Department of Chemical & Biomolecular Engineering

THE NATIONAL UNIVERSITY

of SINGAPORE

Chemical Engineering Process Laboratory I

SEMESTER 4

Experiment H2

Forced Convection Heat Transfer

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Metric No. :

Group :

Date of Expt. :

Demonstrator’s : signature

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Objectives: • To determine heat transfer coefficients in forced convection external flows. Apparatus Blower, metal spheres (d=50mm), electrical heater, chart recorder, thermocouple, air velocity meter. Theory The transient heat transfer processes such as cooling of a solid sphere are normally multidimensional in nature because of the temperature within the body is a function of time and at least one space dimension. However, approximate analysis can be obtained if the Biot number (h (V/A)/k) is small. Under this condition, the variation of temperature with the spatial co-ordinates will be very small, such that the temperature can be taken as a function of time only. This type of analysis is called the lumped-heat-capacity method. The cooling of a solid sphere initially at a uniform temperature, Ti is considered now. The solid sphere is cooled by blowing air over it. If we consider the resistance to heat transfer by conduction within the body is small compared with the convective resistance at the surface, then an energy balance gives the following equation (1).

q = h As(T - T∞) = -cs ρ V dtdT (1)

Equation (1) when integrated, gives the following equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

−−

∞

∞

s

s

i cVtAh

TTTT

ρexp (2)

The equation (2) can also be written as

o

o

i

rhk

rtTTTT

/3ln

2

−=⎟⎟⎠

⎞⎜⎜⎝

⎛−−

∞

∞

α (3)

The rate of heat dissipation from the surface over a length of time τ is given by the following equation:(2)

Qc = ρ V cs (Ti - T∞)⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

s

s

cVAh

ρτ

exp1 (4)

The maximum amount of heat that can be dissipated from the surface is (Qc)max = Qmax = ρ V cs(Ti - T∞) and hence the fractional heat loss is given by the following equation:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−−= 2

2

max

1exp1k

hBiQ

Qc τα (5)

where

Bi= ( )krh

kAVh o

31/

=

• Validity of lumped-heat-capacity method The lumped-heat-capacity method yields reasonable estimates when the following condition is met:

a. Biot number, Bi = ( )k

AVh / < 0.1 (6)

b. Compare the h ro/k value obtained from the plot of ln (T - T∞)/(Ti - T∞) against αt/ro2 with that

obtained from the Heisler temperature charts. A good agreement indicates a reasonable approximation of the analysis. • Convection heat transfer coefficient Equation (3) shows that the slope of straight line obtained by drawing the variation of ln

⎟⎟⎠

⎞⎜⎜⎝

⎛−−

∞

∞

TTTT

i

with α t/ro2 is -3 h ro/k.

Hence, for each of these spheres, the heat transfer coefficient can be calculated by knowing the slope of the straight line. The heat transfer coefficient can also be calculated by using the following empirical equation: (2)

Nu = 2 + (0.4 Re0.5 + 0.06 Re2/3) Pr0.4 (iμ

μ∞ ) 0.25 (7)

where 3.5 ≤ Re ≤ 7.06 × 104 ; 0.71 ≤ Pr ≤ 380 Experiment Procedure The metal spheres are heated to a temperature of about 160 oC. The heating should be carried out slowly to ensure uniform temperature inside the spheres. Start the motor of the blower and set the speed controller. Place one sphere in the wind tunnel and start recording the sphere temperature. The cooling is carried out until the temperature of the sphere is about 5 oC higher than the room temperature. Record the air flow rate in the wind tunnel. Repeat the cooling with the remaining two spheres. Repeat the experiment with a different motor speed. Tabulation and Calculations: Material of the sphere: Room Temperature: Plot the ln (T-T∞)/(Ti-T∞) vs. αt/ro

2 and determine the slope. Check the Validity of lumped-heat-capacity method. Determine the empirical heat transfer coefficient by using the equation (7). Compare your experimental results with that obtained from the Heisler Chart. Results and Discussions:

Conclusions: References 1. Holman, J.P., Heat Transfer, McGraw-Hill, 1972, p. 83 - 88. 2. Thomas, L.C., Fundamentals of Heat Transfer, Prentice Hall, 1980. LIST OF DEFINITIONS AND SYMBOLS A surface area of the sphere

Bi Biot number = ( )

s

s

kAVh /

Cf specific heat of fluid cs specific heat of solid g acceleration due to gravity h average heat transfer coefficient kf thermal conductivity of the fluid ks thermal conductivity of the material of the sphere

Nu average Nusselt number = ( )f

o

krh 2

Pr Prandtl number, μ cf /kf Qc Convective heat transfer from the surface of the sphere

Re Reynolds number, ( )μρ orU 2

ro radius of sphere T Temperature Ti Temperature of the sphere at the commencement of cooling T∞ Ambient temperature t time U velocity V volume α thermal diffusivity of the material of the sphere = ks/ρ cs μi viscosity of fluid at the commencement of cooling μ∞ viscosity of fluid at ambient temperature ρ density Thermal Diffusivity Values of Solid Metals αb = 3.412 × 10-5 m 2/s αAl = 8.418 × 10-5 m2/s

αST = 1.474 × 10-5 m2/s Properties of materials at 20 oC ρ (kg/m3) Cp (KJ/kg oC) k(w/m oC) Aluminium 2.707 0.896 204 Carbon steel (C=0.5%) 7.833 0.465 54 Brass (70% Cu, 30% Zn) 8.522 0.385 111