Heat Transfer: Conduction, Convection, and Radiation Fundamentals

Comprehensive practice flashcards covering fundamental conduction, convection, and radiation principles, boundary layers, thermal resistances, dimensionless numbers, and thermodynamic properties.

What two physical mechanisms are involved in convection heat transfer?

Convection involves conduction at the fluid-surface interface and fluid motion that transports energy away from or toward the surface.

In the context of fluid convection, how do the driving mechanisms differ between natural convection and forced convection?

In natural convection, fluid flow is driven primarily by density differences resulting from temperature differences (buoyancy and gravity). In forced convection, fluid flow is driven by an external factor or mechanical device such as a fan, pump, or blower.

What is the hydrodynamic boundary layer, and what fluid property causes it to form?

The hydrodynamic boundary layer is the region of fluid near a solid surface where fluid velocity changes from zero at the wall (due to the no-slip condition) to approximately the free-stream velocity farther away, caused by fluid viscosity.

What is the thermal boundary layer in convective heat transfer?

The thermal boundary layer is the region of fluid near a solid surface where fluid temperature changes from the surface temperature to the free-stream fluid temperature.

What are the flow regime criteria based on the Reynolds number ($Re$)?

Flow is laminar when $Re \le 2{,}000$ (or $2{,}300$); transitional when $2{,}000 < Re < 4{,}000$; and turbulent when $Re \ge 4{,}000$.

How is the Prandtl number ($Pr$) defined, and what physical ratio does it describe?

The Prandtl number is defined as $Pr = \frac{\nu}{\alpha} = \frac{c_p \mu}{k}$. It describes the relative thickness of the velocity (hydrodynamic) boundary layer and the thermal boundary layer (momentum diffusivity divided by thermal diffusivity).

What is the physical meaning of the Nusselt number ($Nu$), and what does a value of $Nu = 1$ represent?

The Nusselt number ($Nu = \frac{hL}{k}$) represents the ratio of convective heat transfer to conductive heat transfer across a fluid boundary. A value of $Nu = 1$ indicates that heat transfer occurs purely by conduction through a stagnant fluid layer.

What is the Grashof number ($Gr_L$), and how is it defined mathematically for natural convection?

The Grashof number represents the ratio of buoyancy forces to viscous forces acting on a fluid. It is defined as $Gr_L = \frac{g\beta(T_s - T_\infty)L^3}{\nu^2}$, where $g$ is gravitational acceleration, $\beta$ is volumetric thermal expansion, and $\nu$ is kinematic viscosity.

When surface temperature $T_s$ and ambient temperature $T_\infty$ are fixed, what two approaches can increase the convective heat-transfer rate?

1. Increase the convection heat transfer coefficient $h$ (such as by installing or enlarging a fan or pump). 2. Increase the surface area $A_s$ by attaching extended surfaces called fins made of highly conductive materials such as aluminum.

How does Fourier's law of heat conduction express the one-dimensional conduction rate through a plane area $A$?

$\dot{Q}_x = -kA \frac{dT}{dx}$, where $k$ is thermal conductivity, $A$ is the area normal to heat flow, and $\frac{dT}{dx}$ is the temperature gradient. The minus sign ensures heat flows in the direction of decreasing temperature.

What is the conduction thermal resistance ($R_{cond}$) for a plane wall of thickness $L$, area $A$, and thermal conductivity $k$?

$R_{cond} = \frac{L}{kA}$, with units of temperature divided by heat flow rate ($K/W$ or $^\circ R \cdot hr/BTU$).

What is the formula for the steady-state radial heat conduction rate ($\dot{Q}_{cond}$) through a cylindrical wall?

$\dot{Q}_{cond} = \frac{2\pi k L (T_1 - T_2)}{\ln(r_2/r_1)}$, where $r_1$ and $r_2$ are the inner and outer radii, $k$ is the material's thermal conductivity, and $L$ is the length of the cylinder.

According to Fourier's law, how do temperature difference, area, thermal conductivity, and wall thickness affect conduction heat transfer?

Heat transfer increases when temperature difference increases, area increases, or thermal conductivity $k$ increases; heat transfer decreases when wall thickness increases.

What is surface-film conductance ($h$), and what are its standard metric units?

Also called the film coefficient or convective heat transfer coefficient, it is the time rate of heat flow from a unit area of a solid surface to its surrounding fluid (or vice versa) induced by a unit temperature difference, expressed in $W/(m^2 \cdot ^\circ C)$ or $W/(m^2 \cdot K)$.

How is the overall heat-transfer coefficient ($U$) related to total thermal resistance ($R_{Total}$) and surface area ($A$)?

$Q = UA\Delta T = \frac{\Delta T}{R_{Total}}$, which yields the relation $UA = \frac{1}{R_{Total}}$ or $U = \frac{1}{A R_{Total}}$.

What is the total thermal resistance ($R_{Total}$) expression for heat transfer from an internal fluid to an external fluid through a two-layer composite pipe?

$R_{Total} = \frac{1}{A_i h_i} + \frac{\ln(r_2/r_1)}{2\pi k_1 L} + \frac{\ln(r_3/r_2)}{2\pi k_2 L} + \frac{1}{A_o h_o}$, which accounts for inner convection, conduction through both layers, and outer convection.

What is the operational function of guard heaters in a guarded-hot-plate apparatus used to measure thermal conductivity?

Guard heaters are placed next to the main heater to retard heat flow in any lateral direction, ensuring heat flows strictly in one dimension from the main heater through the two material samples to the cooled chambers.

What microscopic carriers dominate heat conduction in metallic versus nonmetallic solids?

In metallic solids, heat conduction is primarily dominated by the transport of free electrons (the electron gas). In nonmetallic solids, heat is predominantly transmitted by molecular vibrational waves called lattice waves or phonons.

What is the conversion factor $g_c$ in the English Engineering system, and why is it needed?

$g_c = 32.174\,\frac{lbm \cdot ft}{lbf \cdot s^2}$. It is required in Newton's second law ($F = \frac{ma}{g_c}$) because both pound-force ($lbf$) and pound-mass ($lbm$) are treated as fundamental units.

What is the general one-dimensional unsteady heat conduction equation with internal heat generation for constant thermal conductivity?

$\frac{\partial^2 T}{\partial x^2} + \frac{q'''}{k} = \frac{1}{\alpha}\frac{\partial T}{\partial t}$, where $q'''$ is the volumetric heat generation rate and $\alpha = \frac{k}{\rho c}$ is the thermal diffusivity.

What is the steady-state temperature distribution in a plane wall with uniform internal heat generation ($q'''$) and equal surface temperatures ($T_w$) at $x = \pm L$?

It forms a symmetric parabolic profile given by $T(x) - T_w = \frac{q''' L^2}{2k}\left[1 - \left(\frac{x}{L}\right)^2\right]$, with the maximum temperature occurring at the center ($x = 0$).

What equation expresses the rate of radiation emission from an ideal black body, and what is the value of the Stefan-Boltzmann constant ($\sigma$) in SI units?

$q_r = \sigma A T^4$, where $\sigma = 5.67 \times 10^{-8}\,W/(m^2 \cdot K^4)$ (or $0.1714 \times 10^{-8}\,BTU/(hr \cdot ft^2 \cdot ^\circ R^4)$) and temperature must be in absolute units.

How is the radiation view factor (shape factor) $F_{1-2}$ defined between two surfaces?

The view factor $F_{1-2}$ is the fraction of total radiant energy that leaves surface 1 and arrives directly on surface 2; it is dimensionless and ranges between 0 and 1.

How are reflectivity, absorptivity, and transmissivity defined in radiation heat transfer?

Reflectivity is the fraction of incident radiant energy reflected by the surface; absorptivity is the fraction absorbed by the surface; transmissivity is the fraction transmitted through a layer of the material.

How is the equivalent thermal resistance ($R_{k2}$) calculated for two materials (2a and 2b) placed in parallel over a wall thickness $\Delta x_2$?

$R_{k2} = \frac{\Delta x_2}{k_{2a}A_{2a} + k_{2b}A_{2b}}$, derived from $\frac{1}{R_{k2}} = \frac{1}{R_{2a}} + \frac{1}{R_{2b}}$, where $R_i = \frac{\Delta x_2}{k_i A_i}$.

What distinguishes an endothermic system from an exothermic system in terms of enthalpy change ($\Delta H$) and heat exchange with the surroundings?

An endothermic process has $\Delta H > 0$, where the system absorbs heat from the surroundings and the surroundings get cooler. An exothermic process has $\Delta H < 0$, where the system releases heat to the surroundings and the surroundings get warmer.

What is the definition of a British Thermal Unit (BTU)?

A BTU is the amount of energy required to raise the temperature of $1\,lb$ of water at sea level by $1\,^\circ F$ (specifically at $68\,^\circ F$).

What is the key difference between sensible heat and latent heat?

Sensible heat produces an observable temperature change in a substance without altering its phase, while latent heat is heat absorbed or released during a phase change (such as fusion or vaporization) at constant temperature.

What is the relationship between absolute pressure ($p$), atmospheric pressure ($p_0$), and gauge pressure ($p_g$)?

Absolute pressure is the sum of atmospheric pressure and gauge pressure: $p = p_0 + p_g$. For pressures below atmospheric, the absolute pressure is given by $p = p_0 - p_g$ (vacuum pressure).

What is kinematic viscosity ($\nu$), and how is it related to dynamic viscosity ($\mu$) and density ($\rho$)?

Kinematic viscosity measures a fluid's resistance to flow under gravity and is calculated by dividing dynamic viscosity by density: $\nu = \frac{\mu}{\rho}$, commonly expressed in $m^2/s$ or centistokes ($cSt$).