You subjected a rod under the cyclic stress with the maximum stress of 200 MPa and minimum stress of 20 MPa. The fatigue limit was determined to be ~100 MPa. How many cycles can this materials sustain before failure?

Answer:

Hello the needed relation is missing below is the required relation

[tex]X_{p} = \frac{x_{s} }{1+x_{s} }[/tex]   composition : propane = 0.70, butane = 0.3

Answer : ≈ 5.75 hrs

Explanation:

Applying the data given in regards to the material balance

Butane balance input into the still = 5 mole feed/hr | 0.30 mol butane/molfeed

since the total volume of the liquid in the still is constant

The output from the still is = 5mol condensed/hr | x[tex]_{p}[/tex] mol butane/mol condensed

unsteady state equation = [tex]\frac{dx_{s} }{dt}[/tex] = 0.15 - [tex]0.5X_{p}[/tex]

note : to reduce the equation a single dependent variable we have to substitute for [tex]x_{p}[/tex]

[tex]\frac{dx_{s} }{dt}[/tex] [tex]= 0.15 + x_{s} / 1 + (0.5)x_{s}[/tex]

In order to find the time it will take for X to change from 0.3 to 0.35

integrate the above equation using the limits : t = 0, x[tex]_{s}[/tex] = 0.3 and t = Ф,

x[tex]_{s} = 0.35[/tex]

= [tex][ - (x_{s} /0.35 - (1/(0.35)^2)* In(0.15 - 0.35x_{s} ) ]_{0.3} ^{0.35}[/tex]

hence t = Ф ≈ 5.75 hrs

Answer:

P=11 kW

Explanation:

Given that

Number of poles= 8

I.E.C. 180L motor frame

From data book , for 8 poles motor at 50 Hz

Speed = 730 rpm

Power factor = 0.75

Efficiency at 100 % load= 89.3 %

Efficiency at 50 % load= 89.1 %

Output power = 11 kW

Therefore the rated output power of 8 poles motor will be 11 kW. Thus the answer will be 11 kW.

P=11 kW

Answer:

1) There are  three (3) PWM generator blocks in LM3S1968 and they are

2)  Two (2) independent  PWM outputs can be generated on an LM3S1968

3) Applications for PWM

4) NVIC in a timer stand for ; Nested Vectored Interrupt Controller

its significance is that it is used to handle  and give priorities to exception and Interrupts

5) The counter/timer derive its time period from  counting the output pulses for one cycle which is the duration over which gate is open

Explanation:

1) There are  three (3) PWM generator blocks in LM3S1968 and they are

2)  Two (2) independent  PWM outputs can be generated on an LM3S1968

3) Applications for PWM

4) NVIC in a timer stand for ; Nested Vectored Interrupt Controller

its significance is that it is used to handle  and give priorities to exception and Interrupts

5) The counter/timer derive its time period from  counting the output pulses for one cycle which is the duration over which gate is open

6) THE WAVEFORM DIAGRAMS IS ATTACHED BELOW

it can be seen  that 50 % rises and goes down at half interval. 75 % goes down at half more of 50% and 25% goes down at half less of 50%

The red and green lights are sidelights that are positioned on the port side (red) (left as facing the bow) and starboard (green) (right as facing the bow) side of the boat. Various white lights are required depending on the size of the boat, but generally, a white masthead light and stern light are required. See the US Coast Guard site in the link below for more specific information.

Hope this helps

Answer:

hello your question is incomplete here is the complete question

. “ABC construction Inc.” company becomes the lowest in the bed process to get a $21 million construction project for “Northern Inc.”. Now “ABC construction Inc.” planning to make a formal contract agreement with the “Northern Inc.”. What are the main elements of this agreement to consider it as a legal contract?

Answer : elements of the agreement

Explanation:

Offer : an offer is the beginning element for any valid agreement to be started or reached between two or more bodies. ABC construction would have to make an offer first for the agreement to be valid

Acceptance: This is part where by the company "Northern Inc" after receiving the offer from ABC construction Inc would have to consent to the approval of the offer made.

capacity : This the element of the agreement that helps to ensure that both parties have the legal and financial backings to embark on the contract agreement .

certainty : This element ensures that both parties understands the terms and conditions attached to the agreement and this to ensure that there are no bogus conditions

Consideration : This is a very vital element because the both parties have to give something in return while going into a valid agreement

Intention to create legal relation : Legal relations are applied to contract agreements whereby both parties want the contract agreement to b legally enforced and this is important in order to prevent contract breach by any party involved in the agreement

Answer:

Both technician A and technician B are correct.

Explanation: Vehicle manufacturers always specify the size of the tires required for a given vehiclefor optimal efficiency,this will ensure that the speedometer is accurate and the level of the vehicle is good enough to ensure the vehicle works efficiently.

It is also a known fact that an increase in a vehicle's rpm(revolution per minute) will eventually lead to increased fuel consumption which means the fuel economy of the vehicle will be reduced making the vehicle less efficient in its fuel consumption.

Answer: 0.002174

Explanation:

Given that the

Yield strength rho = 450 MPa

Length = 2 m

Elastic modulus E= 207 GPa

According to Hook's law, if the elastic limits is not reached, the elastic modulus is the ratio of elastic strength to the elastic strain ə

E = rho/ə

Make ə the subject of formula

ə = rho/ E

ə = (450 × 10^6) / (207 × 10^9)

ə = 2.174 × 10^-3

Therefore, the engineering strain which depends on engineering stress and elastic modulus is 2.174 × 10^-3

Elastic Strain has no S.I Units.

Answer:

Maneuvering speed.

Explanation:

The speed above which an airplane will experience structural damage when a load is applied, instead of stalling, is called the maneuvering speed and varies with weight.

In aeronautical engineering, the maneuvering speed (Va) of an aircraft such as an aeroplane, helicopter, or jet is an airspeed limitation which is mainly selected by an aircraft designer.

Generally, at speeds higher or greater than the manoeuvring speed, aircraft pilots are advised not to attempt a full deflection of any flight control surface because it's capable of resulting in a damage to the structure of an aircraft.

If you're a pilot, to find the maneuvering speed of an aircraft, you should look at the flight manual of the aircraft or on the cockpit placard in the aircraft. The maneuvering speed of an aircraft is a calibrated speed and should not be exceeded by any pilot.

Answer:

Voltage across resistor = 2 v

Explanation:

Given data

pulse height = 2 v

pulse width = 4s

calculate voltage across resistor ( the free hand sketch attached below explains more )

pulse height is also = amplitude of voltage ) = 2v

The voltage across the resistor = 2v  Since  the voltage from the source of the circuit is equal to the amplitude voltage in the circuit ( assuming no loss of voltage )

also the graphical representation of the problem is attached below

Answer:

a. True

Explanation:

Apply the principle of conservation of mass.

and also the expression for the steady flow energy equation.

kinetic and potential energy effects can be neglected.

The given statement by the inventor who is claiming the development of a device that requires no work or heat transfer input yet is able to produce hot and cold air streams at a steady state is definitely false.

Heat transfer may be characterized as a type of process which involves the migration of heat from one object or component to another by numerous mechanisms like conduction, convection, and/or radiation.

The process of heat transfer may occur where there is a temperature difference between two objects exist. It significantly utilizes the mechanism of exchanging thermal energy between two or more physical systems.

According to the concept of physics, no object or thing has the ability to perform its function without the utilization of any source of heat or energy. Then, how it is possible for that device to produce hot and cold air streams at a steady state.

Therefore, the given statement by the inventor is absolutely false.

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Answer:

The liquids are TOLUENE because the equilibrum vapor above it will be flammable ( D )

Explanation:

Liquids stored at : 1 atm , 25⁰c  and they are vented with air

Determining whether the equilibrum vapor above the liquid will be flammable

We can determine this by using Antoine equation to calculate saturation vapor pressure also apply Dalton's law to determine the volume % concentration of air and finally we compare answer to flammable limits to determine which liquid will be flammable

A) For acetone

using the Antoine equation to calculate saturation vapor pressure

[tex]In(P^{out} ) = A - \frac{B}{C + T}[/tex]

values gotten appendix E ( chemical process safety (3rd edition) )

A = 16.6513

B = 2940.46

C = -35.93

T = 298 k      input values into Antoine equation

therefore ; [tex]p^{out}[/tex] = 228.4 mg

calculate volume percentage using Dalton's law

= V% = (saturation vapor pressure / pressure ) *100

         = (228.4 mmHg / 760 mmHg) * 100 = 30.1%

The liquid is not flammable because its UFL = 12.8%

B) For Benzene

using the Antoine equation to calculate saturation vapor pressure

[tex]In(P^{out} ) = A - \frac{B}{C + T}[/tex]

values gotten appendix E ( chemical process safety (3rd edition) )

A= 15.9008

B = 2788.52

C = -52.36

T = 298 k   input values into the above equation

[tex]p^{out}[/tex] = 94.5 mmHg

calculate volume percentage using Dalton's law

V% = (saturation vapor pressure / pressure ) *100

      = (94.5 / 760 ) * 100 = 12.4%

Benzene is not flammable under the given conditions because its UFL =7.1%

C) For cyclohexane

using the Antoine equation to calculate saturation vapor pressure

[tex]In(P^{out} ) = A - \frac{B}{C + T}[/tex]

values gotten appendix E ( chemical process safety (3rd edition) )

A = 15.7527

B = 2766.63

c = -50.50

T = 298 k

solving the above equation using the given values

[tex]p^{out}[/tex] = 96.9 mmHg

calculate volume percentage using Dalton's law

V% = (saturation vapor pressure / pressure ) *100

      = ( 96.9 mmHg /760 mmHg) * 100 = 12.7%

cyclohexane not flammable under the given conditions because its UFL= 8%

D) For Toluene

using the Antoine equation to calculate saturation vapor pressure

[tex]In(P^{out} ) = A - \frac{B}{C + T}[/tex]

values gotten from appendix E ( chemical process safety (3rd edition) )

A = 16.0137

B = 3096.52

C = -53.67

T = 298 k

solving the above equation using the given values

[tex]p^{out}[/tex] = 28.2 mmHg

calculate volume percentage using Dalton's law

V% = (saturation vapor pressure / pressure ) *100

     = (28.2 mmHg / 760 mmHg) * 100 = 3.7%

Toluene is flammable under the given conditions because its UFL= 7.1%

Answer:

A.) 0 > K > 9.6

B.) K = 9.6

C.) w = +/- 2 sqrt (3)

Explanation:

G(s)= K(s+4)/s(s+1.2)(s+2)

For a closed loop stability, we can analyse by using Routh - Horwitz analysis.

To make the pole completely imaginary, K must be equal to 9.6 Because for oscillations. Whereas, one pair of pole must lie at the imaginary axis.

Please find the attached files for the solution

Answer:

See calculation below

Explanation:

Given:

W = 30 kN = 30x10³ N

d = 75 mm

p = 6 mm

D = 300 mm

μ = tan Φ = 0.2

1. Force required at the rim of handwheel

Let P₁ = Force required at the rim of handwheel

Inner diameter or core diameter of the screw = dc = do - p = 75 - 6 = 69 mm

Mean diameter of screw:    *d = [tex]\frac{do + dc}{2}[/tex] = (75 + 69) / 2 = 72 mm

and

tan α = p / πd  =  6 / (π x 72)  =  0.0265

∴ Torque required to overcome friction at he threads is  T = P x d/2

T = W tan (α + Ф) d/2

T =  [tex]W(\frac{tan \alpha + tan \theta}{1 - tan \alpha + tan \theta } ) * \frac{d}{2}[/tex]

T = 30x10³ * ((0.0265 + 0.2) / (1 - 0.0265 x 0.2)) x 72/2

T = 245,400 N-mm

We know that the torque required at the rim of handwheel (T)

245,400 = P1 x D/2 = P1 x (300/2) = 150 P1

P1 = 245,400 / 150

P1 = 1636 N

2. Maximum compressive stress in the screw

                         30x10³

Qc = W / Ac = -------------- = 8.02 N/mm²

                      π/4 * 69²

Qc = 8.02 MPa

Bearing pressure on the threads (we know that number of threads in contact with the nut)

n = height of nut / pitch of threads = 150 / 6 = 25 threads

thickness of threads, t = p/2 = 6/2 = 3 mm

bearing pressure on the threads = Pb = W / (π d t n)

Pb = 30 x 10³ / (π * 72 * 3 * 25)

Pb = 1.77 N/mm²

Max shear stress on the threads = τ = 16 T / (π dc³)

τ = (16 * 245,400) / ( π * 69³ )

τ = 3.8 M/mm²

*the mean dia of the screw (d) = d = do - p/2 = 75 - 6/2 = 72

∴max shear stress in the threads τmax = 1/2 * sqrt(8.02² + (4 * 3.8²))

τmax = 5.5 Mpa

3. efficiency of the straightener

To = W tan α x d/2 = 30x10³ * 0.0265 * 72/2 = 28,620 N-mm

∴Efficiency of the straightener is η =  To / T = 28,620 / 245,400

η = 0.116 or 11.6%

By assuming the coefficient of friction for the collar as 0.2. efficiency of straightner is 11.6%.

Wheels are circular frames or disks that are mounted on machines or vehicles and are designed to rotate around an axis.

Given:

W = 30 kN = 30x10³ N

d = 75 mm

p = 6 mm

D = 300 mm

μ = tan Φ = 0.2

1. Force required at the rim of handwheel :

Let P₁ = Force required at the rim of handwheel

Inner diameter or core diameter of the screw = dc = do - p = 75 - 6 = 69 mm

Mean diameter of screw:    *d =  = (75 + 69) / 2 = 72 mm and

tan α = p / πd  =  6 / (π x 72)  =  0.0265

Torque required to overcome friction at he threads is  T = P x d/2

T = W tan (α + Ф) d/2

T = 30x10³ * ((0.0265 + 0.2) / (1 - 0.0265 x 0.2)) x 72/2

T = 245,400 N-mm

We know that the torque required at the rim of handwheel (T)

245,400 = P1 x D/2 = P1 x (300/2) = 150 P1

P1 = 245,400 / 150

P1 = 1636 N

2. Maximum compressive stress in the screw :

30x10³

Qc = W / Ac = -------------- = 8.02 N/mm²

π/4 * 69²

Qc = 8.02 MPa

Bearing pressure on the threads (we know that number of threads in contact with the nut)

n = height of nut / pitch of threads = 150 / 6 = 25 threads

thickness of threads, t = p/2 = 6/2 = 3 mm

bearing pressure on the threads = Pb = W / (π d t n)

Pb = 30 x 10³ / (π * 72 * 3 * 25)

Pb = 1.77 N/mm²

Max shear stress on the threads = τ = 16 T / (π dc³)

τ = (16 * 245,400) / ( π * 69³ )

τ = 3.8 M/mm²

*the mean dia of the screw (d) = d = do - p/2 = 75 - 6/2 = 72

max shear stress in the threads τmax = 1/2 * sqrt(8.02² + (4 * 3.8²))

τmax = 5.5 Mpa

Therefore, efficiency of the straightener :

To = W tan α x d/2 = 30x10³ * 0.0265 * 72/2 = 28,620 N-mm

Efficiency of the straightener is η =  To / T = 28,620 / 245,400

η = 0.116 or 11.6%

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Answer:

(a) The magnitude of force is 116.6 lb, as exerted by the rod CD

(b) The reaction at A is (-72.7j-38.1k) lb and at B it is (37.5j) lb.

Explanation:

Step by step working is shown in the images attached herewith.

For this given system, the coordinates are the following:

A(0, 0, 0)

B(26, 0, 0)

And the value of angle alpha is 20.95°

Hope that answers the question, have a great day!

Answer:

56.47%

Explanation:

Determine the efficiency of the Engine

Given data :  T1 (k) = 325, P1 (kpa) = 185,

V1 (cm^3) = 410 , r = 8, T3(k) = 3420

speed ( RPM) = 4800

USING THIS FORMULA

efficiency ( n ) = [tex]1 - (\frac{1}{(rp)^{r-1} })[/tex]

= 1 -  [tex](\frac{1}{(8)^{r-1} })[/tex] = 1 - (1/8^1.4-1 )

= 0.5647 = 56.47%

Answer:

The discharge temperature is 259.82 K

Explanation:

In this question, we are concerned with calculating the discharge temperature

Please check attachment for complete solution

Answer:

a) 0.42

b) Independent

c) 30%

d) 0.88

Explanation:

Person chooses Chicken's item : 70% = 0.7

Person chooses fish's item : 30% = 0.3

Visits in which he orders Afghani Chicken = 60% = 0.6

a) Probability that he goes to KARIM and orders Afghani Chicken:

P = 0.7 * 0.6 = 0.42

b) Two events are said to be independent when occurrence of one event does not affect the probability of the other event's occurrence. Here the person orders Afghani Chicken regardless of where he visits so the events are independent.

c)  P = 0.30 because he orders Afghani Chicken regardless of where he visits.

d)  Let A be the probability that he goes to KARIM:

P(A) = 0.7 * ( 1 - 0.6 ) = 0.28

Let A be the probability that he orders Afghani Chicken:

P(B) =  0.3 * 0.6 = 0.18

Let C be the probability that he goes to KARIM and orders Afghani chicken:

= 0.7 * 0.6 = 0.42

So probability that he goes to KARIM or orders Afghani Chicken or both:

P(A) + P(B) + P(C) = 0.28 + 0.18 + 0.42 = 0.88

Answer:

A.) 0.08 kJ/kg.K

B.) 207.8 KJ/Kg

C.) 0.808

Explanation:

From the question, the use of fluids mechanic table will be required. In order to get the compressor processes, the kinetic energy and the potential energy will be negligible while applying the ideal gas model.

Since the steam is a closed system, the carbon dioxide will be compressed adiabatically.

Please find the attached files for the solution and the remaining explanation.

Answer:

A. Forces that act perpendicular to the surface and pull an object apart exert a tensile stress on the object.

Explanation:

Tensile stress is due to tension forces on a material. Tensile force acts perpendicularly away from the surface of the substance. The pull on the material due to the tensile force exerts tensile stress on the material, that tends to pull the material apart. The magnitude of the tensile stress is given as

σ = [tex]\frac{P}{A}[/tex]

where σ is the tensile stress

P is the tensile force pulling the material apart

A is the cross-sectional area through which the tensile force acts perpendicularly.

Answer:

from the below explanation...  we can say that, in the series circuit, flowing current remains the same at each part of the circuit. While in parallel circuits, the voltage across two endpoints of the branches is the same as the supplied voltage.

Explanation:

1.

The components in a series circuit are arranged in a single path from one end of supply to another end. However, the multiple components in a parallel circuit are arranged in multiple paths wrt the two end terminals of the battery.

2.

In a series circuit, a common current flows through all the components of the circuit. While in a parallel circuit, a different amount of current flows through each parallel branch of the circuit.

3.

In the series circuit, different voltage exists across each component in the circuit. Whereas in the parallel circuit, the same voltage exists across the multiple components in the circuit.

4.

A fault in one of the components of the series circuit causes hindrance in the operation of a complete circuit. As against fault in a single component in a parallel network do not hinder the functioning of another part of the circuit.

5.

The detection of a fault in case of a series circuit is difficult, but it is quite easy in parallel circuits.

6.

The equivalent resistance in case of a series circuit is always more than the highest value of resistance in the series connection. While the equivalent resistance in the parallel circuit is always less than any of the individual resistances in parallel combination.

Answer:

The normal stress is 0.7821 MPa

Explanation:

The external diameter D = 160 mm

The thickness t = 3.8 mm = 3.8 x 10^-3 m

gauge pressure P = 78 kPa = 78 x 10^3 Pa

The maximum shear stress τmax = ?

The external radius of the shell from the external surface R = D/2 = 160/2 = 80 mm

The internal radius of the shell r = R - t

==> 80 - 3.8 = 76.2 mm

Therefore the internal diameter d = 2r = 2 x 76.2 = 152.4 mm

==> d = 152.4 x 10^-3 m

The normal stress σ = [tex]\frac{Pd}{4t}[/tex] = [tex]\frac{78*10^{3}*152.4*10^{-3} }{4*3.8*10^{-3} }[/tex] = 782052.63 Pa

==>  σ = 0.7821 MPa

Answer + Explanation:

For computing the displacement at point B and D we need to determine the following calculations

Pnet = Pc + Pe + Pb

Pnet = 250 + 350 - 50

Pnet = 550 N

Now the deflection for bar AB is

           PLab

δab = -------------

            ae

     550 * 500

= -------------------------

     6,000 * 200 x 10³

= 2.292 x 10⁻⁴mm

Now for bar BC it is

           PLbc

δbc = ------------

             ae

  (550 + 50) * 250

=  ----------------------

   5,000 * 200 x 10³

= 1.5 x 10⁻⁴mm

And for bar CD it is

           PLcd

δcd = ------------

             ae

  (550 - 250 + 50) * 250

=  --------------------------------

   5,000 * 200 x 10³

= 0.875 x 10⁻⁴mm

Now the displacement is as follows

For B = 2.292 × 10⁻⁴ mm

For D = 4.667 × 10⁻⁴ mm

= 2.292 × 10⁻⁴ + 1.5 × 10⁻⁴ + 0.875 × 10⁻⁴

= 4.667 × 10⁻⁴ mm

We simply applied the above formulas for determining the  displacements at points B, D and the same is to be considered

Answer:

An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of integration

Explanation:

Answer:

Explanation:

If the museum is running short of funds, and you decide to increase revenue. An increase or decrease in the price of admission into the museum depends on the following:

1. If demand for admission into the museum is elastic there are two possible outcomes

a. An increase in the price of admission leads to a decrease in the quantity demand of admission into the museum

b. A decrease in price of admission into the museum leads to an increase in the quantity demand of admission into the museum.

This follows the law of demand which states that "the higher the price, the lower the quantity demanded and the lower the price, the higher the quantity demanded".

2. If the demand for admission into the museum is inelastic, then an increase in price will lead to an increase in revenue of the museum.

Therefore, before the curator increase the price of admission into the museum, he should first determine the price elasticity of demand of the museum.

Answer:

no need for that

Explanation:

they are not the same at all

Answer:

There are six conditions

1. Poles should contain some residual flux.

2. Field and armature winding must be correctly connected so that initial mmm adds residual flux.

3. Resistance of field winding must be less than critical resistance.

4. Speed of prime mover of generator must be above critical speed.

5. Generator must be on load.

6. Brushes must have proper contact with commutators.

Explanation:

Answer:

24 hours

Explanation:

you must exchange insurance details after a collision if someone is injured. Otherwise you must report the collision to us as soon as possible (and no later than 24 hours). Although you must report such a collision straight away you should always seek medical help in the first instance.

Answer:

(a) The value of the resistance is 3.431 Ω

(b) The value of the inductance is 0.0264 H

Explanation:

Given;

frequency of the source, f = 60 Hz

rms voltage, V-rms = 220 V

real power, Pr = 1500 W

apparent power, Pa = 4600 VA

(a). Determine the value of the resistance

[tex]P_r = I_{rms}^2R[/tex]

where;

R is resistance

[tex]I_{rms} = \frac{Apparent \ Power}{V_{rms}} \\\\I_{rms} = \frac{P_a}{V_{rms}}\\\\I_{rms}= \frac{4600}{220} \\\\I_{rms}= 20.91 \ A[/tex]

Resistance is calculated as;

[tex]R = \frac{P_r}{I_{rms}^2} \\\\R = \frac{1500}{(20.91)^2} \\\\R = 3.431 \ ohms[/tex]

(b). Determine the value of the inductance.

[tex]Q_L = I_{rms}^2 X_L[/tex]

where;

[tex]Q_L[/tex] is reactive power

[tex]X_L[/tex] is inductive reactance

[tex]Apparent \ power = \sqrt{Q_L^2 + P_r^2} \\\\P_a^2 = Q_L^2 + P_r^2\\\\Q_L^2 = P_a^2 - P_r^2\\\\Q_L^2 = 4600^2 - 1500^2\\\\Q_L^2 = 18910000\\\\Q_L = \sqrt{18910000}\\\\Q_L = 4348.56 \ VA[/tex]

inductive reactance is calculated as;

[tex]X_L = \frac{Q_L}{I_{rms}^2} \\\\X_L = \frac{4348.56}{(20.91)^2} \\\\X_L = 9.95 \ ohms[/tex]

inductance is calculated as;

[tex]X_L = \omega L\\\\X_L = 2\pi f L\\\\L = \frac{X_L}{2\pi f} \\\\L = \frac{9.95}{2\pi *60} \\\\L = 0.0264 \ H\\\\L = 26.4 \ mH[/tex]

Answer:

max shear = R = V = 15 kN

Explanation:

given:

load = 10 kn/m

span = 3m

max shear = R = V = wL / 2

max shear = R = V = (10 * 3) / 2

max shear = R = V = 15 kN

Answer:

Explanation:

Known: flow rate and inlet temperature for automobile radiator.

Overall heat transfer coefficient.

Find: Area required to achieve a prescribed outlet temperature.

Assumptions: (1) Negligible heat loss to surroundings and kinetic and

potential energy changes, (2) Constant properties.

Analysis: The required heat transfer rate is

q = (m c)h (T h,i - T h,o) = 0.05 kg/s (4209J / kg.K) 70K = 14,732 W

Using the ε-NTU method,

Cmin = Ch = 210.45 W / K

Cmax = Cc = 755.25W / K

Hence, Cmin/Cmx(Th,i - Th,o) = 210.45W / K(100K) = 21,045W

and

ε=q/qmax = 14,732W / 21,045W = 0.700

NTU≅1.5, hence

A=NTU(cmin / U) = 1.5 x 210.45W / K(200W) / m² .K) = 1.58m²

1. the air outlet is..

Tc,o = Tc,i + q / Cc = 300K + (14,732W / 755.25W / K) = 319.5K

2. using the LMTD approach ΔTlm = 51.2 K,, R=0.279 and P=0.7

hence F≅0.95 and

A = q/FUΔTlm = (14,732W) / [0.95(200W / m².K) 51.2K] = 1.51m²