# Lab Report: Unsteady State Heat Transfer you Will find everything you need in the Attached files. IT IS IMPORTANT TO READ THEM CAREFULLY. will be repo repo

Lab Report: Unsteady State Heat Transfer you Will find everything you need in the Attached files. IT IS IMPORTANT TO READ THEM CAREFULLY. will be

repo

reports and you need to submit the revised rer

the lab reports are:

1. Title Page: This page shows the title of the experiment, the date performed, the date

submitted, authors and team members.

2. Abstract: A concise (normally 200 words or less) statement of the essential

contents of the report for the reader who must get your message in 60 to 90

seconds. The abstract should include a brief statement of the objective, methods

used, significant results and major conclusions.

3. Introduction The introduction presents the background of the project and

describes how the project relates to the “big picture”. It should explain fully:

Why the work is being done? (what are the learning objectives)

What has been done previously in the field both at Widener and at other

locations? What the reader (assume another engineering student) will need

to know to understand your report

4. Procedure: Describe what was done in sufficient detail that an engineer who was

no associated with the project could duplicate your work.

5. Results: An objective discussion of the principle results and observations from

any experimental work. You are to show that the conclusions are justified. This

is the most important section of the report. Discuss what you have accomplished

in a positive manner. Do not dwell on minor factors or attempt to “lay blame” for

failures.

6. Conclusions: Conclusions reached in the results are to be restated here in a more

general, less specific manner. In the Interim Report, these are honest answers to

the questions in Section 2. In the Final Report these are the principle things

learned during the project.

7. Safety Protocols: Write list of safety protocols you have undertaken in the course

of experiments.

8. List of References: Put all the references in the number format in word’s endnote.

9. Appendices (optional): This part may contain symbols listings, sample

calculations, computer program listings, communications, detailed test results

etc.

Unsteady State Heat Transfer

Objective

To perform the experiments related to unsteady state heat transfer and calculate the

differences in thermal parameters with the knowledge of heat transfer phenomena.

Apparatus

Several solids of cylindrical, spherical, or cubical shape; the solids have holes

1.

drilled to attach thermocouples.

2. Thermocouples

3. Thermocouple reader.

Background

дt pc,

k =

The temperature distribution inside a solid in which there is no internal heat

generation can be found from the Fourier field equation:

ᏧᎢ k

ᏙᎢ

……. (1)

where Cp = heat capacity or specific heat (Btu/lb°R, W/kgK)

thermal conductivity (Btu/(hr ft ‘R),

W/(m K)) T = temperature (°R, K)

t = time (sec)

p= density (lb/ft”, kg/mº)

The group k/pCp is the thermal diffusivity (a). This equation has been solved for simple

geometrical systems with appropriate boundary conditions. In one dimension the

Fourier equation is

ОТ

k д?Т

діt pc, дх*

(2)

The heat flux normal to a given cross section is given by

ОТ

дх (3)

where A = the area of the cross section (ft?, m?)

(x = the heat flux (Btu/hr, W)

…..

9x =-KA

Analogous forms exist in cylindrical and spherical coordinate systems.

If a film surrounds the external surface with a temperature drop across it, the

surface temperature, which determines the boundary condition, is given by

9x

dT

=-k =h(T.-T.)

A

dx

surface

surface

….(4)

where h = convective (plus radiation) heat transfer coefficient from surface to

surroundings

Too = (constant) surrounding temperature

To = surface temperature

The solution of the differential equations can be obtained in different ways. In order to

ease the calculations, a new dimensionless number has been introduced and known as

Biot Number (Bi) and given by

hLe

Bi=

k

…..(5)

Where Lc is the characteristics length, given by volume (V)/area (A). If Bi0.1, i.e., conductive resistance is more than convective

resistance (for mostly non-metals where the conductive resistance is the controlling

factor), the analytical solution is given by

T-T. – 45 пл.

e-(nt/2) F.

To To

L

…(9)

–

sin

n

TT

n=

The solution to this equation can also be obtained from the graphical form often

referred to as the Gurney-Lurie charts. These charts use the following terms to describe

the temperature profile.

10

T-T

Y =

To-To

…(10)

at

X = 1

2

X; … (11)

х

n=

X, … (12)

k

m=

hX) …(13)

where h = the heat transfer coefficient of

the liquid k = the thermal

conductivity of the solid

n = relative position (a value of the charts)

m = relative thermal resistance (a value on the charts)

t= time

T = local temperature at timet

T. = the initial temperature

To = Temperature of surrounding medium

X = relative time

x = length

X1 = a key dimension, such as radius, the exact definition is specified on each chart

Y = unaccomplished temperature change

k

a = thermal diffusivity

PC,

2

Cp= heat capacity

p = density

The ratio m represents the relative resistance of the outside film 1/h to the

resistance of the path of longest distance for heat flow x1/k. The differential equations

have been solved for various geometric shapes and values of m, n, X and Y. Solutions are

presented in the references.

This value can be compared to the one-dimensional graphical or analytical solution.

General Procedure

1) Before starting experiment, get familiarized with experimental set up.

2) Turn on the oven on for about 100 °C (around position “3” for the knob). Wait till it

gets desired temperature.

11

3) Make all measurements necessary to determine volume/mass of each cylinder

4) When the oven ready, put the cylinde pone at a time) for 30 mins.

5) Take out the cylinder carefully (it iſ hot, need gloves) and hang it on the stand.

6) Take the temperature reading from each hole by using the thermocouple. Take the

reading for 30 mins in the interval of 0,2,5,10,15,20 & 30 mins.

7) While taking reading, put the other cylinder inside oven for heating to save time.

Treatment of Results:

1. Get the thermodynamic properties of the materials (thermal conductivity, specific

heat etc.)

2.

For metals, assume Biot number approximations and calculated the heat transfer

coefficients for cooling medium. Cross-check the validity of Biot number

assumptions.

3. For non-metallic samples, employ Gurney-Lurie charts and calculate the thermal

parameters.

{References

1. C. O. Bennett and J. E. Myers, Momentum, Heat, and Mass Transfer, 3rd Edition, Ch. 19,

McGraw-Hill, New York, 1982.

** 2. J. R. Welty, C. E. Wicks, and R. E. Wilson, Fundamentals of Momentum, Heat, and Mass

Transfer, 3rd edition, Ch. 18, John Wiley, New York, 1984

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