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Estimation of Convective Heat Transfer Coefficient
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Convective heat transfer coefficient
• Convective heat transfer coefficient (h) is predicted from empirical correlations.
• The coefficient is influenced by such parameters as type and velocity of fluid, physical properties of fluid,
temperature difference, and the geometrical shape of the physical system underconsideration.
• Dimensional analysis is used to develop empirical correlations that allow estimation of h.
• Following correlations apply to Newtonian fluids only. For expression for non-Newtonian fluids, the textbook by
Heldman and Singh (1981) is recommended.
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Force convection
Fluid is forced to move over an object by external mechanical means
NNu = (NRe, NPr)
Where NNu = Nusselt number = hD/kh = convective heat-transfer coefficient (W/ m2oC)
D = characteristic dimension (m)k = thermal conductivity (W/moC)
NRe = Reynolds number = uD/ NPr = Prandtl number = Cp/k
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Laminar flow in horizontal pipesWhen Reynolds number < 2100
DL
For (NRe x NPr x ) 100
DL
For (NRe x NPr x ) > 100
All physical properties are evaluated at bulk fluid temp. except w is at surface temp of wall.
D = characteristic dimension = diameter of pipe
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Example
• Water flowing at a rate of 0.02 kg/s is heated from 20 to 60C in a horizontal pipe (inside diameter = 2.5 cm). The inside pipe surface temperature is 90C. Estimate h if the pipe is
1 m long.
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Transition flow in horizontal pipesWhen Reynolds number between 2100 and 10000
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Turbulent flow in horizontal pipe
When Reynolds number > 10000
All physical properties are evaluated at bulk fluid temp. except w is at surface temp of wall.
D = characteristic dimension = diameter of pipe
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Example
• Water flowing at a rate of 0.2 kg/s is heated from 20 to 60C in a horizontal pipe (inside diameter = 2.5 cm). The inside pipe surface temperature is 90C. Estimate h if the pipe is
1 m long.
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Example
• What is the expected percent increase in convective heat transfer coefficient if the velocity of the fluid is doubled while all other related parameters are kept the
same for turbulent flow in a pipe.
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Convection in non-circular ducts
Equations for circular tube with hydraulic diameter
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Flow past immersed objects• For flat plate
• For cylinder if fluid is gas NNu = C NRe
if fluid is liquid NNu = C NRenNPr
1/3
NNu = 0.664 NRe NPr
1/3
1/2
NRe C n
0.4-44-40
40-40004000-40000
40000-400000
0.9890.9110.6830.1930.0266
0.3300.3850.4660.6180.805
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Flow past immersed objects
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Flow past immersed objects
• For single sphere
NNu = 2 + 0.60NRe0.5 X NPr
1/3
where 1 < NRe < 70,000
0.6 < NPr < 400
Fluid properties are evaluated at film temperature (Tf) where
Tf = (Twall + Tmedium) / 2
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Example
• Calculate convective heat transfer coefficient when air at 90C is passed
through a deep bed of green peas. Assume surface temperature of a pea to be 30C. The diameter of each pea is 0.5 cm. The velocity of air through the bed is
0.3 m/s.
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Free convection
Free convection occurs due to density differences in fluids as they come into contact with a heated
surface. The low density of fluid at a higher temperature causes buoyancy forces, and
as a result, heated fluid moves upward and colder
fluid takes its place
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NNu = = a (NGr NPr)m
where a, m = constants
NGr = Grashof number = D32gT/2
D = characteristic dimension (m)
= coefficient of volumetric expansion (K-1)
T = Temperature difference between wall and surrounding bulk (oC)
All physical properties are evaluated at film temperature (Tf = (Tw+Tb)/2)
hD k
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Use Figure A
Use Figure B
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Figure A
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Figure B
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ExampleEstimate the convective heat transfer coefficient for convective heat loss from a horizontal 10 cm diameter stem pipe. The surface temperature of
the uninsulated pipe is 130C, and the air temperature is 30C
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Other empirical equations for h estimation
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1. Forced Convection Flow Inside a Circular Tube
• All properties at fluid bulk mean temperature (arithmetic mean of
inlet and outlet temperature). • Nusselt numbers Nu0 from sections 1-1 to 1-3 have to be
corrected for temperature-dependent fluid properties according to section 1-4.
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1-1 Thermally developing, hydrodynamically developed laminar flow (Re < 2300)
Constant wall temperature:
(Hausen)
Constant wall heat flux:
(Shah)
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1-2 Simultaneously developing laminar flow (Re < 2300)
Constant wall temperature:
(Stephan)
Constant wall heat flux:
which is valid over the range 0.7 < Pr < 7 or if Re Pr D/L
< 33 also for Pr > 7.
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1-3 Fully developed turbulent and transition flow (Re > 2300)
Constant wall heat flux:
(Petukhov, Gnielinski)
where
Constant wall temperature: For fluids with Pr > 0.7 correlation for constant wall
heat flux can be used with negligible error.
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1-4 Effects of property variation with temperature
Liquids, laminar and turbulent flow:
Subscript w: at wall temperature, without subscript: at mean fluid temperature
Gases, laminar flow: Nu = Nu0 Gases, turbulent flow:
Temperatures in Kelvin
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2. Forced Convection Flow Inside Concentric Annular Ducts, Turbulent (Re > 2300)
All properties at fluid bulk mean temperature (arithmetic mean of inlet
and outlet temperature).
Dh = Do - Di
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Heat transfer at the inner wall, outer wall insulated:
(Petukhov and Roizen)
Heat transfer at the outer wall, inner wall insulated:
(Petukhov and Roizen)
Heat transfer at both walls, same wall temperatures:
(Stephan)
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3. Forced Convection Flow Inside Non-Circular Ducts, Turbulent (Re > 2300)
Equations for circular tube with hydraulic diameter
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4. Forced Convection Flow Across Single Circular Cylinders
D = cylinder diameter, um = free-stream velocity, all properties at fluid bulk mean temperature.
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4-1 Smooth circular cylinder
Valid over the ranges 10 < Rel < 107 and 0.6 < Pr < 1000
(Gnielinski)
where
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4-2 Effects of property variation with temperature
Liquids:
Subscript w: at wall temperature, without subscript: at mean fluid temperature. Gases:
Temperatures in Kelvin.
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5. Forced Convection Flow over a Flat Plate
All properties at mean film temperature
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Laminar boundary layer, constant wall temperature:
(Pohlhausen)
valid for ReL < 2x105, 0.6 < Pr < 10
Turbulent boundary layer along the whole plate, constant wall temperature:
(Petukhov)
Boundary layer with laminar-turbulent transition:
(Gnielinski)
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6. Natural Convection
All properties at
L = characteristic length
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Nu0 "Length" L
Vertical wall 0.67 H
Horizontal cylinder 0.36 D
Sphere 2.00 D
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For ideal gases: (temperature in K)
(Churchill, Thelen)
valid for 10-4 < Gr Pr < 4x1014, 0.022 < Pr < 7640, and constant wall temperature
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Combined free and forced convection
• From J.P. Holman (1992)
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UWT = uniform wall temp., UHF = uniform heat flux
Aiding flow = forced and free convec. Are in the same direction while opposite flow means they are in opposite direction.
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= =