A 10-cm-thick aluminum plate (α = 97.1 × 10−6 m2/s) is being heated in liquid with temperature of 550°C. The aluminum plate has a uniform initial temperature of 25°C. If the surface temperature of the aluminum plate is approximately the liquid temperature, determine the temperature at the center plane of the aluminum plate after 15 s of heating. Solve this problem using the analytical one-term approximation method. The temperature at the center plane after 15 s of heating is

Answers

Answer 1

Answer:

356°C.

Explanation:

(1). The first step to the solution to this particular Question/problem is to determine the Biot number, and after that to check the equivalent value of the Biot number with plate constants.

That is, Biot number = (length × ∞)÷ thermal conductivity. Which gives us the answer as ∞. Therefore, the equivalent value of the ∞ on the plates constant = 1.2732 for A and 1.5708 for λ.

(2). The next thing to do is to determine the fourier number.

fourier number = [α = 97.1 × 10−6 m2/s × 15 s] ÷ (.05m)^2 = 0.5826.

(3). The next thing is to determine the temperature at the center plane after 15 s of heating.

The temperature at the center plane after 15 s of heating = 500°C [ 25°C - 500°C ] [1.2732] × e^(-1.5708)^2 ( 0.5826).

The temperature at the center plane after 15 s of heating = 356°C.


Related Questions

FIGURE 1 shows a horizontal human arm lifting a dumbbell. The forearm is
in equilibrium under the action of the weight of the dumbbell, the tension
in the tendon connected to the biceps muscle, and the force exerted on the
forearm itself. (For clarity, the point A where the tendon is attached is drawn
farther from the elbow than its actual position) Given the weight of the forearm
is 20 N and the mass of the dumbbell is 20 kg. The angle between the tension
force and the horizontal, is 80°. The length of the horizontal arm is 0.30 m.
The horizontal distance between elbow pivot and point A is 0.050 m. Find and
the vector and draw free body diagram for this case

Answers

Answer:

Explanation:

See attached file for answer.

To a stationary observer, a man jogs east at 2 m/s and a woman jogs west at
3 m/s. From the woman's frame of reference, what is the man's velocity?

Answers

Answer:

5 m/s east

Explanation:

i just took the test and it was correct

Answer:

Just took the test. 5 m/s east.

Explanation:

A 30.0 g object fell from a height y = 2.94 m. It’s velocity when y is zero is approximately equal to (in m/s) (a) 0 (b) 19.6 (c) 29.4 (d) 8.64

Answers

Analysing the question:

We are given:

mass of object (m) = 0.03 kg

height of object (h) = 2.94 m

acceleration due to gravity (a) = 10 m/s²

initial velocity (u) = 0 m/s [the object fell, we are NOT given any initial velocity]

final velocity (v) = v m/s

Solving for Final velocity:

from the third equation of motion:

v² - u² = 2ah

replacing the variables

(v)² - (0)² = 2(10)(2.94)

v² = 58.8

v = 7.67 m/s

What element has similar chemical properties to lodine?*

Answers

Answer:

Iodine is most similar  to the other non- metals in the Halogen Family, such as Fluorine, Chlorine, Bromine, Astatine .

Explanation:

Why does a sound come out when you blow into a bottle?

When does the jet of air convert to vibrations?​

Answers

When you blow across the top of the bottle, you set the air molecules vibrating and produce sound waves. ... When the bottle has a small amount of water in it, the air molecules have lots of room and vibrate slower.

Physics Vectors-- Please could you help me ? For first question.

Answers

F1: x component = 0. y component= F1
F2: x component = F2 Sin 30. y component = - F2 Cos 30
F3: x component = - F3 Sin 50. y component = - F3 Cos 50

PLS HELP THIS IS FOR AN EXAM!!!
How many exercises encompass stretching in the human body
A) eight
B) too many to count
C) that depends on each individual
D) none​

Answers

Answer: (B) Too many to count

Explanation: Have a wonderful day everyone! :D

The exercises that encompasses stretching in the human body is : B) too many to count

Meaning of exercise

exercises can be defined as any activity that puts your muscle to work and helps burn calories in your body.

exercises are one of the keys to staying and living healthy.

exercises are of different types and forms and some encompasses stretching in the human body.

In conclusion, The exercises that encompasses stretching in the human body is too many to count

Learn more about exercises : https://brainly.com/question/1365564

#SPJ2

Which direction is the force of gravity on earth

Answers

The force of gravity on earth is towards the center of it
In the downward direction

Answer:

It is toward the center

Explanation:

What are tides?
O Circulation of water
O Glaciers melting causing rising water
O Wind pushing ocean water
O Rise and fall of the water level on the shore

Answers

Answer:

4th

Explanation:

Rise and fall of the water level on the sea shore

The last one


Rise and fall of the water level on the shore

A metric unit of volume equal to a milliliter

Answers

Cubic centimeter is the answer

g A person exploring a deep cave system becomes injured and needs to be rescued. The fastest way to get them is to pull them straight up out of the cave through a small opening just overhead, using a motor-driven cable. The lift is performed in three stages, each of them 10 m in height (total of 30 meters to extract the person). In the first stage, the person is accelerated to a speed of 5 m/s. They are then lifted at constant speed of 5 m/s, then in the last stage they are slowly decelerated to zero speed. If the person weighs 80 kg, how much work is done in each stage

Answers

Answer:

1. W = 8848 J

2. W = 7848 J

3. W = 6848 J

Explanation:

The work (W) can be found using the following equation:

[tex] W = E_{k} + E_{p} [/tex]

Where: E(k) is the kinetic energy and E(p) is the potential energy

Now let's find the work for every stage.

Stage 1:

[tex] W = E_{k} + E_{p} = \frac{1}{2}mv^{2} + mgh [/tex]

Where: m is the mass, g is the gravity, h is the height, v is the speed  

[tex] W = \frac{1}{2}mv^{2} + mgh = \frac{1}{2}80 kg*(5 m/s)^{2} + 80 kg*9.81 m/s^{2}*10 m = 8848 J [/tex]

Stage 2:

[tex] W = E_{k} + E_{p} = 0 + E_{p} [/tex]

The kinetic energy is equal to zero because the acceleration is constant.

[tex] W = E_{p} = mgh = 80 kg*9.81 m/s^{2}*10 m = 7848 J [/tex]

Stage 3:

[tex] W = E_{k} + E_{p} = \frac{1}{2}mv^{2} + mgh = -\frac{1}{2}80 kg*(5 m/s)^{2} + 80 kg*9.81 m/s^{2}*10 m = 6848 J [/tex]      

I hope it helps you!

Wanda is afraid of gaining weight and putting herself at high risk for disease. she works out on a regular basis and eats right most of time. recently, Wanda some testing done. her BMI with some 17.2 and her waist circumference is 30 inches. what statement best describes next move for Wanda so she will be at the least risk for disease?​

Answers

Answer:

C. Wanda's waist circumference indicates that she is not at risk, but her BMI indicates that she underweight. She should develop a plan to move her BMI into the normal range.

Explanation:

edge 2020 Brainliest would be appreciated

Answer:

Wanda's waist circumference indicates that she is not at risk, but her BMI indicates that she underweight. She should develop a plan to move her BMI into the normal range.

Explanation:

I just did the Cumulative Exam Review

Someone is spinning a basketball on his finger. If it is spinning at a rate of 8.92 times per second, what is the basketball's angular velocity in units of radians per second?

Answers

Answer:

angular velocity = 56.04 rad/s.

Explanation:

It is given that,

The baseball is spinning at the rate of 8.92 times per second.

We need to find the basketball's angular velocity in units of radians per second.

Here, frequency of the baseball is 8.92 Hz.

We know that Angular velocity is given by :

[tex]\omega=2\pi f\\\\\omega=2\pi \times 8.92 \\\\\omega=56.04\ rad/s[/tex]

So, the angular velocity of the basketball is 56.04 rad/s.

I WILL MARK YOU AS BRAINLIEST IF RIGHT
In order to climb up a mountainside, a train needs to start at a speed of 40 mph. The speed limit on the track, however, is 25 mph. How much time does the train need to get up to 40 mph if it can accelerate 4 mph per minute ?

Answers

Does it take the train 10 minutes to accelerate at 40mph because 4*10=40
I think the answer is 10

Position vs Time

for Two Cars

Which statements describe the motion of car A and car

B? Check all that apply.

Car A and car B are both moving toward the origin.

Car A and car B are moving in opposite directions.

Car A is moving faster than car B.

A

B

O Car A and car B started at the same location.

Position (m)

O Car A started ahead of car B.

Time (s)

) Intro

Done

Answers

Explanation:

Based on the diagram below we can make the following conclusions that:

Car A and Car B are moving in opposite directionsCar A is moving faster than Car B.

This conclusion is based on the type of slope evident in each case. One has a positive slope, the other a negative slope.

A target lies flat on the ground 4 m from the side of a building that is 10 m tall, as shown below.
The acceleration of gravity is 10 m/s^2.
Air resistance is negligible.
A student rolls a 4 kg ball off the horizontal
the roof of the building in the direction of the
target.
The horizontal speed v with which the ball
must leave the roof if it is to strike the target
is most nearly

1. v =√3 /4 m/s.
2. v =4√3 /3 m/s.
3. v = 4 m/s.
4. v = 2√2 m/s.
5. v =√2 / 4 m/s.
6. v =√5 / 4 m/s.
7. v = 4√3 m/s.
8. v = 4√5 m/s.
9. v = 6 m/s.
10. v = 4√2 m/s.

Answers

Answer:

v = 2√2 m/s

Explanation:

The following data were obtained from the question:

Height (h) = 10 m

Acceleration due to gravity (g) = 10 m/s²

Horizontal distance (s) = 4 m

Horizontal velocity (v) =.?

Next, we shall determine the time taken for the ball to get to the target.

This can be obtained as shown below:

Height (h) = 10 m

Acceleration due to gravity (g) = 10 m/s²

Time (t) =?

h = ½gt²

10 = ½ × 10 × t²

10 = 5 × t²

Divide both side by 5

t² = 10/5

t² = 2

Take the square root of both side.

t = √2 s

Finally, we shall determine the horizontal velocity as shown below:

Horizontal distance (s) = 4 m

Time (t) = √2 s

Horizontal velocity (v) =.?

s = vt

4 = v × √2

Divide both side by √2

v = 4 /√2

Rationalise the denominator

v = (4 /√2) × √2/√2

v = 4 × √2 / √2 × √2

v = 4 × √2 / 2

v = 2√2 m/s

what happends when you slowly pull out the paper while theirs a coin on top​

Answers

The coin would probably slowly slide down whichever end it is closer to, weigh down the end of the paper, and fall off. It kinda depends on how you hold the paper though, because if it is directly in middle, and you hold it on both ends, it will stay on the paper.
The correct answer is “ the coin will stay on the same place on the paper and will move along with the paper “

A small mailbag is released from a helicopter that is rising\ steadily at 2.32 m/s.
(a) After 5.00 s, what is the speed of the mailbag?
(b) How far is it below the helicopter?
(c) What are your answers to parts (a) and (b) if the helicopter is rising steadily at 2.32 m/s?

Answers

Given parameters:

Velocity of the helicopter  = 2.32m/s

Time given  = 5.00s

Unknown:

a. Speed of the mailbag after 5s

b. How far is the mail bag below the helicopter

Solution:

In this problem, we must apply the appropriate motion equation to solve.

For a;

               v  = u + gt  

 v is the velocity of the mail bag

 u is the initial velocity

 g is the acceleration due to gravity

  t is the time taken

         Notice that the initial velocity of the mail bag is 0;

         V  = 0 + 9.8 x 5 = 49m/s

For b;

  Using;

                    h = ut + [tex]\frac{1}{2}[/tex] gt²

   where u is 0;

                  h  = [tex]\frac{1}{2}[/tex] x 9.8 x 5²  = 122.5m

Lien is pushing a box across a table. She used a force of 100 N to get the box moving. Which force did she overcome
to get the box moving?
O the downward force of gravity on the box
O the upward force of the table on the box
the reaction force on the box
O the push force on the box

Answers

Answer:

the reaction force on the box

Explanation:

In order to push or pull an object, an external force is needed to overcome the weight of that object. This force is called ACTION FORCE. However, according to 3rd law of Newton, which states that for every action, there is an equal and opposite reaction, an opposite force counters the object in an opposite direction. This force is called REACTION FORCE.

According to this question, Lien is pushing a box across a table. She used a force of 100 N to get the box moving. This means that she had to overcome an opposite force called REACTION FORCE, with an ACTION FORCE of 100N

Answer:

C. the reaction force on the box

Explanation:

i literally just finished the quiz

An electron is accelerated from rest by a potential difference of 435 V. It then enters a uniform magnetic field of magnitude 167 mT with its velocity perpendicular to the field. Calculate (a) the speed of the electron and (b) the radius of its path in the magnetic field.

Answers

Answer:

(a) the speed of the electron is 1.237 x 10⁷ m/s

(b) the radius of its path in the magnetic field is 4.21 x 10⁻ m

Explanation:

Given;

potential difference, V = 435 V

magnetic field, B = 167 mT = 0.167 T

(a) the speed of the electron

eV = ¹/₂mv²

[tex]v = \sqrt{\frac{2eV}{m} }\\\\ v = \sqrt{\frac{2(1.6*10^{-19})(435)}{(9.1*10^{-31})}}\\\\v = 1.237*10^7 \ m/s[/tex]

(b) the radius of its path in the magnetic field

[tex]r = \frac{mv}{eB}\\\\r = \frac{(9.1*10^{-31})(1.237*10^7)}{(1.6*10^{-19})(0.167)}\\\\r = 4.21 *10^{-4} \ m[/tex]

PLEASE HELP! WILL MARK BRAINLIEST!
In this graphical representation of a vector, which direction is designated as positive?
a) horizontal
b) vertical
c) downward
d) upward

Answers

Answer:

D

Explanation:

when you try to find out if it is positive, the line goes from left to right, and in this question the line is going upward.

Explain whether the size of an object's displacement could be greater than the distance the object travels

Answers

Answer:

Displacement is always less than or equal to distance. Note that distance is a scalar whereas displacement is a vector. So displacement cannot be more than distance.

The size of an object's displacement can never be greater than the distance the object travels by the object because displacement is the shortest distance traveled between the initial and the final position.

What is displacement?

An object's position changes if it moves in relation to a reference frame, such as when a passenger moves to the back of an airplane or a professor moves to the right in relation to a whiteboard.

Displacement can never be greater than the distance covered by any moving body.

Since displacement is the smallest distance between the beginning and final positions, the size of an object's displacement can never be more than the distance the object travels.

Learn more about displacement here, refer to the link;

brainly.com/question/10919017

#SPJ2

If you had a 30 pound barbell at home and you wanted to compare your muscular endurance to your younger brother's which method would be the best to use.

Answers

Answer:A

Explanation:

Absolute method

Answer:

absolute method

Explanation:

trust


What happens to the acceleration of a ball if the force increases while the mass remains the same?

Answers

Answer:

if the force increases while the mass of the ball remains the same, the acceleration increases.

Explanation:

According to Newton's second law of motion, the acceleration of an object produced by a net force is directly proportional to the magnitude of the net force Fn and inversely proportional to the mass of the object m.

[tex]\displaystyle a=\frac{Fn}{m}[/tex]

Suppose the net force doubles to 2Fn. The new acceleration will be:

[tex]\displaystyle a'=\frac{2Fn}{m}=2\frac{Fn}{m}=2a[/tex]

The acceleration doubles too. Thus, if the force increases while the mass of the ball remains the same, the acceleration increases.

Invisible fence for dogs. In this type of system, a wire is buried under the surface and a current at a given frequency passes through the wire. The dog wears a small unit made of a pickup coil and electronics that delivers a short high-voltage pulse to the dog through a couple of electrodes pressed against its skin. The pulse is not harmful, but it does provide a correction that encourages the dog to keep away. In an invisible fence, the wire carries a 10kHz sinusoidal current with an amplitude of 0.5 Amps. The dog carries a sensoron its collar made as a coil with 150 turns and 30 mm in diameter.If the detection level at the coil inside the collar is set at 200 μV RMS (i.e., the level at which the dog will receive a correction pulse), what is the furthest distance from the wire the dog will "feel" the presence of the fence?

Answers

Answer:

The distance is  [tex] s =  2.3 \  m [/tex]

Explanation:

From the question we are told that

   The  frequency of the current is  [tex]f =  10\ kHz  = 10 *10^{3} \  Hz[/tex]

   The magnitude of the  current  is  [tex]I_o  =  0.5\ Amps[/tex]

     The number of turns is  [tex]N =  150\  turns[/tex]

     The  diameter is  [tex]d =  30 mm  = 0.03 \ m[/tex]

      The detection level is  [tex]V_{rms}  =  200 \mu V  =  200 * 10^{-6} \  V[/tex]

Generally the radius is mathematically represented as

      [tex]r =  \frac{d}{2}[/tex]

=>    [tex]r =  \frac{0.03}{2}[/tex]

=>      [tex]r 0.015 \ m [/tex]

Generally the magnetic field  generated by the fence is mathematically represented as

      [tex]B  =  \frac{\mu_o *  N * I}{2 *  \pi * s}[/tex]

Here s is the point where the do will feel the magnetic field

      [tex]\mu_o[/tex] is the permeability of free space with value  [tex]\mu_o =   4\pi * 10^{-7} N/A^2 [/tex]    

   So

         [tex]B  =  \frac{ 4\pi * 10^{-7}  *  150 *  I}{2 * 3.142  * s}[/tex]

Generally the magnetic flux is mathematically represented as

     [tex]\Phi =  B *  \pi * r^2[/tex]

=>   [tex]\Phi =   \frac{ 4\pi * 10^{-7}  *  150 * I}{2 * 3.142  * s} *  \pi * r^2[/tex]

=>   [tex]\Phi  =  \frac{2.121 *10^{-8} *  I }{s}[/tex]

Generally the induced emf is mathematically represented as

      [tex]\epsilon  =- \frac{d \Phi}{dt}[/tex]

=>    [tex]\epsilon  =- \frac{ 2.121 *10^{-8} }{ s } *  \frac{d I}{dt}[/tex]

Generally the angular frequency is mathematically represented as

   [tex]w =  2 \pi f[/tex]

=>        [tex]w =  2 *  10*10^{3} \pi [/tex]

=>       [tex]w =  20000 \pi [/tex]

So the current is mathematically represented as

        [tex]I = I_o sin (wt)[/tex]

=>     [tex]I = I_o sin ( 20000 \pi * t)[/tex]

So

  [tex]\epsilon  =- \frac{ 2.121 *10^{-8} }{ s } *  \frac{d [ I_o sin ( 20000 \pi * t)]}{dt}[/tex]

  [tex]\epsilon  =- \frac{ 2.121 *10^{-8} }{ s } *  I_o * 20000 \pi   [  cos ( 20000 \pi * t) [/tex]  

   [tex]\epsilon  =- \frac{ 2.121 *10^{-8} }{ s } * 0.5 * 20000 \pi   [  cos ( 20000 \pi * t) [/tex]    

    [tex]\epsilon  =- \frac{ 6.6*10^{-4} }{ s } [  cos ( 20000 \pi * t) [/tex]  

Here the  

    [tex]\epsilon_{rms} = \frac{ \frac{ 6.6*10^{-4} }{ s }}{\sqrt{2} }[/tex]

=>     [tex]\epsilon_{rms} = \frac{ 6.6*10^{-4} }{ s\sqrt{2}  }[/tex]

But from the question we are told that  [tex]V_{rms}  =  200 \mu V  =  200 * 10^{-6} \  V[/tex]

So

    [tex]\frac{ 6.6*10^{-4} }{ s\sqrt{2}  } = 200 * 10^{-6}[/tex]

=>  [tex]6.6*10^{-4}= 2.8284 *10^{-4} * s[/tex]

=>  [tex] s =  2.3 \  m [/tex]

Where is the magnetic south pole compared to the geographical north pole?

Answers

Currently, the magnetic south pole lies about ten degrees distant from the geographic north pole, and sits in the Arctic Ocean north of Alaska. The north end on a compass therefore currently points roughly towards Alaska and not exactly towards geographic north.

please please please please ​

Answers

Answer:

....................

Answer:

20

Explanation:

40/2.0=20.......

hope it helps

this is a Physical Education question

Answers

B. Because your thumb has it’s own pulse that you may feel.

A car traveling at 30 m/s is brought to rest at a constant rate in 20 s by applying the brake. a) What is its acceleration? b) How far did it travel after the brake was applied?

Answers

acceleration = -30/20 = -1.5 m.s^2
V^2 = U ^2 + 2 a s
0 = 900 - 2 x 1.5 x s
3 s = 900
s = 300 m

True or false:
A small wire can conduct an infinite amount of current.

Answers

Answer:

True

Explanation:

Answer: very true

Explanation:

Other Questions
Which phrase in "Harun al-Rashid & One Thousand and One Nights" uses imagery to describe the Middle East?"knowledge and education were so prized and supported""a hotbed of discovery, invention, and ingenuity""widely considered to be the start of what is now known as the Islamic Golden Age""painting a vivid and memorable (if not wholly realistic) picture of a world of deep intrigue" Los estudiantes _________ padirle perdon a la profesora A. DevrianB. DeberanC. Deberia D. Debian Identify three common shortfall nutrients will give brainllest :)The two angles shown in the figure are supplementary. What is the value of x? Simplify: 2y + x + 3x - y Given the equation 9x - 3y - 27 in standard form. Show how you wouldconvert the equation into slope-intercept form - y = mx + b. You mustshow your work to receive full credit. (3 points) What is 20 times the difference of nine and a number in an algebraic expression The sum of the first three terms of a sequence is 6 and the fourth term is 16 Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs. You need a $ loan. Option 1: a 30-year loan at an APR of %. Option 2: a 15-year loan at an APR of %. Find the monthly payment for each option. The monthly payment for option 1 is $ nothing. The monthly payment for option 2 is $ nothing what can you say about the logo in general? A car dealer paid $21,000 for a car and marked it up by 1/3 of the price he paid.How much did he sell the car for? Solve for ABCDHurry please!!! Ill give the brainliest answer to whoever shows their works first!!!! A block of lead has dimensions of 4.50 cm by 5.20 cm by 6.00 cm. The block weights 1587 g. From this information, calculate the density of lead. how do i add 3=5 jejekfewnfkwnwewkjfnw Many cities in Texas, such as El Paso and San Antonio reflect the cultural legacy of A. France B.England C.Portugal D. Spain. How did the rise of the Mauryan empire change India? using this format fill out the doc Driving to distortion MandiKyleAaronChanceFacts Choose all that apply.Examples of primary sources would include _____.fictional worksartifactshuman remainsscholarly worksdiaries 0.00000001073 as a scientific notation "Mirror"-The metaphor (eye of a little god) in line 5 gives the impression that....