Heat and Mass Transfer Practice Flashcards

Comprehensive practice flashcards created from lecture transcript notes covering heat conduction, convection, radiation, and mass transfer.

What is the formula for the critical radius of insulation for a sphere?

For a spherical body, the critical radius of insulation is $r_c = \frac{2k}{h}$, where $k$ is the thermal conductivity and $h$ is the convective heat transfer coefficient.

What is thermal diffusivity and what is its mathematical formula?

Thermal diffusivity measures the rate of heat propagation through a material and is given by $\alpha = \frac{k}{\rho C_p}$, with SI unit $m^2/s$.

What is the formula for the critical radius of insulation for a cylindrical pipe?

For a cylindrical pipe, the critical radius of insulation is $r_c = \frac{k}{h}$.

What happens to heat loss when insulation is added to a pipe up to its critical radius?

Adding insulation up to the critical radius increases the heat loss from the pipe.

Why does glass-wool exhibit the maximum temperature drop across a given thickness for a specified heat flow?

Because glass-wool has a very low thermal conductivity ($k = 0.075\,W/m\cdot K$), and temperature drop is inversely proportional to thermal conductivity ($dT \propto \frac{1}{k}$).

What is the SI unit of thermal conductivity?

The SI unit of thermal conductivity ($k$) is $W/m\cdot K$.

What is the main purpose of adding fins to a heat transferring surface?

Fins are added to increase the total surface area exposed to the fluid, thereby increasing the rate of heat transfer.

What is the ratio of heat flow $Q_1/Q_2$ through two walls of equal thickness if $k_1 = 2k_2$?

The heat flow ratio $Q_1/Q_2$ is $2$, since heat transfer rate is directly proportional to thermal conductivity.

Which common substance among air, water, brick, and copper has the lowest thermal conductivity?

Air, with a thermal conductivity of approximately $0.024\,W/m\cdot K$ at $0^\circ C$.

Which non-dimensional number determines whether extended surfaces (fins) act as insulation or enhance heat transfer?

The Biot number ($Bi$).

What is the equivalent thermal conductivity $k_{eq}$ of a composite wall made of two layers of equal thickness with thermal conductivities $k_1$ and $k_2$?

The equivalent thermal conductivity is $k_{eq} = \frac{2 k_1 k_2}{k_1 + k_2}$.

In which heat transfer problems is the concept of overall heat transfer coefficient used?

In problems involving combined conduction and convection heat transfer.

How does the thermal conductivity of air change as temperature rises?

The thermal conductivity of air increases with temperature due to increased molecular diffusion and lattice vibration.

Which fin configuration yields the highest fin effectiveness?

Thin, closely spaced fins.

What is the uniform internal heat generation rate $q$ in a long cylindrical rod of radius $R$ with surface heat flux $q_0$?

The internal heat generation rate is $q = \frac{2q_0}{R}$.

Which dimensionless numbers are used simultaneously in transient heat conduction analysis?

The Biot number ($Bi$) and the Fourier number ($Fo$).

Under what Biot number condition is the lumped heat capacity approach valid?

The lumped heat capacity method is valid when $Bi < 0.1$.

How does the thermal conductivity of solid metals generally vary with temperature?

The thermal conductivity of solid metals generally decreases with an increase in temperature (exceptions include mercury, aluminum, and uranium).

Which material has the highest known thermal conductivity?

Diamond, with a thermal conductivity of approximately $2300\,W/m\cdot K$.

What is the fundamental governing law of heat conduction?

Fourier's law of heat conduction, expressed as $Q = -k A \frac{dT}{dx}$.

How is the characteristic length $L_c$ defined in the Biot number calculation?

Characteristic length $L_c$ is defined as the ratio of body volume to its surface area ($L_c = \frac{V}{A}$).

What is the thermal conduction resistance formula for a hollow sphere of inner radius $r_1$ and outer radius $r_2$?

The thermal resistance is $R_{th} = \frac{r_2 - r_1}{4 \pi k r_1 r_2}$.

What are the dimensions of thermal conductivity in the $MLT\theta$ system?

The dimensions are $[M^1 L^1 T^{-3} \theta^{-1}]$.

What is the mathematical pattern of temperature variation over time in a lumped heat capacity model?

The temperature variation with time is exponential: $\frac{T - T_\infty}{T_i - T_\infty} = e^{-\left(\frac{h A}{\rho V C_p}\right) t}$.

What does a very low Biot number ($Bi < 0.1$) signify regarding thermal resistance?

It signifies that internal conduction resistance within the solid is negligible compared to external convection resistance.

What is the 3D steady-state heat conduction equation without internal heat generation called?

It is called the Laplace equation: $\nabla^2 T = 0$.

What is the 3D steady-state heat conduction equation with constant internal heat generation called?

It is called the Poisson equation: $\nabla^2 T + \frac{q_g}{k} = 0$.

What defines transient heat conduction?

Transient heat conduction occurs when the temperature at any point within the system varies with time.

How is the time constant of a thermocouple defined?

It is defined as the time required for the sensor to respond to $63.2\%$ of a step change in initial temperature difference.

Why is a heat pipe considered a superconductor in heat transfer applications?

Because it transfers heat via evaporative and condensation phase-change cycles, providing an extremely high effective thermal conductivity.

Why is cork a good thermal insulator?

Because cork is a porous material containing small enclosed air cells that inhibit heat conduction.

What physical ratio does the Fourier number ($Fo$) represent?

The Fourier number represents the ratio of the rate of heat conduction through a body to the rate of thermal energy storage: $Fo = \frac{\alpha t}{L_c^2}$.

How does temperature distribute radially across a long hollow cylinder under steady 1D conduction with constant $k$?

The temperature varies logarithmically with radius: $T(r) \propto \ln(r)$.

What is the temperature distribution profile across a plane wall under steady 1D conduction with constant $k$ and no heat generation?

The temperature distribution is linear.

What is the characteristic length $L_c$ of a solid cube of side length $L$?

The characteristic length is $L_c = \frac{V}{A} = \frac{L^3}{6L^2} = \frac{L}{6}$.

How is the convective heat transfer coefficient ($h$) defined?

It is defined as the amount of heat transmitted for a unit temperature difference between a fluid and unit surface area in unit time.

What is the fin efficiency formula for an infinitely long fin?

The fin efficiency is $\eta_{fin} = \frac{1}{m L}$, where $m = \sqrt{\frac{h P}{k A_c}}$.

What is the physical significance of thermal diffusivity $\alpha$?

It represents the ability of a substance to conduct thermal energy relative to its ability to store thermal energy.

Under what condition are the hydrodynamic and thermal boundary layer thicknesses equal in forced convection?

When the Prandtl number is equal to 1 ($Pr = 1$).

Which dimensionless parameter governs the transition from laminar to turbulent flow in free convection?

The Rayleigh number ($Ra = Gr \times Pr$).

What is the definition of the Prandtl number ($Pr$)?

Prandtl number is the ratio of kinematic viscosity (momentum diffusivity) to thermal diffusivity: $Pr = \frac{\nu}{\alpha} = \frac{\mu C_p}{k}$.

What is the physical meaning of the Nusselt number ($Nu$)?

Nusselt number is the ratio of convective heat transfer to conductive heat transfer across a fluid layer: $Nu = \frac{h L_c}{k}$.

What ratio does the Grashof number ($Gr$) represent in natural convection?

The Grashof number represents the ratio of buoyant forces to viscous forces in a fluid.

If Prandtl number $Pr > 1$, how does the thermal boundary layer thickness ($\delta_t$) compare to the hydrodynamic boundary layer thickness ($\delta$)?

The thermal boundary layer is thinner than the hydrodynamic boundary layer (\delta_t < \delta).

What is the Peclet number ($Pe$)?

The Peclet number is the product of the Reynolds number and Prandtl number ($Pe = Re \times Pr$).

What is Stefan-Boltzmann's law for black body radiation?

It states that total emissive power of a black body is directly proportional to the fourth power of its absolute temperature: $E_b = \sigma T^4$, where $\sigma = 5.67 \times 10^{-8}\,W/m^2\cdot K^4$.

What is the definition of a grey body?

A grey body is one whose monochromatic absorptivity and emissivity are constant and independent of wavelength and temperature.

What does Kirchhoff's law of radiation state?

At thermal equilibrium, the total emissivity of a body is equal to its total absorptivity ($\epsilon = \alpha$).

What is Wien's displacement law?

It states that the wavelength corresponding to maximum monochromatic emissive power is inversely proportional to absolute temperature: $\lambda_{max} T = 2898\,\mu m\cdot K$.

What classification of heat exchanger is an automobile radiator?

An automobile radiator is a cross-flow type heat exchanger.