Heat Transfer in Laminar Flow
Objective:
To determine the overall heat transfer coefficient making use of logarithmic mean
temperature difference. From overall heat transfer coefficient, determine the individual film
heat transfer coefficient and verify the Seider-Tate equation for laminar flow heat transfer.
Apparatus:
1. Stainless steel double pipe heat exchanger with facility to measure inlet and outlet
temperature of hot fluid with accuracy of 0.1◦C. The inlet and outlet temperature of cold
fluid is measured with liquid in glass thermometer of 1◦C accuracy.
2. A stainless steel insulated tank with a heater. Pin n heat exchanger.
3. Hot fluid circulation pump with speed variation mechanism. Bare pipe without ns.
4. Cold fluid circulation pumps with speed variation mechanism. Steam generator to
generate steam at constant pressure. The steam generator is also provided with
temperature indicator and a dead weight safety valve.
5. An insulated stainless steel tank with bottom discharge to measure the flow rate of hot
fluid.
Theory:
In a heat exchanger, heat is transferred from hot fluid to cold fluid through metal wall, which
generally separates these two fluids. Heat transfer through metal wall is always by conduction
while on both sides of metal wall it is generally by convection. Generally resistance offered to
heat transfer by the metal wall is negligible as compared to resistance offered by convection.
The wall temperature is always between local temperatures of the two fluids. The actual value
depends upon individual heat transfer coefficient on either side.
At low Reynolds’s number (Re < 2100), the flow pattern is laminar and the fluid flows in an
ordered manner along generally parallel "Filament like" streams which do not mix. It follows
that in this type of flow that the heat transferred to and through the fluid is essentially by
conduction.
When heat is transferred through resistances in series, the total resistance to heat transfer is
the sum of individual resistances in series. Thus, for heat exchanger, one can write,
1/UiAi = 1/hiAi + x/KAlm + 1/hoAo
OR
1/Ui = 1/h1 + ∆xAi/KAlm + Ai/hoAo
Once the heat exchanger material and its geometry are fixed, then the metal wall resistance
x/KAlm becomes constant. Similarly, if the flow rate of cold fluid is fixed and its mean
temperature does not differ much for different flow rates of hot fluid, then the resistance by
the outside will remain almost constant. Thus, the overall heat transfer coefficient will depend
upon the value of inside heat transfer coefficient alone. If flow through inner tube is in the
turbulent flow regime, then Sieder-Tate equation can be used to predict the inside lm heat
transfer coefficient.
Nu = 1.86*Re1/3*Pr1/3
If the bulk mean temperature does not differ much for different flow rates, then all the physical
properties will remain nearly the same and equation (3) can be re-written as:
Nu = constant × (velocity)1/3
Substituting equation (4) in equation (2), one can write it as:
1/Ui = C1 / U1/3 + C2
Thus, the graph of 1/Ui vs 1 / U1/3 (which is known as Wilson plot) should be a straight line with
a slope equal to constant1 and intercept equal to constant2. From this graph, inside lm heat
transfer coefficient can be calculated which can be used to verify Sieder-Tate equation.
Observations
1. Inside diameter of inner tube (d1)
2. Outside diameter of inner tube (d2)
=
=
1.0 cm.
1.27 cm.
3. Inside diameter of outer tube (D1)
=
2.20cms.
4. Length of heat exchanger (L)
=
85 cms.
5. Inner heat transfer area of heat exchanger (A)
=
0.0267m2
6. Zero error of hot fluid digital thermometers
=
0◦C
7. Volume of measuring tank between bottom and middle mark =
(V1)
8. Specific heat of the oil, Cp = 0.625 kcal/kg °C = 2625
Ns/m2
.000880m3
9. Specific gravity of oil = 0.835
10. Viscosity of oil, μ = 4 * 10-3 Pa s
Result & Conclusion:
1. The Graph for the 1/U Vs 1/V
1/3
is approximately a linear graph and hence it satisfies Seider
Tate equation for laminar and parallel flow heat exchanger.
2. Graetz number (Gz) Vs Nusselt number(Nu) Graph are showing approximately linear trend
and hence they also possess a linear relationship with respect to each other.
Heat Transfer in Turbulent Flow
Aim
To determine the overall heat transfer coefficient making use of logarithmic mean temperature
difference. From overall heat transfer coefficient, determine the individual lm heat transfer
coefficients and verify the Dittus-Boelter equation for turbulent flow heat transfer.
Apparatus
1. Stainless steel double pipe heat exchanger with facility to measure inlet and outlet
temperature of hot fluid with accuracy of 0.1◦C. The inlet and outlet temperatures of cold
fluid are measured with liquid in glass thermometer of 1◦C accuracy.
2. A stainless steel insulated tank with a heater.
3. Hot fluid circulation pump with speed variation mechanism.
4. Cold fluid circulation pumps with speed variation mechanism.
5. An insulated stainless steel tank with bottom discharge to measure the flow rate of hot
fluid.
Theory
In a heat exchanger, heat is transferred from hot fluid to cold fluid through metal wall which
generally separates these two fluids. Heat transfer through metal wall is always by conduction
while on both sides of metal wall it is generally by convection. Generally resistance offered to
heat transfer by the metal wall is negligible as compared to resistance offered by convection.
The wall temperature is always between local temperatures of the two fluids. The actual value
depends upon individual lm heat transfer coefficient on either side. At higher Reynolds’s
number (Re >10,000), the ordered flow pattern of laminar flow regime is replaced by randomly
moving eddies thoroughly mixing the fluid and greatly assisting heat transfer. However, this
enhancement of lm heat transfer coefficient is accompanied by much higher pressure drop
which demands higher pumping power. Thus, although desirable, turbulent flow is usually
restricted to fluids of low viscosity. When heat is transferred through resistances in series, the
total resistance to heat transfer is the sum of individual resistances in series. Thus, for heat
exchanger, one can write,
(22.1)
Or
(22.2)
Once the heat exchanger material and its geometry is fixed, then the metal wall resistance
(∆x/KAlm) becomes constant. Similarly, if the flow rate of cold fluid is fixed and its mean
temperature does not differ much for different flow rates of hot fluid, then the resistance by
the outside lm will remain almost constant. Thus, the overall heat transfer coefficient will
depend upon the value of inside lm heat transfer coefficient alone. If flow through inner tube is
in the turbulent flow regime, then Ditturs-Boelter equation can be used to find out inside lm
heat transfer coefficient.
Nu = 0.023(Re)0.8(Pr)n (22.3)
If the bulk mean temperature does not differ much for different flow rates, then all the physical
properties will remain nearly the same and equation (3) can be re-written as:
Nu = constant × (velocity)0.8 (22.4)
Substituting the above equation in equation (2), we get:
constant
constant 2
(22.5)
Thus, the graph of 1/Ui vs 1/u0.8 (which is known as Wilson plot) should be a straight line with a
slope equal to constant1 and intercept equal to constant2. From this graph, inside lm heat
transfer coefficient can be calculated which can be used to verify Dittus-Boelter equation.
Observations:
1. Inside diameter of inner tube (d1) =
1.0cm.
2. Outside diameter of inner tube (d2) =
1.27cm.
3. Inside diameter of outer tube (D1) =
2.20cm.
4. Length of heat exchanger (L) =
85cm.
5. Inner heat transfer area of heat exchanger (A) = .0267m2.
6. Zero error of hot fluid digital thermometers =
0◦C
7.Specific heat of the oil, Cp = 0.625 kcal/(kg .K) = 2615 J/kg.K
8.Thermal conductivity of hot fluid, k = 0.609 W/(m.K)
Observation Table:
Observation
Inlet
Outlet
Inlet
Outlet
Number
Temp of
Temp of
Temp of
Temp of
1
2
3
4
5
6
7
Hot Fluid
Hot Fluid
Cold Fluid
Cold Fluid
(°C)
41.7
42.6
44.2
45.1
45.8
46.2
46.7
(°C)
37.3
38.8
39.2
41.6
42.5
43.3
44
(°C)
29.6
29.8
29.8
29.8
29.8
29.8
29.9
(°C)
30.6
31.2
31.4
31.75
31.9
32.2
32.3
volumetric Flow rate
cc/sec
Amount of Heat
Transfer Q
Velocity of
Hot fluid
u
LMTD
Delta T
Overall heat transfer
coefficient U (Kcal/hr
m2◦C)