# To increase the heat transfer from a wood burning stove fins are going to be attached to the metal chimney pipe. The fins will be 3 cm wide at the base and have a thickness of approximately 2mm. The surface temperature of the pipe is 500°C, and the surrounding air temperature is assumed to be a constant 25°C. Select a suitable material for the fins and also justify an appropriate length. The material and length should be based an attempted to maximize heat transfer and minimize cost. Assume a reasonable value for the convection heat transfer coefficient.

Finding will be presented in a report with a memo cover sheet. A narrative including an
Introduction, Analysis Methods, Results, and Conclusions needs to be provided.
Introduction: Describe the problem and reason for the design.
Analysis Methods: Describe the methods used to analyze the problem. Include equations used
and any other tools used.
Results: Provide a dimensioned drawing of the design along with any results obtained from
calculations or other analysis methods. Such as heat transfer rates, cost of materials and
manufacturing, and payback period.
Conclusions: Provide a summary of the problem, analysis, and results. Lastly discuss the
method used to manufacture and attach the fins.
Notes:
The report must be created in a word processing program.
All drawings must be created with a computer aided drafting program.

Response

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Introduction

Known heaters, ovens and stoves typically allow heat to flow from the source of heat and escape out via the chimney without restriction to the flow of the heated air. To enhance the heat transfer, some devices employ metallic fins to cause the heated air flow in a back and forth pattern around the fins. Generally, fins are preferred in large number of applications and the material used in such applications must have high metal conductivity. It is the purpose of this design to specify a suitable selection of a material to be used for the fin, approximating the length that will maximize the rate of transfer while keeping costs to low level.

Essentially, we have two methods that we may use to enhance transfer the transfer of heat. We can try enhancing the transfer by raising the coefficient of convectional heat transmission or we can extend the surface area by providing an attachment to an extended surface known as fins, made of  a conductive material like aluminum. Fundamentally, fins can take different shapes such as rectangle, trapezoidal, concave, extra. For the specifications given, this project will deal with rectangular fin.

In my design approach, I will make the following assumptions: the fin has a length L and the heat transfer coefficient is known to be h. The end of the fin has a different coefficient identified as hL. From Figure 1.0 below, which is my model configuration for design, the temperature in the fin is only a function of x; A is the cross-section area of the fin and P is its perimeter such that the characteristic dimension in the transverse direction becomes A/P=r/2 (since the fin is circular).

Method analysis

With the dimensions given for this analysis, the best length for the required fin was 10.1cm. With calculated value of the resistance, the material of choice is aluminum. Since the design assumes a rectangular fin, the corrected length is given by the formula:

Lc=L+(Ac/P) …………………………………………… Equation 1

Where Lc and Ac are the corrected length and cross-sectional area respectively

: Ac=Wt, P=2(W+t)»2W, since t << W…………………. Equation 2

However, since the fin is thin, we need to modify equation 1 such that:

Lc=L+(Ac/P)=L+(Wt/2W)=L+(t/2)…………………… .. Equation3

In which case,

Ac=Wt, P=2(W+t)»2W, since t << W…………………. Equation 4

This is the corrected length of the fin. However, a longer length means a higher heat transfer. But along fin will require more material thereby increasing the cost. To determine the optical length, equation 5 will apply

qf =M tanh mL…………………………………………. Equation 5

qflong=M……………………………………………… Equation 6

for an infinitely long fin.

This gives a ratio R(mL)=qf /qflong……………………   Equation 7

Since the rate of heat transfer increases with mL, a plot of this ratio against mL will appear as shown.

The above equations assume a fin with a diabetic length.

Now, let the total heat loss be

qf =M tanh (mL)………………………………………… Equation 8.

for an adiabatic fin, or qf=Mtanh(mLC)…………………. Equation  9, if the tip has convective heat transfer.

M=(hPkAc)^(1/2)*(Tb-T∞)………………………….   Equation 10

m=(hP/kAc) ^(1/2)……………………………………  Equation 11

Using thermal resistance:

Rtf=(T-Tb)/qf =1/((hPkAc) )^(1/2)tanh(mL))…………Equation 12

Results

Given: width=W=3cm=0.3m, Height=t=2mm=0.002m, Tb=500oC, T=25OC

Therefore: Ac=0.0006m2 (from equation 4)

P=0.6m (from equation 4)

Assuming that the convective heat transfers coefficient h=k=1 and a non-corrected length L=10cm

Lc=10.001cm

From equation 11, m=10 and M=(0.6*0.0006) )^(1/2)*(500-450)=0.162.

The total heat loss will be

qf =0.162*tanh (100)=0.33

Thermal resistance R for the material will be

R=8.01

Conclusion

Fins are a way to obtain more heat exchange between surfaces. However, when a designer chooses to use the fin approach, the efficiency of the system is dictated by the material chosen for fins and the fin design. In systems where a transfer enhancement method is not used, heat that exits out of the chimney ends up wasted. This reduces the efficiency of the firebox. Fins are used in known systems like stove to increase the surface area in contact with the heated air. This attempts to permit more heat conduction to the outside of the firebox thereby increasing the overall efficiency

The most common method used to manufacture and attach the fins is the heat sink method.

The design of a heat sink is to maximize the surface area that connects with the cooling medium surrounding it. The performance of a heat sink is determined by factors such as Air velocity. The attachment method of the thermal material of the heat sink will also affect the die temperature.

Work cited

Killander, Anders, and John C. Bass. “A stove-top generator for cold areas.” Thermoelectrics, 1996., Fifteenth International Conference on. IEEE, 1996.

Nuwayhid, R. Y., and R. Hamade. “Design and testing of a locally made loop-type thermosyphonic heat sink for stove-top thermoelectric generators.” Renewable Energy 30.7 (2005): 1101-1116.

Smith, Richard D., and Samuel J. Van Grouw. “Clean burning solid fuel stove and method.” U.S. Patent No. 4,545,360. 8 Oct. 1985.