Basics of Heat Transfer

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Questions and Answers

What is heat transfer and what causes it?

Heat transfer is thermal energy in transit due to a temperature difference.

Differentiate between thermal energy, temperature, and heat transfer.

Thermal energy is the energy associated with the microscopic behavior of matter, temperature is an indirect measure of that energy, and heat transfer is the transport of thermal energy due to temperature differences.

What is the formula for heat transferred over a time interval?

The heat transferred is denoted by $Q$ and measured in joules (J).

What is conduction in the context of heat transfer?

Conduction is heat transfer in a solid or stationary fluid due to the random motion of atoms, molecules, or electrons. Signup and view all the answers

How does knowledge of heat transfer apply to the first law of thermodynamics?

Knowledge of heat transfer allows for the analysis of thermal systems and energy conservation as described by the first law of thermodynamics. Signup and view all the answers

What is the primary mechanism of heat transfer in conduction?

Conduction primarily transfers heat through direct contact of particles in a material. Signup and view all the answers

How does convection differ from conduction in terms of heat transfer?

Convection transfers heat through fluid motion, while conduction transfers heat through direct particle contact within solids. Signup and view all the answers

What role does a vacuum play in the transfer of radiant energy?

Radiation can occur in a vacuum without a material medium, making it efficient for transferring energy over distances. Signup and view all the answers

Using Fourier’s Law, how is the heat flux (q'') expressed in one-dimensional conduction?

Heat flux is expressed as q'' = -k * (dT/dx), where k is thermal conductivity and dT/dx is the temperature gradient. Signup and view all the answers

Calculate the heat rate (q) through a wall with specified dimensions and temperatures: if a 0.15 m thick wall has temperatures of 1400 K and 1150 K, and dimensions 0.5 m x 1.2 m, given k = 1.7 W/m.K.

The heat rate is calculated using q = q'' * A, resulting in 214.5 W. Signup and view all the answers

What does Newton’s law of cooling quantify in terms of convection?

It quantifies the heat transfer rate, given by the equation $q'' = h(T_s - T_{ ext{inf}})$. Signup and view all the answers

What does the emissive power $E$ represent in radiation heat transfer?

It represents the energy emitted per unit area by a surface, measured in $W/m^2$. Signup and view all the answers

In the context of radiation, what condition is presented when $ ext{α} = ext{ε}$?

This condition indicates a gray surface, where absorptivity equals emissivity, leading to a simplified analysis of net radiation heat flux. Signup and view all the answers

How can the net radiation heat flux between a surface and its surroundings be expressed mathematically?

It can be expressed as $q_{ ext{rad}}'' = ext{ε} ext{E}_b(T_s) - ext{α} G$. Signup and view all the answers

What is the formula for the combined heat transfer from convection and radiation?

The formula is $q'' = q_{ ext{conv}}'' + q_{ ext{rad}}''$ which integrates both convection and radiation contributions. Signup and view all the answers

Study Notes

What is Heat Transfer?

Heat transfer is thermal energy in transit due to a temperature difference
Thermal energy is associated with the motion of atoms and molecules within matter
This motion includes translation, rotation, vibration, and electronic states
Thermal energy is directly linked to the temperature of matter

Key Definitions

Thermal energy: Energy associated with microscopic behavior of matter (Symbol: U or u, Units: J or J/kg)
Temperature: Indirect assessment of thermal energy stored in matter (Symbol: T, Units: K or °C)
Heat Transfer: Thermal energy transport due to temperature gradients (Symbol: Q, Units: J)
Heat: Amount of thermal energy transferred over a specific time interval (Symbol: Q, Units: J)
Heat Rate: Thermal energy transfer per unit time (Symbol: q, Units: W)
Heat Flux: Thermal energy transfer per unit time and surface area (Symbol: q", Units: W/m²)

Modes of Heat Transfer

Conduction: Heat transfer through a solid or stationary fluid due to the random motion of atoms, molecules, and electrons
Convection: Heat transfer due to the combined influence of bulk and random motion of fluids
Radiation: Energy emitted by matter as electromagnetic waves due to changes in electron configurations
Conduction and convection require the presence of temperature variations in a material medium
Radiation does not require a material medium and is most efficient in a vacuum

Conduction Heat Transfer Rates

General form of Fourier's Law: q" = -k∇T (where q" is heat flux, k is thermal conductivity, and ∇T is the temperature gradient)
One-dimensional, steady conduction across a plane wall of constant thermal conductivity: qx = -k * A *(T₁ - T₂)/L (where qx is the heat rate, A is the area, L is the thickness, and T₁ and T₂ are the temperatures on either side of the wall)

Convection Heat Transfer Rates

Newton's Law of Cooling: q" = h (T_s - T_∞) (where h is the convection heat transfer coefficient, T_s is the surface temperature, and T_∞ is the fluid temperature)

Radiation Heat Transfer Rates

Emissive power: E =  * σ * T_s⁴ (where E is the emissive power,  is the surface emissivity, σ is the Stefan-Boltzmann constant, and T_s is the surface temperature)
Energy absorption due to irradiation: G_abs = α * G (where α is the surface absorptivity and G is the irradiation)
Net radiation heat flux from a gray surface: q"_rad = σ * (T_s⁴ - T_sur⁴) (where ε is the emissivity, σ is the Stefan-Boltzmann constant, and T_sur is the surrounding temperature)
Radiation heat transfer coefficient: h_r = εσ (T_s + T_sur)(T_s² + T_sur²)
Combined convection and radiation heat flux: q" = h(T_s - T_∞) + h_r(T_s - T_sur)

First Law of Thermodynamics in Heat Transfer Analysis

The First Law of Thermodynamics provides a basis for determining the temperature of a system
The First Law can be applied to a control volume at an instant: Ein - Eout + E_g = E_st
The First Law can be applied to a control volume over a time interval: E_in - E_out + E_g = ΔE_st

Methodology of First Law Analysis

Define the control surface by a dashed line
Choose an appropriate time basis
Identify relevant energy transport, generation, and storage terms
Write the governing form of the Conservation of Energy requirement
Substitute appropriate expressions for energy terms
Solve for the unknown quantity

Summary of Heat Transfer Processes

Conduction: Diffusion of energy due to random molecular motion (q" = -k∇T)
Convection: Diffusion of energy due to random molecular motion and fluid motion (q" = h(T_s - T_∞))
Radiation: Energy transfer by electromagnetic waves (q = h_r A (T_s - T_sur) or q"_rad = εσ (T_s⁴ - T_sur⁴))

Typical values of heat transfer coefficients

Free or Natural Convection: Gases (2-25 W/m².K), Liquids (50-1000 W/m².K)
Forced Convection: Gases (25-250 W/m².K), Liquids (100-20,000 W/m².K)
Convection with Phase Change: 2500-100,000 W/m².K

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Description

Explore the fundamentals of heat transfer, including key definitions and modes such as conduction, convection, and radiation. This quiz covers the relationship between thermal energy, temperature, and heat transfer mechanisms. Test your understanding of these crucial concepts in thermodynamics.