Applied Heat Transfer: Foundations, Conduction, and Radiation

Comprehensive vocabulary flashcards covering atomic structure, classical and quantum foundations, thermodynamics, conduction, convection, fluid governing equations, numerical solvers, and thermal radiation from the Applied Heat Transfer course.

Thomson Model (Raisin Cake Model)

An atomic model proposed around 1903 by Joseph John Thomson stating that an atom consists of a uniformly distributed, positively charged mass in which negatively charged electrons move, with electrons alone responsible for mass.

Rutherford's Radiation Experiment

An experiment where alpha particles were directed at an extremely thin gold foil; most passed unhindered, but approximately 1 in 8,000 were deflected backward, revealing a tiny, dense, positively charged atomic nucleus surrounded by mostly empty space.

Bohr's Atomic Model

A 1913 atomic model postulating that electrons orbit a positively charged nucleus only on fixed, quantized circular paths (shells) and emit or absorb energy quanta in the form of photons when transitioning between levels.

Wave-Particle Duality

The quantum physical principle demonstrated by the double-slit experiment showing that entities such as electrons and photons exhibit properties of both discrete particles and continuous waves.

Schrödinger Equation

The fundamental quantum mechanical equation, formulated as i\ħ \frac{\partial \psi}{\partial t} = -\frac{\ħ^2}{2m}\nabla^2\psi + V\psi, which describes the total energy and evolution of a particle's wave function $\psi$ by combining classical mechanics with wave mechanics.

Orbital

A mathematically described region of space defined by a wave function $\psi$ where there is a 90% to 95% probability ($P = \int_{x_1}^{x_2} \psi^* \psi\,dx$) of locating an electron.

Alpha ($\alpha$) Radiation

A type of particle radiation consisting of emitted protons and/or neutrons that travels only on the centimeter scale (~$5\,\text{cm}$) and can be blocked easily by a sheet of paper.

Beta ($\beta$) Radiation

A type of particle radiation consisting of emitted electrons and/or positrons that travels on the meter scale (~$1\,\text{m}$) and can be blocked by aluminium foil.

Gamma ($\gamma$) Radiation

High-energy electromagnetic radiation emitted as photons that travels on the kilometer scale and requires dense shielding such as lead to be attenuated.

Phonons

Quantized lattice vibrations in ionic or crystalline solid structures that act as microscopic thermal energy carriers propagating heat through the lattice.

First Law of Thermodynamics

The law of conservation of energy stating that energy cannot be created or destroyed, expressed for a closed system as $\Delta E_{\text{st}} = E_{\text{in}} - E_{\text{out}} + E_g$ and at an instant as $\dot{E}_{\text{st}} = \dot{E}_{\text{in}} - \dot{E}_{\text{out}} + \dot{E}_g$.

Second Law of Thermodynamics

The empirical law stating that natural spontaneous processes occur in the direction that increases the entropy of the universe, dictating that heat flows spontaneously from hotter to colder bodies and never vice versa.

Third Law of Thermodynamics

The principle stating that no system can reach absolute zero temperature ($T = 0\,\text{K}$) and establishing zero entropy ($S = 0$) at absolute zero via the statistical relationship $S = k_B \ln(W)$.

Ludwig Boltzmann

The physicist who established statistical thermodynamics by connecting microscopic atomic arrangements (microstates, $W$) to macroscopic entropy through $S = k_B \ln(W)$.

Zeroth Law of Thermodynamics

The principle stating that if two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other, providing the physical foundation for defining a unique temperature scale.

Thermal Conduction

The microscopic transport of thermal energy in solids, liquids, or gases via atomic or molecular collisions and the motion of free electrons and lattice vibrations.

Fourier's Law

The phenomenological law governing conductive heat flux, formulated in one dimension as $q_x'' = -k \frac{dT}{dx}$ and generally as $\mathbf{q}'' = -k\nabla T$.

Thermal Conductivity ($k$)

A material property representing the rate of heat transfer by conduction per unit area per unit temperature gradient, expressed in units of $\text{W}/(\text{m}\cdot\text{K})$.

Thermal Convection

Heat transfer in a gas or liquid occurring via the macroscopic bulk movement of fluid matter combined with microscopic conduction.

Newton's Law of Cooling

The governing relation for convective heat flux between a solid surface and an adjacent moving fluid: $q'' = h(T_s - T_\infty)$.

Convective Heat Transfer Coefficient ($h$)

A parameter quantifying the rate of convective heat exchange between a surface and a fluid, depending on fluid properties, thermodynamic state, and flow conditions, given in $\text{W}/(\text{m}^2\cdot\text{K})$.

Stefan-Boltzmann Constant ($\sigma$)

The universal physical constant in radiation heat transfer with the value $\sigma = 5.670 \times 10^{-8}\,\text{W}/(\text{m}^2\cdot\text{K}^4)$.

Emissivity ($\varepsilon$)

The dimensionless ratio ($0 < \varepsilon < 1$) of radiation emitted by a real surface to that emitted by an ideal blackbody at the same temperature.

Hydrodynamic Analogy

The mathematical correspondence between linear transport processes, modeling thermal conduction as an electrical resistor network where $R_{t,\text{cond}} = \frac{L}{kA}$, $R_{t,\text{conv}} = \frac{1}{hA}$, and $R_{t,\text{rad}} = \frac{1}{h_r A}$.

Eulerian Approach

A fluid flow description framework that observes fluid properties (density, velocity, temperature) moving through control volumes fixed at specific locations in space.

Lagrangian Approach

A fluid flow description framework that tracks individual fluid parcels or control volumes as they move through space over time.

Stokes' Hypothesis

The fluid mechanics assumption relating bulk viscosity $\gamma$ to dynamic shear viscosity $\mu$ as $\gamma = -\frac{2}{3}\mu$, used to close the Newtonian viscous stress tensor.

Elliptic Partial Differential Equations

A class of PDEs (such as the steady-state Laplace equation $\frac{\partial^2 \phi}{\partial x^2} + \frac{\partial^2 \phi}{\partial y^2} = 0$) governing equilibrium problems where a disturbance at any single point instantaneously influences every point throughout the domain.

Marching Problems

Transient problems governed by parabolic or hyperbolic PDEs (such as the heat diffusion equation $\frac{\partial \phi}{\partial t} = \alpha \frac{\partial^2 \phi}{\partial x^2}$) where disturbances propagate forward in time and cannot affect states at earlier times.

Yttria-Stabilised Zirconia (YSZ)

A ceramic material exhibiting a cubic fluorite structure used in gas turbine blade thermal barrier coatings to exploit micro- and nanoscale phonon scattering and significantly reduce thermal conductivity.

Nanofluids

Engineered suspensions formed by dispersing solid nanoparticles (such as $\text{Al}_2\text{O}_3$, $\text{Cu}$, or $\text{CuO}$) within base liquids (like water or oil) to enhance thermal conductivity or tailor magnetic and optical properties.

Thermal Diffusion Equation (Cartesian)

The differential energy equation for conductive heat transfer in Cartesian coordinates: $\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k\frac{\partial T}{\partial y}\right) + \frac{\partial}{\partial z}\left(k\frac{\partial T}{\partial z}\right) + \dot{q} = \rho c_p \frac{\partial T}{\partial t}$.

Thermal Contact Resistance ($R_{t,c}''$)

The apparent temperature discontinuity and thermal resistance across the interface of two contacting solids caused by surface roughness and interstitial air gaps, defined as $R_{t,c}'' = \frac{T_A - T_B}{q_x''}$.

Conduction Shape Factor ($S$)

A geometric factor used to approximate two- and three-dimensional steady-state heat conduction rates across complex geometries via the relation $q = Sk\Delta T_{1-2}$, giving an effective resistance of $R_{t,\text{cond}(2D)} = \frac{1}{Sk}$.

Fin Effectiveness ($\varepsilon_f$)

The ratio of the fin heat transfer rate to the heat transfer rate that would exist without the fin, defined by $\varepsilon_f = \frac{kP}{hA_c}$, where $P$ is the perimeter, $A_c$ is the cross-sectional area, $k$ is thermal conductivity, and $h$ is the convective coefficient.

Fin Efficiency ($\eta_f$)

The ratio of actual heat dissipated by an extended surface (fin) to the ideal maximum heat dissipation possible if the entire fin surface were maintained at its base temperature ($T_b$).

Overall Surface Efficiency ($\eta_0$)

The total thermal performance measure of a finned surface array calculated as $\eta_0 = 1 - \frac{N A_f}{A_t}(1 - \eta_f)$, yielding a total heat rate of $q_t = \eta_0 h A_t (T_b - T_\infty)$.

Lumped Capacitance Method

A transient thermal analysis method assuming a spatially uniform temperature within a solid undergoing convection, resulting in an exponential temperature decay of $\frac{T - T_\infty}{T_i - T_\infty} = \exp\left(-\frac{hA_s}{\rho V c}t\right)$.

Thermal Time Constant ($\tau_t$)

The characteristic response time of a lumped thermal capacitance system, defined as $\tau_t = \frac{\rho V c}{h A_s} = R_{t,\text{conv}} C_t$, at which the dimensionless temperature difference decays to $1/e \approx 0.368$.

Biot Number ($Bi$)

A dimensionless number comparing internal conductive resistance to external convective resistance, defined as $Bi = \frac{hL}{k}$; the lumped capacitance method requires $Bi \ll 1$ to be valid.

Gauss-Seidel Method

An iterative relaxation algorithm for linear algebraic systems that sweeps through mesh cells sequentially, computing updated values using the latest calculated values of adjacent neighbor cells and boundary sources.

Multigrid Method

An accelerated numerical solver technique that utilizes the smoothing ability of basic relaxation methods (like Gauss-Seidel) on high-frequency error components on a fine grid, followed by restriction to coarser grids to eliminate lingering low-frequency error modes.

Conjugate Gradient Method

An iterative mathematical optimization method for solving symmetric positive-definite linear systems ($\mathbf{A}\mathbf{x} = \mathbf{B}$) by minimizing the quadratic form $f(\mathbf{x}) = \frac{1}{2}\mathbf{x}^T\mathbf{A}\mathbf{x} - \mathbf{B}^T\mathbf{x} + C$ along mutually orthogonal search directions.

Solid Angle ($\omega$)

The two-dimensional angular span in three-dimensional space subtended on a unit sphere, defined in differential form as $d\omega \equiv \frac{dA_n}{r^2} = \sin(\theta)\,d\theta\,d\phi$ and integrating to $2\pi\,\text{sr}$ over a hemisphere.

Spectral Intensity ($I_{\lambda,e}$)

The rate at which radiant energy is emitted at a specific wavelength $\lambda$ in a given direction ($\theta, \phi$) per unit area normal to that direction, per unit solid angle, and per unit wavelength interval.

Blackbody

An idealized physical body that completely absorbs all incident electromagnetic radiation at all wavelengths and angles, and emits the maximum possible diffuse thermal radiation at any given temperature.

Ultraviolet Catastrophe

The classical physics failure of the Rayleigh-Jeans law ($I_{\lambda,b}(T) = \frac{8\pi k_B T}{\lambda^4}$), which incorrectly predicted that emitted energy density approaches infinity as wavelength approaches zero.

Planck's Law

The quantum spectral distribution formula for blackbody emissive intensity: $I_{\lambda,b}(T) = \frac{2hc_0^2}{\lambda^5\left(e^{\frac{hc_0}{\lambda k_B T}} - 1\right)}$, which introduced the quantization of energy and Planck's constant ($h = 6.626 \times 10^{-34}\,\text{J}\cdot\text{s}$).

Wien's Displacement Law

The physical law stating that the peak wavelength of blackbody radiation emission is inversely proportional to absolute temperature: $\lambda_{\text{max}} T = C_3 = 2898\,\mu\text{m}\cdot\text{K}$.

Irradiation ($G$)

The total rate of incident thermal radiation arriving at a surface from all directions per unit surface area, expressed in $\text{W}/\text{m}^2$.

Radiosity ($J$)

The total rate at which thermal radiation leaves a surface per unit area, consisting of the sum of directly emitted power and reflected irradiation: $J = E + G_{\text{ref}} = E + \rho G$.

View Factor ($F_{ij}$)

The geometric fraction of diffuse radiative energy leaving surface $A_i$ that is directly intercepted by surface $A_j$, governed by the reciprocity relation $A_i F_{ij} = A_j F_{ji}$ and summation rule $\sum_{j=1}^N F_{ij} = 1$.

Radiative Transfer Equation (RTE)

The governing differential equation for the variation of radiative intensity $I$ along a path length $s$ in a participating medium, balancing emission, absorption, out-scattering, and in-scattering: $\frac{dI(\mathbf{r},\mathbf{s})}{ds} = \kappa I_b(\mathbf{r}) - \kappa I(\mathbf{r},\mathbf{s}) - \sigma_s I(\mathbf{r},\mathbf{s}) + \frac{\sigma_s}{4\pi}\int_{4\pi} I_-(\mathbf{s}_i)\Phi(\mathbf{s}_i,\mathbf{s})\,d\Omega_i$.

Discrete Transfer Method (DTM)

A deterministic radiation numerical simulation approach that traces a discrete set of directional rays through a mesh domain to update cell radiation intensities and account for participating media.

Monte Carlo Method (Radiation)

A statistical simulation technique that models radiative transfer by tracking randomly emitted bundles of energy rays using stochastic sampling of spatial coordinates and emission angles.