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Description of quizzes

Author: Christian Ghiaus

INSA Lyon, France, 18/04/2020

Three quizzes are presented:

  1. PyClz00: given the names and the ages of three children, find the mean age, the eldest child and the longest name.
  2. PyClz01: find the thermal resistance, the heat flux and the heat transfer rate of a flat wall.
  3. PyClz02: find the coefficient of heat exchange in forced and in natural convection.

For a quick visualization of the quizzes, import one of the PyClz__.xml files in Moodle. See Tutorial_xml2moodle.md for further details on how to create a quiz with random questions (i.e. questions different for each student).

To visualize a PyClz__.xml file, open it with a browser. The file structure is according to .xml format.

Convenctions used in the descriptions of the problems:

  • input data is in bold,
  • embedded answers are between { }.

Quiz PyClz00

Problem

John Smith has 3 children: name_1, age age_1, name_2, age age_2, name_3, age age_3.

The mean age of the children is μ ={:NUMERICAL:}.

The eldest child is {:MULTICHOICE:}.

The child with the longest name is {:SHORTANSWER:}.

The input data for the problem:

Child_1 Child_2 Child_3
Names
1. Antoinette Lawrence Sebastian
2. Anastasia Catherine Quentin
Ages
1. 10.2 12.9 9.7
2. 23.4 12.5 17.2
3. 4.9 14.1 8.5

This set of data will generate 2 (name_list) x 3 (age_list) = 6 combinations of inputs from which one will be randomly assigned to a student.

Quiz PyClz01

Problem

Let's consider a flat concrete wall of width w [m] and surface area S [m²]. The surfaces at x = 0 and at x = w are maintained at temperatures θ0 [°C] and θw [°C]. It will be assumed that the heat transfer is in one direction and in steady state, without internal sources and that the thermal conductivity of concrete is λ [W/m·K].

Give the values of:

U = {:NUMERICAL:} W/m²·K, thermal transmittance,

R = {:NUMERICAL:} K/W, (absolute) thermal resistance,

= {:NUMERICAL:} W/m², heat flux,

= {:NUMERICAL:} W, heat transfer rate.

The input data for the problem:

w = np.arange(0.10, 0.30, 0.10)     # width [m] (2 values)
S = np.arange(20, 30, 10)           # surface area [m2] (1 value)
θ0 = np.arange(0, -10, -5)          # temperature at x = 0 [°C] (2 values)
θw = np.arange(20, 22, 2)           # temperature at x = w [°C] (1 value)
λ = np.array([0.5, 1.0, 1.8])       # thermal conductivity [W/m·K] (3 values)

This set of data will generate 2 x 1 x 2 x 1 x 3 = 12 questions from which one will be randomly assigned to a student.

Solution

Quiz PyClz02

Problem

Evaluation of convective exchange coefficients

Let's consider a copper pipe in which a pump circulates water. The tube is in still air. It is considered that the temperature of the outer surface of the tube is almost equal to the temperature inside the tube. By using existing correlations for forced convection in the tube and for natural convection in the air (based on the Grashof number), find the values of the coefficients of convective exchange in the tube (water - tube) and outside of the tube (air - tube) for the water temperature in the pipe θw [K], and the air temperature θa [K].

Data

Thermo-physical properties

Substance T [K] λ [W/m·K] μ [Pa·s] ρ [kg/m³] c [J/kg·K] β [1/K]
Water Tw λw μw ρw cw βw
Air Ta λa μa ρa ca βa

Pipe

D [m] w [m] v [m/s]
D w v

Give the values of:

$h_i$ = {:NUMERICAL:} W/m²·K, coefficient of convective exchange between water and pipe.

$h_{o,min}$ = {:NUMERICAL:} W/m²·K, minimum value of the convective exchange coefficient of the pipe with the air.

$h_{o,max}$ = {:NUMERICAL:} W/m²·K, maximum value of the convective exchange coefficient of the pipe with the air.

Fill in the sentence:

The correlation used for forced convection in a tube is called the formula of {:SHORTANSWER}.

Choose the correct answer:

The type of air flow is {:MULTICHOICE:}

The input data for the problem

Thermophysical properties:

T[K] λ[W/m·K] μ[Pa·s] ρ[kg/m³] c[J/kg·K] β[1/K]
water
1 330 0.650 489e-6 984 4184 504.0e-6
2 340 0.660 420e-6 979 4188 566.0e-6
3 350 0.668 365e-6 974 4195 624.2e-6
4 360 0.674 324e-6 967 4203 697.9e-6
5 365 0.677 306e-6 963 4209 701.1e-6
air
1 250 22.3e-3 15.96e-6 1.3947 1.006e3 4.08e-3
2 300 26.3e-3 18.46e-6 1.1614 1.007e3 3.38e-3

Copper pipe:

D[m] w[m] v [m/s]
1 0.022 0.001 0.63
2 0.035 0.001 0.81
3 0.042 0.001 0.89

This set of data will generate 5 x 2 x 3 = 30 questions from which one will be randomly assigned to a student.

Solution

Find the convective coeficient for water:

  • Find Reynolds number for the water in the tube:

  • Find Prandtl number for water:

  • If 0.7 < Pr < 160 and 10000 < Re < 120000, then:

Find the convective coeficient for air:

If 1e3 < Gr < 1e9, the flow is laminar;

if 1e9 < Gr < 1e12, the flow is turbulent;

otherwise, the corelations are not applicable.

From

with

Flow type C n
laminar 0.2 ... 0.6 1/4
turbulent 0.07 ... 0.15 1/3

it results

The minimum and maximim values of $h_o$ are given by considering the minimum and maximum values of C.