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13. Radial Steady State Conduction
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15. Derivation of Cylindrical Conduction
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16. Composite Radial Wall Similar concept to the planar wall
Apply thermal circuit to each wall
Add the resistances that are in series
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17. The radial heat rate is constant across the circuit
Can analyze in sections or across complete circuit depending on problem
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18. Spherical Coordinates
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19. Conduction with generation
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20. With equal wall temps
Becomes parabolic
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21. Once the rate of heat transfer is available, the temperature drop across any layer can be determined from:
The thermal resistance concept can also be used to solve steady heat transfer problems involving parallel layers or combined series-parallel arrangement
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22. Radial Generation Typical in electrical heating elements (wires)
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