Heat Transfer Principles and Equations

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Questions and Answers

What is the primary mode of heat transfer through a solid material, like a metal bar?

  • Conduction (correct)
  • Convection
  • Radiation
  • Evaporation

Which of the following is NOT a factor in determining the rate of heat transfer by conduction through a plane wall?

  • Thickness (x) of the wall
  • Temperature difference ($t_1 - t_2$) across the wall
  • Thermal conductivity (k) of the wall material
  • Surface area (A) of the wall
  • Density of the wall material (correct)

Which of the following is an example of forced convection?

  • Heat transfer from a hot stove burner to a pot of water
  • Heat transfer from a warm air balloon to the surrounding air
  • Heat transfer from a hot cup of coffee to your hand
  • Heat transfer from the sun to the Earth
  • Heat transfer from a fan blowing air over a computer's processor (correct)

In the equation for heat transfer through a composite wall, what does the term 'R' represent?

<p>Thermal resistance of the wall (D)</p> Signup and view all the answers

In the equation for heat transfer through a plane wall, what does 'k' represent?

<p>Thermal conductivity of the wall material (A)</p> Signup and view all the answers

What is the formula for the overall conductance or overall coefficient of heat transfer (U)?

<p>$U = rac{1}{R_t} = rac{1}{ rac{1}{h_h} + rac{x_1}{k_1} + rac{x_2}{k_2} + rac{1}{h_c}}$ (C)</p> Signup and view all the answers

What is the formula for heat loss in terms of overall resistance (Rt) ?

<p>$Q = rac{A \Delta T}{R_t}$ (B)</p> Signup and view all the answers

What is the formula for resistance to heat flow based on the inner and outer radius?

<p>$R = rac{\ln(r_2/r_1)}{2\pi kL}$ (C)</p> Signup and view all the answers

What is the formula for heat loss based on overall resistance (Rt) and the temperature at the inner and outer radius?

<p>$Q = rac{t_2 - t_1}{R}$ (A)</p> Signup and view all the answers

What is the formula for the overall resistance ($R_T$) of a composite wall, assuming there are three layers and no fluid interfaces?

<p>$R_T = rac{x_1}{k_1} + rac{x_2}{k_2} + rac{x_3}{k_3}$ (B)</p> Signup and view all the answers

Which of these equations correctly represents the heat transfer rate ($Q$) through a composite wall with fluid interfaces?

<p>$Q = rac{A(t_1 - t_4)}{ rac{x_1}{k_1} + rac{x_2}{k_2} + rac{x_3}{k_3} + rac{1}{h_o} + rac{1}{h_i}}$ (D)</p> Signup and view all the answers

What does $Q_3$ represent in the context of a composite wall with three layers?

<p>Heat transfer rate through the third layer. (A)</p> Signup and view all the answers

What is the formula for heat transfer rate ($Q$) from a fluid to a solid layer, assuming a constant heat transfer coefficient ($h_o$) and surface area ($A$)?

<p>$Q = h_o A (t_o - t_1)$ (C)</p> Signup and view all the answers

In the context of a composite wall with three layers, what does the term $k_2$ represent?

<p>Thermal conductivity of the second layer (B)</p> Signup and view all the answers

Which equation represents the heat transfer through the first layer in a composite pipe?

<p>Q1 = (t2 - t1) / [ln(r2/r1)] * 2πk1L (A)</p> Signup and view all the answers

What does the symbol 'kn' represent in the context of the provided equations?

<p>The thermal conductivity of the nth layer (D)</p> Signup and view all the answers

Which of the following equations is used to calculate the total heat transfer through the composite pipe?

<p>Q = Q1 + Q2 (C)</p> Signup and view all the answers

What is the significance of the term ln(r2/r1) in the heat transfer equation for the first layer?

<p>It indicates the thermal resistance of the first layer (A)</p> Signup and view all the answers

Which equation would you use to calculate the heat transfer from a fluid inside the pipe to the inner surface of the pipe?

<p>Q = hiAi(ti -t1) (D)</p> Signup and view all the answers

What are the units of thermal resistance in the equation for steady-state heat transfer?

<p>mC/W (B)</p> Signup and view all the answers

What is the formula for calculating the overall conductance based on the inside surface area of a heat exchanger?

<p>$U_i = rac{Q A_i}{\Delta t}$ (B)</p> Signup and view all the answers

In the equation for steady-state heat transfer, what does the term 'ln(r_2/r_1)' represent?

<p>The natural logarithm of the ratio of the outer radius to the inner radius (A)</p> Signup and view all the answers

Which of these options is NOT an example of a heat exchanger?

<p>Refrigerator (B)</p> Signup and view all the answers

In the equation for heat transfer in terms of overall conductance, what does the term 'U' represent?

<p>Overall conductance of the heat exchanger (C)</p> Signup and view all the answers

Which type of heat exchanger is potentially the most efficient?

<p>Counterflow (B)</p> Signup and view all the answers

What is the purpose of the Logarithmic Mean Temperature Difference (LMTD) formula?

<p>To calculate the average temperature difference between the hot and cold fluids in a heat exchanger. (A)</p> Signup and view all the answers

In which type of heat exchanger do the fluids flow in opposite directions?

<p>Counterflow (B)</p> Signup and view all the answers

What does the term '($\Delta$T)max' represent in the LMTD formula?

<p>The maximum temperature difference between the hot and cold fluids. (C)</p> Signup and view all the answers

In a cross-flow heat exchanger, how does the flow of one fluid relate to the flow of the other fluid?

<p>They flow at an angle to each other. (A)</p> Signup and view all the answers

What is the defining characteristic of a constant temperature heat exchanger?

<p>The temperature of the cold fluid remains constant throughout the exchange process. (B)</p> Signup and view all the answers

Which of these is NOT a characteristic of a variable temperature heat exchanger?

<p>The temperature difference between the hot and cold fluids remains constant throughout the exchange process. (C)</p> Signup and view all the answers

What type of heat exchanger is a steam condenser?

<p>Constant temperature heat exchanger. (B)</p> Signup and view all the answers

What is the defining characteristic of a variable temperature heat exchanger?

<p>The temperature of the hot fluid decreases as the cold fluid gains heat from it. (A)</p> Signup and view all the answers

Which scenario would describe a variable temperature heat exchanger?

<p>A hot fluid flows through a device and its temperature decreases as it gives heat to a cold fluid, both of which are moving. (D)</p> Signup and view all the answers

What does the Stefan-Boltzmann Law calculate?

<p>The heat transferred by radiation between two surfaces (C)</p> Signup and view all the answers

What does a perfect black body do with electromagnetic radiation?

<p>Absorbs all radiation without reflection (D)</p> Signup and view all the answers

In the equation for radiative heat transfer, what does $ au$ represent?

<p>Transmissivity (B)</p> Signup and view all the answers

Which factor is NOT part of the Stefan-Boltzmann equation?

<p>Density of the material (B)</p> Signup and view all the answers

What does the equation $a + r + t = 1$ signify in the context of radiation?

<p>The balance of energy absorbed, reflected, and transmitted (A)</p> Signup and view all the answers

What does Planck's Law indicate about the radiation emitted by substances?

<p>It depends on the material properties and absolute temperature. (B)</p> Signup and view all the answers

Which dimensionless group is crucial for analyzing heat convection systems?

<p>Reynolds Number (D)</p> Signup and view all the answers

According to Kirchhoff's Law, what is true for bodies in thermal equilibrium?

<p>The ratio of total emissive power to absorptivity is a constant at all temperatures. (C)</p> Signup and view all the answers

What is the relationship expressed in the Stefan-Boltzmann Law?

<p>Energy emitted is proportional to the fourth power of the absolute temperature. (D)</p> Signup and view all the answers

Which of the following is NOT a characteristic of convection as a heat transfer mechanism?

<p>It only occurs in solids. (A)</p> Signup and view all the answers

What is the Prandtl Number (NPr) used to compare in heat transfer analysis?

<p>Dynamic viscosity multiplied by specific heat to thermal conductivity (C)</p> Signup and view all the answers

Which dimensionless number represents the ratio of buoyancy forces to viscous forces?

<p>Grashof Number (NGr) (A)</p> Signup and view all the answers

In the formula for Nusselt Number (NNu), which of the following variables represents the heat transfer coefficient?

<p>h (B)</p> Signup and view all the answers

What is the primary role of dimensionless numbers like Prandtl, Nusselt, and Grashof in heat transfer analysis?

<p>To standardize and simplify heat transfer comparisons (D)</p> Signup and view all the answers

Which equation represents the Grashof Number (NGr)?

<p>NGr = (D³ρ²βΔT) / µ² (B)</p> Signup and view all the answers

Flashcards

Heat Transfer

The movement of heat from one body to another by conduction, convection, or radiation.

Conduction

Heat transfer through molecular interaction in bodies in contact.

Convection

Heat transfer due to the mixing and motion of particles in a substance.

Fourier's Equation

Calculates heat transfer through a plane wall: Q = (kA(t1 - t2))/x.

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Composite Wall Heat Transfer

Multiple layers' heat transfer represented by Q = A Δt / R.

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Surface Film Conductance (hot side)

$h_h$ is the surface film conductance on the hot side, expressed in W/m²°C.

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Surface Film Conductance (cold side)

$h_c$ is the surface film conductance on the cold side, expressed in W/m²°C.

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Overall Conductance (U)

$U$ is the overall heat transfer coefficient, calculated using the formula $U = rac{1}{R_t}$.

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Heat Transfer Formula

$Q = U A \Delta T$ quantifies heat transfer in terms of overall conductance, area, and temperature difference.

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Heat Loss Formula

$Q = \frac{\Delta T}{R_t}$ calculates heat loss using temperature difference and resistance.

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Fourier's Equation for Heat Flow

Used for calculating heat transfer rate across layers: $Q = \frac{k A (t_{top} - t_{bottom})}{x}$.

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Overall Resistance ($R_T$)

Total thermal resistance for a composite wall: $R_T = \frac{x_1}{k_1} + \frac{x_2}{k_2} + \frac{x_3}{k_3}$.

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Heat Transfer Equation

Total heat transfer illustrated as $Q = \frac{A(t_{initial} - t_{final})}{R_T}$.

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Conduction from Fluid to Fluid

Heat transfer equation: $Q = h_o A (t_o - t_1)$.

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Heat Exchanger

A device that transfers heat between substances.

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Steady-state heat transfer

Constant heat flow through materials without change over time.

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Thermal Resistance (R)

A measure of a material's ability to resist heat flow.

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Heat Transfer Equation (Q)

Q = U A Δt defines heat transfer based on area and temperature difference.

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Composite Pipe

A pipe made up of multiple layers, each with different thermal properties.

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Q1

Heat transfer through layer 1 of a composite pipe.

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Q2

Heat transfer through layer 2 of a composite pipe.

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Total Heat Transfer (Q)

The sum of heat transfers through all layers in a composite pipe (Q = Q1 + Q2).

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R1 and R2

Thermal resistance for layers, calculated using radii and conductivity.

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Constant Temperature Heat Exchangers

Devices where a fluid at constant temperature transfers heat to a cooler fluid, which heats up.

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Variable Temperature Heat Exchangers

Devices where a warmer fluid loses heat to a cooler fluid, causing the warmer fluid to cool down.

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Steam Condenser

An example of a constant temperature heat exchanger where steam cools down and condenses.

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Steam Boiler

An example of a variable temperature heat exchanger where water is heated by steam, increasing its temperature.

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Temperature Graphs in Heat Exchangers

Graphs showing temperature changes of fluids; hot fluid slopes down, cold fluid is horizontal for variable exchangers.

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Radiation

Heat transfer through electromagnetic waves.

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Stefan-Boltzmann Law

Describes radiation heat transfer using temperature to the fourth power.

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Perfect Black Body

An ideal body that absorbs all radiation without reflection.

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Absorptivity (a)

The fraction of energy absorbed by a surface, related to reflectivity and transmissivity.

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Prandtl Number (NPr)

Ratio of dynamic viscosity times specific heat to thermal conductivity.

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Nusselt Number (NNu)

Ratio of total heat transfer to conductive heat transfer in convection.

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Grashof Number (NGr)

Ratio of buoyancy forces to viscous forces in free convection.

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Dynamic Viscosity (µ)

A measure of a fluid's resistance to flow and deformation.

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Thermal Conductivity (k)

A measure of a material's ability to conduct heat.

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Parallel Flow Heat Exchangers

A type of heat exchanger where fluids flow in the same direction and both change temperature.

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Counterflow Heat Exchangers

Heat exchangers where fluids flow in opposite directions, maximizing efficiency.

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Cross-flow Heat Exchangers

In this type, one fluid flows at an angle to the other, such as in tube banks.

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Logarithmic Mean Temperature Difference (LMTD)

A formula used to find the average temperature difference between two fluids in a heat exchanger.

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Temperature Difference ($ abla T$)

The difference in temperature between hot and cold fluids in a heat exchanger, influencing heat transfer efficiency.

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Planck's Law

Describes how substances emit radiation based on temperature and material properties.

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Kirchhoff's Law

In thermal equilibrium, total emissive power to absorptivity ratio remains constant.

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Reynolds Number

Dimensionless number indicating flow regime influenced by viscosity, velocity, and length.

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Nusselt Number

Dimensionless number that relates convective and conductive heat transfer.

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