fluid lab.docx

Title of the report: Heat transfer through an extended surface.

Heat transfer through an extended surface.ME323: FLUID MECHANICS LABORATORY

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Heat transfer through an extended surface.

1. ABSTRACTThe principal objective of this experiment is to measure the temperature distribution along the extended surface and then compare it with the theoretical data. Also the calculation of heat transferred from an extended surface by radiation and convection heat transfer method and then comparing it with the theoretical results. The objective is also to calculate the thermal conductivity of the material.

To achieve the above mentioned objectives, I use the method that includes the heating of one end of a solid cylinder road and measuring the temperature distribution along the surface of rod by temperature measuring techniques. The equipment that is used in this experiment is the use of HT10X Heat Transfer Service Unit, HT15 Extended Surface Heat Transfer Accessory, and PC with HT10X-90IFD Data Logging Accessory. With the help of these equipments, the desired results would be achieved.

The results of this experiment shows that by measuring the surface temperature from the experiment and theoretical temperature profile and plot them against each other clearly showing the data points on the graph. All the calculation shows us that by measuring the heat input to the heater, we are able to calculate how much heat is lost from the rod. Using these calculations, have measured the thermal conductivity of the rod.


2. Data and Results: Part I. Find the value of constant m using any iterative technique for thermocouple T1 to T8 (the initial guess for the value of m can be taken 8.0). Calculate the theoretical temperature Tx at each point along the rod using average value of m. Estimate the cumulative influence of the experimental errors on your calculated values for m and measured values for T1 to T9, x and L. Plot measured surface temperature Tx from experiment and theoretical temperature profile (calculated using average value of m) against position x (in same plot) along the extended surface clearly showing the data points on the plot. Part II. Compare the measured power Qin to the heater with the calculated heat loss Qtot from the rod. Part III. Compare the measured thermal conductivity with the suggested thermal conductivity for brass rod kbrass = 121 Wm-2K-1

Measurement for 9 V

Heater Voltage V (V) :Heater current I (A) :Heater Power Qin (W) :

ThermocoupleNumberT1T2T3T4T5T6T7T8T9

Description

Location (cm)-

Time 1:

Temperature

Time 2:

Tx (C)

Time 3:

Measurement for 12 V



Description

Location (cm)-

Time 1:

Temperature

Time 2:

Tx (C)

Time 3:

Measurement for 16 V



Description

Location (cm)-

Time 1:

Temperature

Time 2:

Tx (C)

Time 3:

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3. Theory and Analysis:The extended surface is a special case of heat transfer in which the heat is transferred from the solid of the rod by conduction and by convection from the boundaries of the solid. The direction of heat transfer in extended surfaces from the boundaries is perpendicular to the principal direction of heat transfer in the solid. A temperature gradient always exists due to the conductivity of the material and heat loss to the surroundings. The temperature distribution along the fin or pin must be known to determine the heat transfer from the surface to its surroundings. As conduction and convection occurs simultaneously so we also have to consider the effect of both. Conduction is means of heat transfer by molecular action within the material without any motion of the material as a whole. If one end of the rod is at higher temperature than the lower end , the heat transfers to the colder end . As this is the law of nature every material or everything which is at high state tries to move towards the low state. Upon this law, the method of conduction takes place. Heat energy transferred between a surface and a moving fluid at different temperatures is known as convection. In reality this is a combination of diffusion and bulk motion of molecules. Near the surface the fluid velocity is low, and diffusion dominates. Away from the surface, bulk motion increase the influence and dominates.

By considering the steady-state energy balance for an extended surface of uniform material and cross-sectional area, the following equation can be derived: - (1) Where ; Since H, P, Kbrass and A are constant for a given rod with fixed power input, therefore must be a constant


Assuming that the diameter of the pin is small in comparison with its length then heat loss at the tip can be assumed to be negligible (at the tip x=L). (2) Therefore: (3)

Note that the magnitude of the temperature gradient decreases with increasing x. This trend is a consequence of the reduction in the conduction heat transfer with increasing x due to continuous convection and radiation losses from the fin surface.

Part II.

The total heat loss from the rod can be calculated as follows: Qtot = H A s (Ts - Ta) (W)

Where the heat transfer coefficient (HTC) H is the combined coefficient due to natural convection and radiation, i.e. H = Hc + Hr (Wm-2K-1)

And As = D L (Total area of the extended surface)

Where: L = Length of the rod (distance from T1 to T8) = 35 cm

Note: The distance between each thermocouple is 5 cm starting from 0.0 cm at T1.


D = Diameter of the rod = 1 cm

Ts = Average surface temperature of the rod (averaged from temperature T1 to T8) Ta = Ambient air temperature (T9)

The average CHT Hc can be calculated from the formula given below :

(4)WHere (5)

Cn

0.6750.058

1.020.148

0.850.188

0.4800.250

0.1250.333

The thermal conductivity is calculated by : (6)Heat transfer through an extended surface.

Where P = Perimeter of the pin = DA = Cross sectional area of the pin =

Procedure: The procedure to perform this experiment is that we first have to switch on the main switch. Now set the heater voltage to 20V with the help of potentiometer. Now monitor the temperature T1 regularly and when temperature reaches 80C, reduce the heater voltage to 9 voltage. Now allow the temperature to become stabilize to reach the steady state. Now record the voltage and current supplied to the heater. Record the temperature at each position along the rod (T1 to T8) and ambient air temperature (T9). At the end set the heater voltage to 12volts to 16 bolts and follows the above steps.4. Conclusions: As calculating the theoretical power that is transferred to heat the rod is known, but with the help of these equations, net heat lost from the extended surface is calculated and all the results are verified by using above method. Here neglecting the human error and considering that all the heat supplied is to heat the rod and increase the temperature of the system.Practical applications: For the heat transfer, fins are the best example that extends an object to increase the heat transfer by increasing convection. As we already know amount of conduction, convection and radiation of an object determines the rate of heat as how much heat is transferred. We can increase the amount of heat transferred by increasing the temperature gradient, increasing the convection heat transfer coefficient or by simply increasing the surface area. Thus first two options are not so feasible so adding a fin to an object increases the surface area and would be the economical solution to heat transfer.


5. References:Website: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/heatra.htmlhttp://www.engineeringtoolbox.com/convective-heat-transfer-d_430.htmlPaper:Lab Report content: ME-341, Heat and Mass TransferDepartment of Mechanical EngineeringIndian Institute of Technology, KanpurKanpur (UP) 208016, INDIA

6. Appendix:Equation 1 Steady state energy balance equation .Equation 2To make the heat loss negligible.Equation 3Consequence of the reduction in the conduction heat transferEquation 4,5The average CHT can be calculated Equation 6 Calculation of thermal conductivity

fluid lab.docx

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