Heat Transfer: Concepts, Conduction & Convection

• Course: Heat Transfer (MENG 335) for the 1st Semester (Fall 2023)
• Course Designation is Core
• Credit hours: 3 (including 3 hours of lectures and 1 hour lab/tutorial)
• Number of Sessions per Week: 2
• Total Session Duration: 3 hours
• Instructor: Abdul Waheed Badar

Recommended Books

• Heat and Mass Transfer A Practical Approach by Y. A. Cengel, A. J. Ghajar (2nd/6th Ed.)
• Fundamentals of Heat and Mass Transfer by T. L. Bergman, A. S. Lavine, F. P. Incropera (8th Ed.)
• Heat and Mass Transfer by J.P Holman (10th Ed.)

Course contents

• Introduces elementary heat transfer concepts
• Covers the heat diffusion equation, including boundary and initial conditions
• Explores 1D steady-state heat conduction
• Discusses heat transfer through extended surfaces
• Examines transient heat conduction
• Studies convection, including free and forced, internal and external
• Covers thermal radiation principles
• Investigates heat exchangers

Course Assesment

• Quizzes contribute 10% to the final grade
• Laboratory/Practical assessments contribute 5%
• Assignments/Projects contribute 5%
• Examinations contribute 40%
• The final examination contributes 40%
• All assesment details are subject to change
• Test 1: 6th week, October 24, 2023, from 15:00 to 16:00 hours
• Test 2: 11th week, November 28, 2023, from 15:00 to 16:00 hours

Introduction to Heat Transfer

• Thermodynamics deals with the amount of heat transfer, focusing on equilibrium states
• Thermodynamics does not provide information on how long a process will take or the mechanisms of energy transfer
• Heat transfer studies what heat transfer is, how it occurs, its relevance, and importance
• Knowledge of heat transfer allows the determination of how long coffee in a thermos stays hot
• Heat transfer is "energy in transit" due to temperature difference (or gradient)

Temperature Difference

• Temperature difference drives heat transfer akin to voltage driving electric current and pressure driving fluid flow
• Thermodynamics reveals the amount of heat transferred and work done
• Thermodynamics also shows the final state of a system
• Heat transfer explains how and at what rate heat (δQ) is transferred and the temperature distribution within a body

Applications of Heat Transfer

• Determining temperature distribution and heat flow is important across science and technology
• Power engineering: heat exchangers, boilers condensers, burners, nuclear reactor cores, radiators, solar energy conversion, steam power plants
• Domestic applications: ovens, stoves, toasters
• Heating and Air-conditioning: building structure, estimate insulation, prevent excessive heat losses
• Electronic and Electrical Engineering: heat distribution, heat stress, dissipation
• Manufacturing / Materials Processing: welding, casting, soldering, laser machining
• Automobiles / Aircraft Design

Modes of Heat Transfer

• Conduction Heat Transfer: Occurs through a solid or stationary fluid
• Convection Heat Transfer: Occurs between a solid surface and an adjacent moving fluid at different temperatures
• Thermal Radiation: Heat transfer between surfaces not in contact, often without an intervening medium, via electromagnetic waves

Conduction

• Transfer of energy from more energetic to less energetic particles by collisions between atoms/molecules
• Conduction occurs in solids, liquids, and gases
• In gases and liquids, this is due to collisions and diffusion of molecules during random motion
• In solids, it's due to vibrations of molecules in a lattice and energy transport by free electrons

Heat Conduction Law—Fourier Law

• Heat conduction results from Biot's experimental observation and Fourier's analysis theory
• The rate of heat conduction depends on: geometry, thickness, material properties, and temperature difference
• Heat Conduction through a plane layer is proportional to temperature difference and heat transfer area, but inversely proportional to layer thickness
• Formula: Qcond = kA (T1 - T2) / Δx = -kA ΔT / Δx
• k is the thermal conductivity of the material

Fourier Law (Continued)

• In the limiting case where x approaches 0: Qcond = -kA dT/dx, states Fourier's Law of Heat Conduction
• dT/dx is the Temperature Gradient: the slope on a temperature vs. distance diagram at location x
• Heat flows from decreasing temperature, and the temperature gradient is negative when temperature decreases with increasing x
• Heat Flux is the rate of heat transfer per unit area
• heat rate by conduction, qx (W), through a plane wall of area A is then the product of the flux and the area, q".A

Example Problem

• Problem: Electrically heated home roof dimensions: 6 m long, 8 m wide, 0.25 m thick.
• Concrete roof: thermal conductivity (k) is 0.8 W/m·°C
• Temperatures: inner surface at 15°C, outer at 4°C for 10 hours
• Determine: a) heat loss rate, b) heat loss cost if electricity is $0.08/kWh
• Solution:
  • Area (A) = 48 m^2
  • ΔT = 11°C or 11 K
  • Heat loss rate (Q) = 1.69 kW.
  • Total heat loss = 16.9 kWhr
  • Cost = $1.35

Thermal Conductivity

• Measure of a material's ability to conduct heat

• k = 0.608 W/m·°C for water, k = 80.2 W/m·°C for Iron at Room Temp.

• Iron conducts heat more than 100 times faster than water

• Formula: Qcond = -kA dT/dx

• The rate of heat transfer (k) is through a unit thickness of material per unit area per unit temperature difference

• If pure copper at room temperature has k = 401 W/m °C , then a 1-m-thick copper wall will conduct heat at 401 W per m area per °C temperature difference

Thermal Conductivity (Continued)

• Pure crystals and metals possess the highest thermal conductivities; gases and insulating materials, the lowest
• A substance's thermal conductivity (k) typically is highest in the Solid Phase and lowest in the Gas Phase

Thermal Diffusivity

• Represents the heat storage capability of a material
• Represents how fast heat diffuses through a material: α = (Heat conducted) / (Heat stored) = k / (ρCp)
• "k" describes how well a material conducts heat
• "Cp" describes how much energy a material stores per unit volume
• Thermal Diffusivity formula: α = k / (ρ*Cp)
• Larger thermal diffusivity means faster heat propagation
• A small Thermal Diffusivity value heat is mostly absorbed with little conduction
• Thermal diffusivity ranges from 0.14 X 10-6 m²/s for water to 174 X 10-6 m²/s for silver, which is a difference of more than a thousand times

Convection

• Energy transfer by random Molecular Motion (conduction) plus Bulk (Macroscopic) motion of the fluid
• Convection: transport by random motion of molecules and by bulk motion of fluid
• Advection: transport due solely to bulk fluid motion
• Convective Heat Transfer — Fluid flows over a solid body (or inside a channel), while temperature of fluid and solid surface are different, heat transfer takes place as a consequence of fluid motion

Boundary Layer Development in Convection Heat Transfer

• Hydrodynamic, or Velocity, Boundary Layer: fluid-surface interaction causes a region where velocity u varies from zero (at the surface) to essentially the flow velocity u∞
• Thermal Boundary Layer: if surface and flow temperatures differ, a region exists where temperature varies from Ts at y = 0 to T∞ in the outer flow
• Diffusion dominates near the surface where fluid velocity is low
• Bulk Fluid Motion originates from the fact that flow (Boundary Layer) grows in the x-direction

Conditions

• Free or natural convection is induced by buoyancy forces
• Forced convection is induced by external means
• Heat transfer processes with a phase change are convection
• Fluid motion induced during boiling or condensation is considered convection

Newton's Law of Cooling

• Convective Heat Flux is proportional to: q"x α (Ts- T∞)
• Convection Heat Transfer Coefficient "h" (W/m².K) is the constant proportionality
• Convection Heat Transfer formula: q"x = h(Ts-T∞) or Qconv = hAs(Ts-T∞)
• h is not a fluid property, it is an experimentally determined parameter that depends on surface geometry, fluid motion, properties, and bulk fluid velocity

Radiation

• Radiation transfers energy via Electromagnetic Waves (photons) from changes in electronic configurations of atoms/molecules
• Radiation does not require an intervening medium
• Energy transfer by radiation occurs fastest at the speed of light and suffers no attenuation in a vacuum
• Radiation can occur from solids, liquids, and gases
• Thermal Radiation: form of radiation emitted from bodies due to Temperature
• All bodies above Absolute Zero emit Thermal Radiation
• Radiation happens volumetrically in solids, liquids, and gases, which emit, absorb, or transmit radiation

Radiation Surface Phenomenon

• Radiation is usually considered a Surface Phenomenon for solid materials.
• Radiation emitted by interior regions cannot reach the surface
• Radiation incident on bodies mostly gets absorbed within microns of the surface
• The maximum rate of radiation happens at: Qemit max = σΑςΤ⁴
• An idealized surface that emits at this maximum rate is called a Blackbody

Real Surfaces

• formula: Qemit α εσΑ Τ⁴, where emissivity ε is between 0 and 1), while Radiation may also be incident on a surface from its surroundings (such as Sun)
• Irradiation (G): rate at which all such radiation is incident on a unit surface area formula
• Emissivity (ε) = 0, reflects thermal energy; Emissivity (ε) = 1, absorbs all radiation
• Radiant Energy Absorbed per unit area = αG

Absorptivity

• Absorptivity (α): Fraction of radiation energy incident on a surface that is absorbed by the surface
• Blackbody absorbs all entire radiation incident on it which is perfect absorber (α = 1) i.e. a perfect emitter. (ε = 1)
• For an opaque surface: portions of the irradiation get reflected
• For a Semi-Transparent surface: portions of irradiation get transmitted
• α depends on the nature of the irradiation, as well as on the surface itself.
• Absorptivity of a surface varies and depends on source

Radiation: Emissivity and Surface Area

• Net rate of Radiation Heat Transfer can be expresses as Qrad = εσΑ(T⁴-Tsurr⁴ W
• For unit area is: qrad = εσ(T⁴ -Tsurr⁴)

Simultaneous Heat Transfer Mechanisms

• Heat transfer is only by conduction in opaque solids but may have conduction and radiation in semi transparent solids
• Outer surfaces of a cold rock piece warms up because of from air by convection and radiation from sun or warmer surrounding surfaces
• Gases are practically transparent to radiation, except some gases absorb radiation at wavelengths
• Liquids are usually strong absorbers of radiation

Thermodynamics: Rate Basis

• Energy conservation on a rate basis: Ė₁ = dEst/dt = Ėin – Ėout + Ėg
• Inflow and outflow are surface phenomena
• Generation and accumulation are volumetric phenomena

Surface Energy Balance

• Conservation of Energy requirement at the surface of a medium from medium to control system
• Formula: q"cond - q"conv - q"rad = 0