1. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
259
PREDICTION OF FRICTION FACTOR AND NON DIMENSIONS NUMBERS
IN FORCE CONVECTION HEAT TRANSFER ANALYSIS OF INSULATED
CYLINDRICAL PIPE
S.K. Dhakad1
, Pankaj Sonkusare2
, Pravin Kumar Singh3
, Dr. Lokesh Bajpai 4
1
Assistant Professor Department of mechanical Engg. S.A.T.I, Engineering College Vidisha M.P
India
2
Lecturer in Department of mechanical Engg. S.A.T.I Engineering College Vidisha M.P. India
3
Assistant Professor Department of mechanical Engg. BUIT, Bhopal M.P. India
4
Professor and Head of Mechanical Engg. Deptt., S.A.T.I. Engineering College Vidisha M.P. India
ABSTRACT
The heat transfer through convection mode is very important in the thermal engineering and
industrial application. In the present work force convection heat transfer analysis has been done for
40 mm diameter and 400 mm length of pipe subjected to insulated thickness of 5mm on outer span.
The experimental analysis has been done for the 1/3, 2/3, 1 opening positions of the flow control
valve, and along with bypass valve fully opened. This present work an experimental study on the
Nusselt number (Nu), Reynold number (Re), Frictional factor (Ff) has been done with short length
30 mm diameter pipe insert under uniform wall heat flux boundary condition. In the experiment
measured Reynolds number with air as a test fluid. The analysis has been done in steady state
condition and regulated the flow of water so as to obtained temperature rise up-to 3-40
C limits. The
Experimental results are cross validated with analytical results using the open literature as design
data book. The experimental results are also validated with standard references available in open
literature. The experimental results are well compare with analytical results also with standard open
literature results.
KEY WORDS: Force convection, experiment, convective heat transfer coefficient, Frictional
Factor.
1. INTRODUCTION
Heat transfer from a solid surface/ wall in the fluid in contact takes place by conduction to a
very small extent because fluid particles are no more confined to their position as in solid.
Convection involving macroscopic motion of fluids is thus the prominent mode responsible for heat
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ISSN 0976 – 6340 (Print)
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
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transfer in such cases. If motion of fluid is made faster, with the help of pump or fan or blower, for
rapid heat transfer then it is termed as forced convection heat transfer on the other hand if no external
agency is involved to increase the flow velocity then heat transfer continues to takes place at a slow
rate, only due to setting-up of natural convection currents and is called natural or free convection
heat transfer. Rate of heat transfer in both these cases, as per Newton’s law of cooling.
2. EXPERIMENTAL DETAILED
The apparatus consists of a test section surrounded by water jacket complete test rig shown in
figure 1. Air supplied from a blower, regulate with the help of a bypass valve & a flow control valve,
is passed through an orifice, fitted with a manometer for measurement of pressure difference across
it, and a heating section before entering the test section detailed components are shown in figure 2.
Power input to the heater of heating section is regulated by a dimmer & measured by a wattmeter (or
a voltmeter & ammeter). Thermocouples with a selector switch an installed for measurement of
temperature of:-
1. Air before entrance to the test section (at exit of the air heating section).
2. Pipe wall at seven positions in the test section.
3. Air at exit from the test section.
Figure 1 Position of thermocouple in test section
3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
261
Figure 2 Experimental set up
3. PROPOSED METHODOLOGY
Rate of heat transfer in both these cases, as per Newton’s law of cooling, is expressed as:
q = h A (Ts - T∞)………………………………………. (1)
it is evident from this expression that for given surface temperature (Ts), fluid temperature (T∞), and
surface area (A) the rate of heat transfer depends only on the value of heat transfer coefficient (h) ‘h’
in turn depends on a number of parameters including the thermo physical properties of fluid, the
surface dimensions and roughness and velocity of flow. ‘h’ is thus not as simple as it seems to be in
the above mentioned equation. Investigations have arrived at various empirical equations on the basis
of wide range of experiments conducted.
A well known and widely accepted relationship for forced convection heat transfer between
the walls of a circular or non-circular duct or annular passage and the fluid flowing through it in the
fully developed turbulent flow mode (found applicable for constant wall flux as well as constant wall
temperature) named as “Dittus Boelter Equation” is:
Nu = h L / Kf = 0.023 (Re)0.8
(Pr)n
…………………………(2)
for 0.7 < Pr < 100
Where n is a constant having value 0.3 for cooling and 0.4 for heating, L is characterstic
dimension of the body (L = inner dia. of a circular duct or equivalent dia. of a noncircular duct) and
kf is thermal conductivity of the fluid, Nu, Re and Pr are Nusselt number, Reynold number and
Prandtl number respectively. All thermophysical properties are evaluated at average of temperatures
of bulk of the fluid at inlet and exit.
In fully developed laminar flow inside a smooth tube where, Re Pr (d/1) > 10, average value
of nusselt number can be obtained from the equation.
Nu = 1.86 [ Re Pr/(1/d)]0.33
(µ/µs)0.25
……………………….(3)
Suggested by Sieder and Tate, which is applicable to the constant wall temperature situation.
Flow rate of water through the cooling water jacket around the test section & temperature of water at
inlet to & exit from it are measured by a measuring flask & mercury in glass thermometer.
Pressure difference across orifice in mm of air column
h = hm×ρ/ρa …………….. (4)
4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
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Flow rate of air,
ma = C × A √ [2 h / (1-β4
)] …………………….. (5)
Velocity of air in flow sections
V = M /ρ×At …………………… (6)
Where, Ao = π/4 do
2
, At = π/ 4 dt
2
, Ats = π .dt . Lt ……………. (7)
Bulk mean (average) temperature of air in test section
Tst = (Tst + Tse)/2 ………………………. (8)
Mean temperature of tube surface
Tt = (T1 + T2 + T3 + T4 + T5 + T6 + T7)/7 ………………... (9)
Heat lost by air in the test section
q = ma Cpa (Tai - Tae) ……………………………………… (10)
Also, q = hexp Ats (Tat - Tt) ……………………………… (11)
Experimental value of heat transfer coefficient is thus:
hexp = q/[Ats (Tat - Tt)] ………………………………………(12)
Note down properties of air at average temperature of air Tat
Reynold number, Re = ρa Va dt / µa …….. ………….. (13)
Prandtl number, Pr = µa Cpa / ka ………………………….. (14)
The relationship between Reynold number and frictional factor as [1]
f=0.758Re-0.331
………………………………………………. (15)
Theoretical value of heat transfer coefficient hth can be calculated using appropriate equation as per
the type of flow/ value or Re.
4. EXPERIMENTAL RESULTS AND ANALYSIS
The Table 1 has shown the experimental measurement of convective heat transfer coefficient
and Nusselt number, (Nu) Reynold number (Re) corresponding to three flow rate of air by
regulating the bypass valve of the blower.
Table1: Experimental measurement of convective heat transfer coefficient, Nusselt number,
Reynold number
Flow rate of air
Heat transfer
rate
Q (w)
Convective heat
transfer
h (w/m2
°C)
Nusselt
number
(Nu)
Reynold
number
(Re)
1/3, Opening of bypass
valve
1840 287.50 3194.44 2245.48
2/3, Opening of bypass
valve
2050 340.03 3778.11 2568.11
Full Opening of bypass
valve
2295 351.39 3904.3 2636.5
5. ANALYTICAL RESULTS AND ANALYSIS:
The analytical results of convective heat transfer coefficient, Nusselt number (Nu), Reynold
number (Re) corresponding and frictional factor are shown in the tables 2, 3 & 4corresponding to
three flow rate of air by regulating the bypass valve of the blower.
5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
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Table 2 shown Analytical results corresponding to 1/3 opening of bypass valve
Test
section
Length
L(mm)
Heat transfer
rate
Q (w)
Convective
heat transfer
h (w/m2
°C)
Temp
.
(°C)
Mass flow
rate of air
(ma)kg/sec
Velocity
of air
(Va)
M/s
Nusselt
number
Nu.
Reynold
number
Re
Friction
Factor
(Ff)
1 50 1840 162.774 39 0.000061 0.048 226.075 270.58 0.118
2 80 1840 195.329 37.5 0.000061 0.048 434.06 455.98 0.099
3 140 1840 219.965 36.6 0.000061 0.048 855.42 784.60 0.083
4 200 1840 254.77 35.7 0.000061 0.048 1415.4 1173.84 0.073
5 260 1840 271.290 35.4 0.000061 0.048 1959.3 1522.6 0.066
6 320 1840 283.542 35.16 0.000061 0.048 2520.3 1862.42 0.062
7 400 1840 284.85 35.14 0.000061 0.048 3165.05 2234.65 0.059
Table 3: shown Analytical results corresponding to 2/3opening of bypass valve
Test
section
Length
L(mm)
Heat
transfer
rate
Q (w)
Convective
heat transfer
h (W/m2
°C)
Temp.
(°C)
Mass flow
rate of air
(ma)
kg/sec
Velociy
of air
(Va)
M/s
Nusselt
number
Nu.
Reynold
number
Re
Friction
Factor
(Ff)
1 50 2050 204.020 38 0.000061 0.048 283.36 324.175 0.111
2 80 2050 233.166 37 0.000061 0.048 518.14 525.37 0.095
3 140 2050 272.027 36 0.000061 0.048 1057.8 929.94 0.078
4 200 2050 310.888 35.25 0.000061 0.048 1727.1 1376.48 0.069
5 260 2050 326.43 35 0.000061 0.048 2357.57 1765.54 0.063
6 320 2050 337.689 34.8 0.000061 0.048 3001.68 2141.89 0.059
7 400 2050 336.034 34.8 0.000061 0.048 3733.7 2550.4 0.056
Table 4: shown Analytical results corresponding to full opening of bypass valve.
Test
section
Length
L(mm)
Heat
transfer
rate
Q (w)
Convective
heat
transfer
h
(W/m2
°C)
Temp.(°C) Mass
flow rate
of air
(ma)
kg/sec
Velociy
of air
(Va)
M/s
Nusselt
number
Nu.
Reynold
number
Re
Friction
Factor
(Ff)
1 50 2295 228.403 38 0.000063 0.050 317.22 354.80 0.108
2 80 2295 261.03 37 0.000063 0.050 580.07 575.032 0.092
3 140 2295 288.509 36.33 0.000063 0.050 1121.982 974.75 0.077
4 200 2295 317.779 35.75 0.000063 0.050 1765.43 1400.83 0.068
5 260 2295 338.375 35.4 0.000063 0.050 2443.8 1817.03 0.063
6 320 2295 351.390 35.2 0.000063 0.050 3123.4 2211.1 0.059
7 400 2295 358.280 35.1 0.000063 0.050 3980.8 2684.6 0.055
6. RESULTS AND DISCUSSION
The variation of Nusselt number and Reynold number with three different opening of bypass
valve have been shown in figure 3. The analytical as well experimental results are comparing well
with each other. The results are also well comparing along with standard references [1].
6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
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Figure 3: The variation of Nusselt number and Reynold number with three different opening of
bypass valve
The variation of frictional factor with respect to different flow rate has been shown in the
figure 4.The experimental as well analytical validation of friction factor compare well with each
other along with references [1].
Figure 4: the variation of frictional factor with respect to different flow rate
CONCLUSION
The experimental analysis of convective heat transfer coefficient at the different flow rate of
air has been analyzed in this paper. The validation of non dimension numbers and friction factor with
analytical results has been done, using the standard properties of air available in the open literature,
corresponding steady state temperature of the fluid (air).The both the results (experimental and
analytical) are well compared with the standard references [1].
0
500
1000
1500
2000
2500
3000
3500
4000
4500
Nusseltnumber
Reynolds number
1/3 Opening of
blower
valve[Experimental
results]
2/3 Opening of
blower valve
[Experimental results]
Full opening of
blower valve
[Experimental results]
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
500 1000 1500 2000 2500 3000 3500
Frictionfactor
Reynolds number
Experimental Results
Analytical Results
reference results
7. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 4, July - August (2013) © IAEME
265
ABRASION:
Re - Reynold number
Pr - Prandtl number
Nu - Nusselt number
D - Diameter of pipe
Lp - length of pipe
h - convective heat transfer coefficient (W/m2
°C)
ma - mass flow rate of air (kg/sec.)
Va - velocity of air (m/s)
F f - friction factor
T - temperature (°C)
L - length of test section (in mm)
Q - heat transfer rate (W)
Tai - inlet air of temperature
Tae - exhaust air of temperature
hexp - experimental value of heat transfer coefficient
ρa - density of air
µa - dynamic viscosity of air
Ats - area of test section
h - pressure difference
Tt - Mean temperature of tube surface
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[8] Pankajsonkusare, s.k. dhakad et al., “Force convection heat transfer analysis through different
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