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Chapter 6: Problem 108

In any forced or natural convection situation, the velocity of the flowing fluid is zero where the fluid wets any stationary surface. The magnitude of heat flux where the fluid wets a stationary surface is given by (a) \(k\left(T_{\text {fluid }}-T_{\text {wall }}\right)\) (b) \(\left.k \frac{d T}{d y}\right|_{\text {wall }}\) (c) \(\left.k \frac{d^{2} T}{d y^{2}}\right|_{\text {wall }}\) (d) \(\left.h \frac{d T}{d y}\right|_{\text {wall }}\) (e) None of them

Short Answer

Expert verified
Answer: Newton's law of cooling (Option d)

Step by step solution

01

Option (a): Conduction heat transfer formula

Option (a) represents the heat transfer in a conduction situation, which is not convection. The formula states that the heat transferred is proportional to the thermal conductivity (k) and the temperature difference between the fluid and the surface. This option is not the right answer, as we are looking for convection.
02

Option (b): Fourier's law

Option (b) represents Fourier's law, which states that the heat flux through a material is proportional to the thermal conductivity (k) and the temperature gradient (dT/dy) at the wall. This option represents the conduction heat transfer in the direction normal to the surface, so it is not the correct answer for convection heat transfer.
03

Option (c): Second derivative of temperature

Option (c) gives a formula involving the second derivative of temperature with respect to distance (d²T/dy²) at the wall. This option is not related to convection heat transfer, as it represents a curvature in the temperature profile and has no direct relation to heat flux in forced or natural convection situations.
04

Option (d): Newton's law of cooling

Option (d) represents Newton's law of cooling, which states that the rate of heat transfer by convection between a fluid and a surface is proportional to the convection heat transfer coefficient (h) and the temperature gradient (dT/dy) at the wall. This option best fits the required condition of heat flux in forced or natural convection situations near a stationary surface.
05

Option (e): None of them

Option (d) is the correct answer, so we can discard this option. To conclude, the magnitude of heat flux where the fluid wets a stationary surface in any forced or natural convection situation is given by: \(\left.h \frac{d T}{d y}\right|_{\text {wall }}\)

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Most popular questions from this chapter

A metal plate \(\left(k=180 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \rho=2800 \mathrm{~kg} / \mathrm{m}^{3}\right.\), and \(\left.c_{p}=880 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) with a thickness of \(1 \mathrm{~cm}\) is being cooled by air at \(5^{\circ} \mathrm{C}\) with a convection heat transfer coefficient of \(30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). If the initial temperature of the plate is \(300^{\circ} \mathrm{C}\), determine the plate temperature gradient at the surface after 2 minutes of cooling. Hint: Use the lumped system analysis to calculate the plate surface temperature. Make sure to verify the application of this method to this problem.

Consider a hot baked potato. Will the potato cool faster or slower when we blow the warm air coming from our lungs on it instead of letting it cool naturally in the cooler air in the room? Explain.

What is turbulent viscosity? What is it caused by?

Mercury at \(0^{\circ} \mathrm{C}\) is flowing over a flat plate at a velocity of \(0.1 \mathrm{~m} / \mathrm{s}\). Using EES (or other) software, determine the effect of the location along the plate \((x)\) on the velocity and thermal boundary layer thicknesses. By varying \(x\) for \(0

What is forced convection? How does it differ from natural convection? Is convection caused by winds forced or natural convection?
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