40 Questions
What is the formula for convection heat transfer rate?
Qconv = hAs (Ts - T)
What is the thermal resistance of the surface against heat convection?
Rconv = 1 / (hAs)
What is the formula for radiation heat transfer rate?
Qrad = hrad As (Ts^4 - Tsurr^4)
What is the thermal resistance of a surface against radiation?
Rrad = 1 / (hrad As)
What is the unit of convection heat transfer coefficient?
W/m^2K
What is the unit of radiation heat transfer coefficient?
W/m^2K^4
What is the formula for convection heat transfer rate in terms of convection resistance?
Qconv = (Ts - T) / Rconv
What is the formula for radiation heat transfer rate in terms of radiation resistance?
Qrad = (Ts - Tsurr) / Rrad
What is the concept that can be used to solve heat conduction problems without involving differential equations?
thermal resistance
What is the analogy between heat conduction and electrical circuit problems?
thermal resistance corresponds to electrical resistance, temperature difference corresponds to voltage, and heat transfer rate corresponds to electric current
What is the geometric shape of the plane wall considered in the problem of one-dimensional steady heat conduction?
a plane wall of thickness L
What is the relationship between the temperature distribution and the distance x through the wall under steady conditions?
the temperature distribution in the wall is a straight line
What is the expression for the rate of conduction heat transfer Qcond,wall through the wall?
Qcond,wall = kA(T1-T2)/L
What is the thermal resistance of the wall against heat conduction, Rwall?
Rwall = L/(kA)
What is the expression for the heat conduction through a plane wall in terms of thermal resistance?
Qcond,wall = (T1-T2)/Rwall
What are the typical units of thermal resistance, Rwall?
C/W
What are the two ways heat can be transferred in a solid?
conduction and radiation
What happens to heat transfer when a fluid is still (no bulk fluid motion)?
It is by conduction and possibly by radiation
What is the role of gases in radiation?
They are practically transparent to radiation, except at certain wavelengths
What is the primary mode of heat transfer in a vacuum?
radiation
What is the condition for approximating heat conduction as one-dimensional in a large plane wall?
Heat conduction is dominant in one direction and negligible in other directions
What is the relationship between convection and conduction in a fluid?
Convection is a combination of conduction and fluid motion, and conduction is a special case of convection in the absence of fluid motion
What is the primary mode of heat transfer in a liquid?
conduction and absorption of radiation
Can a gas between two solid surfaces interfere with radiation?
No, it acts effectively as a vacuum
What is the main assumption in the heat transfer problem of a single-pane window, considering the temperature variation?
One-dimensional heat transfer, with no variation in the axial direction.
What is the thermal conductivity of the glass window in the example problem?
0.78 W/m°C
What is the purpose of the heat transfer coefficients h1 and h2 in the single-pane window problem?
To include the effects of radiation in the heat transfer process.
What is the temperature of the surroundings in the steam pipe problem?
5°C
What is the assumption made for the thermal conductivity of the wall in the problem of steady one-dimensional heat conduction?
Constant thermal conductivity
What is the thickness of the glass wool insulation in the steam pipe problem?
3 cm
What is the rate of heat loss from the steam per unit length of the pipe?
93.9 W
Why does adding insulation to a wall always decrease heat transfer?
Because the heat transfer area A is constant, and adding insulation increases the thermal resistance of the wall without increasing the convection resistance
What happens to the convection resistance of a cylindrical pipe or a spherical shell when insulation is added?
It decreases
What is the purpose of finned surfaces in heat transfer?
To increase the heat transfer rate from the surface.
What is the total thermal resistance in the steam pipe problem?
3.355 C/W
What is the condition required to determine the value of r2 at which Q reaches a maximum?
dQ/dr2 = 0
What is the temperature of the right surface of the wall at x = L?
T = -4°C
What is the effect of adding insulation to a cylindrical pipe on the conduction resistance?
It increases the conduction resistance of the insulation layer
Why does the heat transfer from a pipe may increase or decrease when insulation is added?
Because the effect of increasing conduction resistance dominates or is dominated by the effect of decreasing convection resistance
What is the expression for the rate of heat transfer from the insulated pipe to the surrounding air?
The equation given in the problem statement
Study Notes
Convection Heat Transfer
- The convection heat transfer rate (Qconv) can be expressed as: Qconv = hAs (Ts - T) where h is the convection heat transfer coefficient, As is the surface area, Ts is the surface temperature, and T is the fluid temperature.
- The convection resistance (Rconv) of a surface can be expressed as: Rconv = 1 / hAs
Radiation Heat Transfer
- The radiation heat transfer rate (Qrad) can be expressed as: Qrad = hrad As (Ts^4 - Tsurr^4) where hrad is the radiation heat transfer coefficient, As is the surface area, Ts is the surface temperature, and Tsurr is the surrounding temperature.
- The radiation resistance (Rrad) of a surface can be expressed as: Rrad = 1 / hrad As
Heat Transfer Modes
- Conduction, convection, and radiation are the three modes of heat transfer.
- Conduction occurs through a stationary medium, convection occurs through a moving fluid, and radiation occurs through electromagnetic waves.
- The mode of heat transfer depends on the presence or absence of fluid motion and the temperature differences between surfaces.
One-Dimensional Heat Conduction
- Heat conduction through a large plane wall, cylinder, or sphere can be approximated as one-dimensional.
- The thermal resistance of a plane wall can be expressed as: Rwall = L / kA, where L is the thickness of the wall, k is the thermal conductivity, and A is the cross-sectional area.
- The rate of heat conduction (Qcond) can be expressed as: Qcond = kA (T1 - T2) / L, where T1 and T2 are the temperatures on either side of the wall.
Thermal Resistance Concept
- Thermal resistance is analogous to electrical resistance, with temperature difference as the driving force and heat transfer rate as the resulting flow.
- Thermal resistance can be used to analyze heat conduction problems in various geometries, including plane walls, cylinders, and spheres.
Critical Radius of Insulation
- Adding insulation to a wall always decreases heat transfer, but adding insulation to a cylindrical pipe or spherical shell can increase or decrease heat transfer, depending on the dominance of conduction and convection resistances.
- The critical radius of insulation is the radius at which the heat transfer rate reaches a maximum or minimum.
Quiz about convection heat transfer, including the equation for heat flow and convection heat transfer coefficient.
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