Heat Transfer Through Extended Surface
1. Objective
To determine the temperature distribution and heat flow along the extended surface and comparing the data with theoretical analysis
2. Equipment Required
Heat transfer service unit
Extended surface heat transfer accessory
Data logging accessory
3. Theory
The term extended surface is commonly used to depict an important special case involving heat transfer by conduction within a solid and heat transfer by convection (and/or radiation) from the boundaries of the solid. Extended surfaces are used to increase the surface area and to increase the total rate of heat transfer. A temperature gradient exist between two different temperature surfaces for heat transfer. The temperature distribution along the fin or pin must be known to determine the heat transfer from the surface to its surroundings. Plate fins are mostly used in aircrafts, cryogenic and other industries. By considering the insulated tip extended surface the temperature distribution in terms of hyperbolic function expressed as
θ/θₒ = Cosh[m(b-x)]/ Cosh(mb) (1)
Where, θ = T(x) - T∞ (⁰C) θₒ = To - T∞ (⁰C)
To = fin base temperature (⁰ C)
T∞= free stream fluid temperature (⁰C) b = fin height (m) x = coordinate (m) m = (4h /k d)½ (1/m) h = heat transfer coefficient (W/m² ⁰C) k = thermal conductivity of fin (W/m ⁰C) d = fin diameter (m)
The heat transfer, Q, for a pin fin is found using the relation
Q = (h P k A)½ tanh(m b) (2)
Wh...
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... 4.5In = 0.1125m
Tx = 45.56 ⁰C
At x = 6In = 0.15m
Tx = 44.17 ⁰C
5. At 16V,
To = 47.2 ⁰C , T∞ = 22.78 ⁰C
Heat Transfer Q = √(hPKA) (To - T∞) tanh(mb)
Q = √0.0422 х (47.2 – 22.78) tanh( 9.01 х 0.1524)
Q = 4.413 W
At 25V,
To = 67.7 ⁰C , T∞ = 22.78 ⁰C
Heat Transfer Q = √(hPKA) (To - T∞) tanh(mb)
Q = √0.0422 х (67.7 – 22.78) tanh( 9.01 х 0.1524)
Q = 8.1178 W
Result
1.The Heat transfer through the fin at supply voltage 25V is approximate double to the heat transfer at supply voltage 16V.
2.As the value of x increases value of Tx decreases continuously.
For 16V,
For 25V,
Conclusion
From the experimental result it is shown that as the distance increase from the heat source temperature decreases. Graphs also shows the continuous temperature decrement in the positive x direction.
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