June 26

# Exam Problem #24 (The Prandtl Number)

## Question

Concerning the Prandtl Number, which of the following statements is FALSE.
A) There is no increase or decrease with a change in density?
B) The Prandtl Number decreases with an increasing thermal diffusivity.
C) The volume of the fluid can increase or decrease the Prandtl Number
D) When the Prandtl Number is low, heat dissipates quickly compared to the velocity.

Today’s PE/EIT problem is about the Prandtl Number and what factors can cause a change.

### Equation

The Prandtl Number (Pr) is the ratio of kinematic viscosity to thermal diffusivity

$Pr = \frac{\nu}{\alpha} = \frac{\frac{\mu}{\rho}}{\frac {k}{c_p \rho}} = \frac{c_p \mu}{k}$

### Variables

ρ is Density
u is Dynamic Viscosity
v is Kinematic Viscosity
k is Thermal Conductivity
cp is Specific Heat
α is Thermal Diffusivity

### Solution

Since thermal diffusivity and the kinematic viscosity both use the same density, the Prandtl number will not change. Choice A is true

With the thermal diffusivity in the denominator a larger value will result in a lower Prandlt Number if the kinematic viscosity is held constant. Choice B is true

Since there is no variable that is for volume, Choice C is false.

When the Prandtl Number is small the heat diffuses very quickly compared to the velocity. Choice D is true

Choice C is correct since it is the only false statement.

June 25

# Exam Problem #23 (Heat Transfer Modes, Radiation)

## Question

Chose one choice out of each group that best describes radiation.
Group I
A) Transfer of energy from higher energy molecules to lower energy molecules.
B) Energy is transmitted by electro magnetic waves.
C) Energy transfer between a solid surface and a fluid that is at a different temperature.

Group II
A) Newton’s Law of Cooling
B) Stefan-Boltzmann Law
C) Fourier’s Law

Group III
A) $\dot{Q} = hA\Delta T$
B) $\dot{Q} = -kA\frac {dT}{dx}$
C) $\dot{Q} = \varepsilon \sigma AT^4$

Today’s EIT/PE question takes a look at radiation, the law that governs radiation, the equation and a brief description

### Solution

The correct choices are I-B, II-B, III-C

Radiation is described as the transfer of energy through electro-mechanical waves.

The law that governs convection is Stefan-Boltzmann’s Law

The standard equation for Stefan-Boltzmann’s Law is $\dot{Q} = \varepsilon \sigma AT^4$

June 24

# Exam Problem #22 (Heat Transfer Modes, Convection)

## Question

Chose one choice out of each group that best describes convection.
Group I
A) Transfer of energy from higher energy molecules to lower energy molecules.
B) Energy is transmitted by electro magnetic waves.
C) Energy transfer between a solid surface and a fluid that is at a different temperature.

Group II
A) Newton’s Law of Cooling
B) Stefan-Boltzmann Law
C) Fourier’s Law

Group III
A) $\dot{Q} = hA\Delta T$
B) $\dot{Q} = -kA\frac {dT}{dx}$
C) $\dot{Q} = \varepsilon \sigma AT^4$

Today’s EIT/PE question takes a look at convection, the law that governs convection, the equation and a brief description

### Solution

The correct choices are I-C, II-A, III-A

Convection is described as the transfer of energy between a solid surface and a fluid that is at a different temperature

The law that governs convection is Newton’s Law of Cooling

The standard equation for Newton’s Law of Cooling is $\dot{Q} = hA\Delta T$

June 23

# Exam Problem #21 (Heat Transfer Mode Conduction)

## Question

Chose one choice out of each group that best describes conduction

Group I
A) Transfer of energy from higher energy molecules to lower energy molecules
B) Energy is transmitted by electro magnetic waves.
C) Energy transfer between a solid surface and a fluid that is at a different temperature.

Group II
A) Newton’s Law of Cooling
B) Stefan-Boltzmann Law
C) Fourier’s Law

Group III
A) $\dot{Q} = hA\Delta T$
B) $\dot{Q} = -kA\frac {dT}{dx}$
C) $\dot{Q} = \varepsilon \sigma AT^4$

Today’s EIT/PE question takes a look at conduction, the law that governs conduction, the equation and a brief description

### Solution

The correct choices are I-A, II-C, III-B

Conduction is described as the transfer of energy from a hot source to a cold source. Think of a bar that has one end placed in a fire. If you hold the other end of the bar your hands will eventually feel the heat coming through the bar.

The law that governs conduction is Fourier’s Law

The standard equation for Fourier’s Law is $\dot{Q} = -kA\frac {dT}{dx}$

May 26

# Exam Problem #1 (Conduction)

### Question

1. The thermal resistance for one-dimensional conductive heat transfer through a flat plane is __________ and through a cylindrical object it is ___________________?

A) exponential and linear
B) linear and logarithmic
C) logarithmic and polynomial
D) exponential and logarithmic

Todays PE/EIT exam problem looks at the equations for the one-dimensional conductive heat transfer. Showing how the magnitude of the heat loss changes with changes in the thickness of the object being looked at.

This can be found by looking at the equations that are used. Equations 1 and 2 are for flat plane and cylindrical.

### Equations

$Q = UA \Delta T$

Equation 1

$Q = 4 \pi k \frac {\Delta T}{\frac {1}{r_1} = \frac {1}{r_2}}$

Equation 2

### Solution

For equation 1 all of the variables are either constant or the product of a constant and the first power of a variable.
In equation 2 there is the natural log for finding out the area. of the cylinder  When either radius of the cylinder changes the resulting heat transfer changes logarithmically.

The correct choice is B