// Numbas version: exam_results_page_options {"name": "Assignment 3", "metadata": {"description": "

MECE3930U: Heat Transfer Assignment 3

Please follow the Numbas guidance first if you did not attend the Numbas session.

Number of attempts = 5

Time to complete: unlimited

All answers should be provided without the units, but attention must be paid to the unit instructions in each question. For example, if your answer is 100.3 W/m2K, type 100.3 only.

All answers must be rounded to one digit, unless otherwise stated. For example, if your answer is 100.27, type 100.3.

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Air flows with a velocity of $\\var{Vf}$ m/s over a flat plate of length $\\var{L}$ m. The air properties are k=$\\var{kf}$ W/mK, ν =$\\var{vs}$ x 10^-6 m²/s, Pr=0.700.

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What is the Reynolds number at the end of the plate?

Provide your answer with at least four significant figures. Also please do not use scientific notation. For example, if your answer is 1.0278 x 10x6, type 1028000 only.

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What type(s) of flow (laminar/turbulent) exist on this plate?

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At what Reynolds number would laminar flow transition to turbulent flow?

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What is the critical plate length at which laminar flow would transition to turbulent flow?

Provide your answer in meters and with two decimal figures. For example, if your answer is 100.271 m, type 100.27 only.

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Hint: You would be using the critical length that you calculated in the previous part as the upper bound of your integration.

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If the following relations are given for the laminar and turbulent local convection coefficients over the plate,

h_laminar(x)= $\\var{a1}$ /x^0.5

h_turbulent(x)= $\\var{b1}$ /x^0.25

where x is the distance from the plate leading edge, find the average convection coefficient (h\u0304_L) over the portion of the plate length where we have laminar flow.

Provide your answer in W/m²K and with only one decimal figure. For example, if your answer is 100.27 W/m²K, type 100.3 only.

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Now, find the average convection coefficient (h\u0304_L) over the entire plate length.

Provide your answer in W/m²K and with only one decimal figure. For example, if your answer is 100.27 W/m²K, type 100.3 only.

Hint: You would be expanding your solution in the previous part.

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The average convection coefficient as a function of distance from the leading edge (h\u0304_x) over the portion of the plate length where we have laminar flow., i.e. the average convection coefficient at length x if we were to pick an x between x = 0 and x_c , has the following format:

0 < x < x_c

What is A? Provide a numerical answer.

Hint: You would have to repeat Part e, but this time set the upper bound of your integration as a variable, x, to find the function.

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The average convection coefficient as a function of distance from the leading edge (h\u0304_x) over the portion of the plate length where we have turbulent flow., i.e. the average convection coefficient at length x if we were to pick an x between x = x_c and L, has the following format:

x_c < x < L

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According to the previous information:

What is B? Provide your answer with only one decimal figure. For example, if your answer is -100.27, type -100.3 only.

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Hint: You would have to repeat Part f, but this time set the upper bound of your integration for the turbulent region as a variable, x, to find the function.

Hint: You would be expanding your solution in the previous part.

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According to the previous information:

What is C? Provide your answer with only one decimal figure. For example, if your answer is 100.27, type 100.3 only.

Hint: You would have to repeat Part f, but this time set the upper bound of your integration for the turbulent region as a variable, x, to find the function.

Hint: You would be expanding your solution in the previous part.

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On a winter day, when the outside temperature is $\\var{To}$°C, the wind blows at $\\var{Vw}$ km/h. A building with a $\\var{Rw}$ m x $\\var{Rl}$ m flat roof maintains a $\\var{Tr}$°C temperature due to solar heat loading.

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What would be the film temperature to be used in reading air properties from the available tables?

Provide your answer in Kelvin with only one decimal figure. For example, if your answer is 100.27 K, type 100.3 only.

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If the air properties are given as below, what is the Reynolds number at the length of the roof if the wind is blowing along the roof length ($\\var{Rl}$ m)?

Provide your answer with at least four significant figures. Also please do not use scientific notation. For example, if your answer is 1.0278 x 10x6, type 1028000 only.

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Based on the Reynolds number that you have calculated, what type of flow(s) do we have?

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Based on the type of flow, what Nusselt number relation is suitable to be used for calculation of the convection heat transfer coefficient?

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", "

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What is the value of Nusselt number?

Provide your answer with at least three significant figures. Also please do not use scientific notation. For example, if your answer is 1.0278 x 10x6, type 1030000 only.

Hint: You would have to use the Nu number relation that you have selected in the previous part.

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What is the convection heat transfer coefficient? Provide your answer, number only, in W/m²K.

Provide your answer with only one decimal figure. For example, if your answer is 100.27 W/m²K, type 100.3 only.

Hint: You would have to use the Nu number that you have calculated in the previous part.

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Calculate the heat loss from the roof in kW.

Provide your answer with only one decimal figure, in kW. For example, if your answer is 100.27 kW, type 100.3 only.

Hint: You would have to use the convection heat transfer coefficient hat you have calculated in the previous part.

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You did not complete all the questions. Are you sure you want to leave?

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Time is up.

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5 minutes left!

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Instructions:

Numbas number of attempts: 5

Time to complete: unlimited

All answers should be provided without the units, but attention must be paid to the unit instructions in each question. For example, if your answer is 100.3 W/m2K, type 100.3 only.

All answers must be rounded to one digit, unless otherwise stated. For example, if your answer is 100.27, type 100.3.

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