Heat Transfer Final

The internal energy of a system is the sum of all its microscopic forms of energy.

True

The enthalpy is the sum of the internal energy and the flow energy (also called the flow work).

True

A temperature difference of 1 degree Celsius is the same as a temperature difference of 1 degree Kelvin.

True

A closed system consists of a variable mass.

False

The 1st law of thermodynamics, also known as conservation of energy, can be written as

(rate of energy storage) = (rate of energy in) - (rate of energy out)

True

The efficiency of a Carnot engine does not depend on the heat rejection temperature.

False

A system cannot reach a steady-state temperature if heat is continually added to it, and there is no means for heat to be transferred from the system.

True

The thermal conductivity of air at 25 degrees Celsius and 1 atm pressure is about 0.026 W m^-1 K^-1.

True

The rate of radiation heat transfer is linearly proportional to the difference in the temperatures between two surfaces.

False

The convective heat transfer coefficient, h, for air is generally higher for forced convection compared with free convection.

True

If the heat capacity c is a function of temperature, then c must be inside the derivative for the “rate of energy storage” term in the thermal energy equation.

False, even if c is a function of time, it is not in the derivative.

For an incompressible substance at constant pressure, the specific heat at constant volume is equal to the specific heat at constant pressure.

True

At an interface between two solids, if the thermal contact resistance is zero, there will be zero temperature drop at the interface.

True

The steady-state form of the general heat conduction equation, with no heat generation, is also referred to as the Poisson equation.

False, the Poisson equation is the steady-state form including energy generation. That refers to the Laplace equation.

The temperature gradient is positive (i.e., the temperature increases with increasing x) if there is a net conductive heat flux in the positive x direction.

False because there is a negative in the equation. q = -kdT/dx

The heat capacity is typically ignored when deriving boundary conditions for the thermal energy equation.

True

The convective thermal resistance is linearly proportional to the convective heat transfer coefficient.

False, it is inversely proportional.

The general heat conduction equation, which relies on the Fourier law of heat conduction, requires that the continuum assumption be valid.

True

Specifying the temperature gradient at a boundary is equivalent to specifying the temperature at a boundary.

False

The solution of the 1D steady-state heat conduction equation, with constant-temperature boundary conditions, can be of the form T(x) = c₁x² + c₂x + c₃.

False. You would see x² if there is internal heat generation. 1D will just be Cx +C.

The overall heat transfer coefficient, U, can have units of m² K W^-1.

False, it should be W m^-2 K^-1

For a given heat transfer fin of area A_fin > A_b, the fin effectiveness is greater than the fin efficiency.

True

Actual heat transfer fins usually have fin efficiencies greater than one.

False, fin efficiencies are always less than one, indicating that real fins lose some effectiveness due to heat loss. Fin efficiency = (Actual heat transfer)/(heat transfer if the entire fin were at the base temperature).

The thermal conduction resistance in the radial direction of a cylinder is proportional to the natural log of the ratio of the outer radius to the inner radius.

True

For an insulated heated cylinder, if the insulation is thicker than the critical radius than adding additional insulation increases the heat transfer rate from the cylinder.

False, critical radius = k/h has the maximum heat transfer.

Thermal conduction resistance is inversely proportional to thermal conductivity.

True

A general rule of thumb when solving 2D steady-state heat conduction problems by separation of variables is to position the minus sign so that the homogeneous direction gets the sin and cos terms.

True

Superposition can only be applied to nonlinear problems.

False, it can only be applied to linear problems

Conduction shape factors are applicable for computing the heat transfer between two surfaces maintained at constant temperatures.

True

The orthogonality property of the sine and cosine functions enables them to be applied to satisfy inhomogeneous boundary conditions for partial differential equations.

True

A typical thermocouple bead (i.e., where the two wires form a junction) can be analyzed as a lumped system.

True

A lumped system analysis assumes that the temperature is uniform throughout a body.

True

In a “flip-chip” geometry for electronic packaging, the primary path for heat transfer from the die is down through the substrate.

False, the primary path for heat transfer from the die is primarily upwards to the heat sink or ambient air.

A heat transfer fin is an example of an extended surface.

True

The thermal resistances considered in a thermal network analysis can include both conduction and convection resistances.

True

The time constant in a lumped analysis is directly proportional to the mass of a body.

True

Thermal capacitance increases with increasing mass density.

True

The time constant for a 1-node thermal network would be equivalent to the time constant for a lumped system, provided that the conduction resistance is negligible.

True

In a multi-node thermal network analysis, the shortest time constant always governs the response of the system.

False, it’s not always the case. The shortest time constant affects the initial response but not the entire system.

The Biot number is the ratio of conduction resistance within a body, and the convection resistance at the surface of a body.

True

A periodic “steady-state” temperature is a function of the initial temperature condition.

False, it’s steady state…

A function f(t) is even if f(t) = - f(t).

False, it is even if f(t) = f(-t).

f(t) = -f(t) is only true for f(t) = 0

A Green’s function (G) is the solution to a homogeneous problem with an instantaneous (impulsive) source.

True

The Dirac delta function can be defined such that it is equal to zero for x < x_o, and equal to one for x > x_o.

False, dirac delta is defined as 0 except for one point.

A complex temperature includes both real and imaginary components.

True

Green’s functions cannot be applied to heat conduction problems with continuous sources.

False, Green’s functions can be applied to both instantaneous and continuous sources.

The units for the strength of an instantaneous plane source, used in Green's functions, are Watts. 

False, the unit of strength for continuous source is: W m^-2 for a plane, Wm^-1 for a line, and W for a point and for instantaneous source is: Jm^-2 for a plane, Jm^-1 for a line, and J for a point.

The "method of images" refers to replicating identical sources (or sinks) on both sides of a boundary, in order to represent an adiabatic or a zero-temperature boundary condition.

True

In general, periodic functions can be modeled as Fourier series.

True

Green’s functions can be useful for determining the temperature distribution due to an arbitrary initial temperature condition.

True

In the boundary-layer momentum equation for flow over a flat plate, a pressure gradient is assumed to exist along the plate.

False, pressure is uniform in the direction along the plate. The momentum equation instead accounts for effects of viscosity and boundary layer development.

There are 3 momentum equations for 3D fluid flow.

True

The velocity and thermal boundary layers are always of the same thickness.

False, but they would be the same when the Prandtl number is one. Pr = (kinematic viscosity nu)/(thermal diffusivity alpha). For Pr>1, velocity is thicker than thermal.

The Reynolds number typically appears in the nondimensional version of the fluid momentum equations.

True

For incompressible flow, there is no time derivative term in the continuity equation, even for transient flow conditions.

True

External "slug" flow can be assumed for fluids where the Prandtl number is much greater than 1.

False, only when Pr«1 or dt/d »1

For steady incompressible flow over a flat plate, momentum diffusion along the plate (in the x direction) is significant within the boundary layer. 

False, the change in x velocity in the x direction is negligible compared to the change in x velocity in the y direction.

The “no-slip” boundary condition describes how a fluid in motion assumes a zero velocity relative to a solid surface.

True

In the boundary-layer approximation for flow over a flat plate, the y-direction (normal to the plate) momentum equation only concerns the pressure gradient in the y direction, not the velocity.

True

A similarity solution can be applied to solve for external boundary layer flow, including slug flow.

True

Axial conduction in the fluid can usually be neglected when analyzing internal forced convection in a pipe.

True

If the Reynolds number is the same for two different fluids flowing in a pipe, the thermal entrance region will be longer for the fluid having the higher Prandtl number.

True

For laminar fully developed flow, the Nusselt number increases with increasing Reynolds number.

False. For laminar fully developed flow, Nu is independent of Re. For internal forced convection, constant wall heat flux, Nu = 4.36, and for constant wall temp, Nu = 3.66

The thermal entrance length is the same as the hydrodynamic entrance length for a fluid having a Prandtl number equal to 1.

True

The magnitude of the radial temperature gradient at the wall of a pipe is greater for a constant-heat-flux boundary condition, compared to a constant-wall-temperature boundary condition.

True

Suppose a pipe of square cross-section has the same hydraulic diameter as a circular pipe. The square pipe therefore has a greater wall surface area available for heat transfer, compared to the circular pipe.

True

For internal forced convection in a circular pipe with constant wall temperature, the mean fluid temperature increases linearly down the length of the pipe.

False, it increases nonlinearly. Constant Wall heat flux increases linearly after it passes the entrance region.

The pressure drop along a pipe under fully developed laminar flow conditions is directly proportional to the square of the pipe diameter.

False

For internal forced convection, the heat transfer coefficient should be defined with respect to the inlet temperature of the fluid.

False, the film/mean temperature should be used.

The Chilton-Colburn analogy relates the friction factor to the Nusselt number in turbulent flow.

True

The volume expansion coefficient relates how the density of a fluid changes with pressure, at constant temperature.

False, the volume expansion coefficient describes how a fluid's volume changes with temperature, at constant pressure.

We expect better cooling, by natural convection from the back of the panel, for a horizontally-mounted photovoltaic (PV) panel compared to one mounted on an inclined roof.

False, the buoyancy driven convection currents are better with the incline because warm air rises more effectively.

The expansion coefficient is inversely related to absolute temperature, for an ideal gas.

True

For natural convection, the Reynolds number is the key dimensionless parameter which describes whether the flow is laminar or turbulent.

False, the key parameter is the Rayleigh Number which = GrPr.

The presence of any convection, natural or forced, will result in a heat transfer rate greater than that of pure conduction through the fluid.

True

The Boussinesq approximation enables the temperature dependence of a fluid's thermal conductivity to be calculated.

False, it enables the temperature dependence of a fluid's density to be calculated. It assumes the fluid properties, like density are constant except for their variation with temperature. Thermal conductivity is assumed to be constant.

The optimal cooling of photovoltaic (PV) panels depends on the spacing between the back of the panel and the surface on which they are mounted.

True

For an enclosure with no natural or forced convection, the effective thermal conductivity is equal to the thermal conductivity of the fluid inside the enclosure.

True

Expansion-driven flow can occur even without the presence of gravity.

True

A plate with a hot surface facing upwards will be more effectively cooled by natural convection than the same plate with the heated surface facing downwards.

True

The heat transfer coefficient in the nucleate boiling regime, for pool boiling, is higher than the heat transfer coefficient in the film boiling regime.

True

The heat flux obtained during boiling heat transfer is proportional to the temperature difference between the wall (Ts) and the mean fluid temperature far from the wall (T∞).

False, it should be the temperature difference between Ts and Tsat.

Dropwise condensation leads to lower heat transfer rates than does film condensation.

False, dropwise condensation leaves a clean surface for new drops to form which is very efficient heat transfer.

During freezing of a single-component substance, the interface between the solid and the liquid phases will be at the melting point, Tm.

True

For pool boiling, the maximum heat flux occurs when the entire heater surface becomes covered with vapor, such that it is difficult for liquid to reach the surface.

True

The Stefan number can be interpreted as the ratio of sensible to convective heat.

False, the Stefan number is the (sensible heat)/(latent heat).

Water has the highest value of heat of fusion (kJ/L) among all known substances used as phase-change materials.

False, salt hydrates and paraffins have higher heat of fusions because they have higher densities.

With regard to cost effectiveness, phase change materials (PCMs) are best applied in buildings in USA climates that are dominated by cooling.

True

The most widely used correlation for the rate of heat transfer in the nucleate boiling regime was proposed by Rohsenow in 1952.

True

The Nusselt relation for the heat transfer coefficient for laminar condensation on a vertical plate is derived assuming a uniform temperature in the condensate film.

False, it assumes a linear temperature gradient across the film.

When designing a heat exchanger, one should always use the average temperature difference between the hot and cold fluid streams.

False, use the log mean temperature difference (LMTD) for more accurate results. delta Tlm

The number of transfer units (NTU) is directly proportional to the overall heat transfer coefficient, U.

True

Within a heat exchanger, the heat transfer to the cold fluid is always equal to the heat transfer from the hot fluid.

False. Only ideal heat exchangers can do this.

The maximum possible heat transfer rate in a heat exchanger is always limited by the mass flow rate and heat capacity of the hotter fluid.

False, it is limited my the minimum heat capacity rate C = mdot*cp

The maximum temperature difference in a heat exchanger is the difference between the inlet temperature of the hot fluid, and the outlet temperature of the cold fluid.

False, it’s the difference between the inlet temperature of the hot fluid and the inlet temperature of the cold fluid.

Microchannel heat exchangers take advantage of the fact that, for laminar fully developed flow, the heat transfer coefficient is inversely proportional to the diameter.

True

One can determine the effectiveness of a heat exchanger from the number of transfer units, NTU, and the capacity ratio, c.

True

If all other parameters are constant, the effectiveness of a counter-flow heat exchanger is larger than that of a parallel-flow heat exchanger.

True

The effectiveness-NTU method for the design of heat exchangers should be used when the mass flow rates and heat transfer area are known, but not the outlet temperatures.

True

For electrification of industrial process heating, types of heating modes that can be considered include Joule heating, infrared heating, microwave heating, and inductive heating.

True