To determine the temperature distribution of the PIN - FIN for forced convection and to find the FIN efficiency
Duct width (b) = 150mm
Duct height (w) = 100mm
Orifice Diameter (d_{O}) = 24mm
Orifice coefficient (C_{d}d) = 0.6
Fin length (L)= 14.5cm
Fin diameter (D_{f}) = 12mm (Characteristic length)
S. No. | Mode | Manometer reading (cm)/h_{1}/h_{1}/h = h_{1}-h_{2} | Power (watts)/V/I/Q= V x I | Temperature/T_{1}/(°C)/T_{2}/(°C)/T_{3}/(°C)/T_{4}/(°C)/T_{5}/(°C)/T_{6}/(°C)/T_{7}/(°C) | Amb temp/T_{8}/(°C) |
1 | Forced convection | ||||
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5 |
Ref:-Heat and Mass Transfer Data book by C.P Kothandaraman & Subramannian , New Age publishers.
Flim Temperature (T_{f}) = --------------
Vo = Cd*a_{1}*a_{2}*V2gh_{a}/(a^{2}1- a^{2}2)
Where Cd = Co-efficient of orifice = 0.6
g= Gravitational constant = 9.81 m/sec ^{2}
h = heat of pipe (p_{w}/p_{a})h
a_{1}= area of the Pipe
a_{2} = area of the orifice
W = width of duct
B = Breadth of the duct
Where Va - Velacity of the duct
ρ_{a} = Density of the duct
μ_{a}= Viscosity of air at T8 ° C
Where Cp_{a} = Specific heat of air
μ_{a} = Viscosity of air
K_{a} = Thermal conductivity of air
Nusselt number (N_{nu})
For 40 < NRe < 4000
N_{nu} = 0.683 (N_{Re}) * 0.466 (N_{pr})^{0.331}
For 1 < NRe < 4
N_{nu} = 0.989 (N_{Re}) 0.33 (N_{pr}) ^{0.33}
For 4< NRe < 40
For 4000 < N_{Re} < 40000 N_{Re}
N_{nu} = 0.193 ( N_{Re}) 0.618 (N_{pr}) 0.33
For N_{Re} > 40000
N_{nu} = 0.0266 ( N_{Re}) 0.805 (N_{pr}) 0.333
Heat transfer co - efficient h = N_{nu} * (K_{a} / L)
K_{a} = Thermal conductivity of air
L = Length of Fin
H= heat transfer co-efficient
L = Length of the fin
m = V(hp / (K_{b}x A))
P = Perimeter of the fin = ( μ* Diameter of the fin)
A = cross section area of the fin
K_{b}= Themal conductivity of brass rod
Temperature distribution = T x = { [(Cosh m(L-X) /Cosh (M )] * (To -Ta)} + T
X= distance between thermocouple and heater
Distance between thermocouples = 20 mm
N_{nav} = (hD)/K = 1.1 (Gr Pr) ^{1/6} for 1/10 < Gr Pr < 104
N_{nav} = 0.53 (Gr Pr)^{1/4} for 104 < Gr Pr < 109
N_{nav} = 0.13 (Gr Pr) ^{1/3} for 109 < Gr Pr < 1012
Where Nnav = average Nusselt Number = (h D)/K
D= Diameter of fin
K = Thermal conductivity of air
G_{r} = Grashof number - g β Δ;D^{3}/ γ^{2}
β = Coefficient of thermal expansion - 1/ ( T_{av} + 273) ΔT = (T_{av} -T _{amb})
Pr = Prandtl number = (μCp/K)
The heat transfer rates of the fin is determined and the values are
Temperature distribution:
Fin efficiency:Orifice- meter is used to measure discharge.
Blower is an external mechanical device which is essential for forced convection process
The rate equations for convective heat transfer between a surface and an adjacent fluid is prescribed by Newton’s law of cooling
Range of 'h'for natural convection in gases is 3-25W/m2 -k & for liquids it is 50- 350W/m2 -k.. Boundary layer is a thin layer at the surface where gradients of both velocity& temperature are large.
Nusselt Number represents the enhancement of heat transfer through a fluid layer as a result of convection relative to conduction across a same layer. Larger the Nu, more effective is convection.
Boundary layer is a thin layer at the surface where gradients of both velocity & temperature are large.
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