Chapter 6: Problem 2
What is forced convection? How does it differ from natural convection? Is convection that is caused by winds forced or natural convection?
Chapter 6: Problem 2
What is forced convection? How does it differ from natural convection? Is convection that is caused by winds forced or natural convection?
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Get started for freeHow does turbulent flow differ from laminar flow? For which flow is the heat transfer coefficient higher?
In turbulent flow, one can estimate the Nusselt number using the analogy between heat and momentum transfer (Colburn analogy). This analogy relates the Nusselt number to the coefficient of friction, \(C_{p}\) as (a) \(\mathrm{Nu}=0.5 C_{f} \operatorname{Re} \mathrm{Pr}^{1 / 3}\) (c) \(\mathrm{Nu}=C_{f} \operatorname{Re} \mathrm{Pr}^{1 / 3}\) (e) \(\mathrm{Nu}=C_{f} \operatorname{Re}^{1 / 2} \operatorname{Pr}^{1 / 3}\) (d) \(\mathrm{Nu}=C_{f} \operatorname{Re} P r^{2 / 3}\)
A \(5-\mathrm{m} \times 5-\mathrm{m}\) flat plate maintained at a constant temperature of \(80^{\circ} \mathrm{C}\) is subjected to parallel flow of air at \(1 \mathrm{~atm}, 20^{\circ} \mathrm{C}\), and \(10 \mathrm{~m} / \mathrm{s}\). The total drag force acting on the upper surface of the plate is measured to be \(2.4 \mathrm{~N}\). Using the momentum-heat transfer analogy, determine the average convection heat transfer coefficient and the rate of heat transfer between the upper surface of the plate and the air. Evaluate the air properties at \(50^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).
Two metal plates are connected by a long ASTM A479 904L stainless steel bar. A hot gas, at \(400^{\circ} \mathrm{C}\), flows between the plates and across the bar. The bar has a square cross section with a width of \(2 \mathrm{~cm}\), and the length of the bar exposed to the hot gas is \(10 \mathrm{~cm}\). The average convection heat transfer coefficient for the bar in crossflow is correlated with the gas velocity as \(h=13.6 V^{0.675}\), where \(h\) and \(V\) have the units \(\mathrm{W} / \mathrm{m}^{2}, \mathrm{~K}\) and \(\mathrm{m} / \mathrm{s}\), respectively. The maximum use temperature for the ASTM A479 904L is \(260^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-1M). The temperature of the bar is maintained by a cooling mechanism with the capability of removing heat at a rate of 100 W. Determine the maximum velocity that the gas can achieve without heating the stainless steel bar above the maximum use temperature set by the ASME Code for Process Piping.
Consider an airplane cruising at an altitude of \(10 \mathrm{~km}\) where standard atmospheric conditions are \(-50^{\circ} \mathrm{C}\) and $26.5 \mathrm{kPa}\( at a speed of \)800 \mathrm{~km} / \mathrm{h}$. Each wing of the airplane can be modeled as a \(25-\mathrm{m} \times 3-\mathrm{m}\) flat plate, and the friction coefficient of the wings is \(0.0016\). Using the momentum-heat transfer analogy, determine the heat transfer coefficient for the wings at cruising conditions. Answer: $89.6 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$
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