Question 18 of 50

For one-dimensional, steady-state conduction in a plane wall with no heat generation and constant thermal conductivity, how does the temperature vary with position?

What is the correct formula for the thermal resistance for conduction, Rt,cond, in a plane wall of thickness L, area A, and thermal conductivity k?

A plane wall is 0.2 meters thick and has a thermal conductivity of 50 W/m K. If the wall area is 5 square meters, what is its thermal resistance for conduction?

What is the principal cause of thermal contact resistance when two solid surfaces are pressed together?

For one-dimensional, steady-state radial conduction through a hollow cylinder with no heat generation, the heat transfer rate (qr) is:

What is the critical radius of insulation (rcr) for a cylindrical pipe with insulation thermal conductivity 'k' and outer surface convection coefficient 'h'?

A long pipe is insulated with a material having a thermal conductivity of 0.055 W/m K. The outer surface convection coefficient is 5 W/m^2 K. What is the critical radius of insulation for this pipe?

How does the temperature profile change in a plane wall with constant thermal conductivity when uniform heat generation is introduced, assuming the surface temperatures are held constant?

In a solid cylinder with uniform heat generation q_dot and constant surface temperature Ts, where does the maximum temperature occur?

What is the primary purpose of adding fins to a surface?

What does the term 'fin effectiveness' represent?

Under what condition is the use of fins generally considered justified from a performance standpoint?

What is the correct expression for the thermal resistance of a hollow sphere for one-dimensional, steady-state radial conduction, with inner radius r1, outer radius r2, and thermal conductivity k?

A hollow spherical container has an inner radius of 0.25 m and an outer radius of 0.275 m. The container is made of a material with a thermal conductivity of 0.0017 W/m K. What is the conduction resistance of the container wall?

For a very long fin, where it can be assumed the tip temperature approaches the ambient fluid temperature, what is the temperature distribution T(x)?

In the 'alternative conduction analysis' for steady-state, one-dimensional heat transfer, what key assumption allows for the direct integration of Fourier's law without first solving the heat equation?

In a symmetrically cooled plane wall of thickness 2L with uniform heat generation q_dot, the heat flux at the midplane (x=0) is:

To what does the Pennes bioheat equation presented in the chapter reduce if the metabolic heat generation and blood perfusion terms are both zero?

When analyzing a composite wall with materials A, B, and C in series, with heat flowing from fluid 1 to fluid 4, the heat transfer rate (qx) can be related to the temperature drop across material B (T2 - T3) by:

What is the tip condition for a fin that is described as 'adiabatic'?

Which of the following would enhance fin effectiveness for an infinitely long fin, according to the expression epsilon_f = (kP / (h*Ac))^0.5?

A composite wall has a layer of material A (k_A = 20 W/m K, L_A = 0.30 m) and a layer of material C (k_C = 50 W/m K, L_C = 0.15 m). A 0.15 m thick layer of material B is between them. The inner surface temperature is 600 C, the outer surface is 20 C, and the oven air is 800 C with h=25 W/m^2 K. What is the heat flux at the inner surface (x=0)?

The overall surface efficiency, eta_o, for a fin array is defined as:

What is the perfusion term in the Pennes bioheat equation intended to account for?

For a fin with an adiabatic tip, the heat transfer rate q_f is given by M*tanh(mL). What does the term M represent?

A composite cylindrical wall consists of an inner layer A and an outer layer B. In the equivalent thermal circuit, the resistance for conduction through layer A is given by:

The heat rate (q) from a fin is related to the fin thermal resistance (Rt,f) and the temperature difference between the base (Tb) and the fluid (T_inf) by which expression?

If adding a layer of insulation to a small-diameter pipe increases the heat loss, it means that the initial radius of the pipe was:

A plane wall of thickness 2L = 40 mm and thermal conductivity k = 5 W/m K has a steady-state temperature distribution of T(x) = 82.0 - 210x - 20000x^2, where x is in meters from the midplane. What is the volumetric heat generation rate q_dot?

The fin efficiency, eta_f, is defined as the ratio q_f / q_max. What is q_max?

A conical section is fabricated from pyroceram (k = 3.46 W/m K). The diameter is D = 0.25x. The small end is at x1 = 50 mm and the large end is at x2 = 250 mm. The end temperatures are T1 = 400 K and T2 = 600 K. What is the heat rate qx through the cone?

In a composite system, how are series and parallel thermal resistances typically represented in an analysis?

The addition of insulation is always beneficial for reducing heat transfer from a plane wall because:

What is the heat transfer rate per unit length for a very long fin with parameter M = 8.3 W?

If a material experiences uniform volumetric heat generation q_dot, can it be represented by a single thermal circuit resistance?

What is the overall heat transfer coefficient, U, for a composite plane wall with a total thermal resistance R_tot and area A?

For the bioheat equation, the perfusion term q_dot_p = omega*rho_b*c_b*(T_a - T) acts as a heat sink when:

A rectangular fin's efficiency can be approximated using a corrected length, Lc, to account for heat loss from the tip. For a fin of length L and thickness t, what is the corrected length?

A long, thin-walled copper tube has a radius ri and is at a temperature Ti. To minimize heat loss to ambient air at T_inf, insulation is added. If the initial radius ri is greater than the critical radius rcr, what is the effect of adding insulation?

A silicon chip and an 8-mm-thick aluminum substrate are separated by a 0.02-mm-thick epoxy joint. The thermal conductivity of the aluminum is 239 W/m K. The contact resistance of the epoxy is 0.9 x 10^-4 m^2 K/W. What is the total thermal resistance of the substrate and joint per unit area?

In a series composite wall, if one assumes that surfaces normal to the x-direction of heat flow are isothermal, how are the resistances of parallel layers F and G combined?

A long conducting rod has a temperature-dependent thermal conductivity given by k(T) = k_o + aT. For one-dimensional, steady-state heat transfer with no generation, what is the integrated form of Fourier's law between x0 (at T0) and x1 (at T1)?

The critical insulation radius for a sphere is given as 2k/h. If insulation with k = 0.04 W/m K is applied to a sphere in an environment with h = 10 W/m^2 K, what is the critical radius?

What is the primary assumption of the 'lumped capacitance method' for transient conduction analysis, as introduced in Chapter 5 but relevant to the limitations of steady-state analysis?

For a plane wall of thickness L, the condition for which the internal conduction resistance is equal to the surface convection resistance is:

A human body is in an environment where the insulation of a snow suit is the dominant thermal resistance. The suit has a thickness of 4.4 mm and thermal conductivity of 0.014 W/m K, covering an area of 1.8 m^2. What is the approximate thermal resistance of the suit?

In a series-parallel composite wall, as shown in Figure 3.3, what assumption is made if the thermal circuit is drawn with surfaces parallel to the x-direction treated as adiabatic?

A solid, truncated cone has its sides well-insulated. If heat flows under steady-state from the large end (x2) to the small end (x1), how does the magnitude of the temperature gradient |dT/dx| change along the direction of heat flow (from x2 to x1)?

Which condition is NOT a requirement for the 'alternative conduction analysis' (direct integration of Fourier's law) to be applicable?