Chapter 6: Problem 7
When is heat transfer through a fluid conduction and when is it convection? For what case is the rate of heat transfer higher? How does the convection heat transfer coefficient differ from the thermal conductivity of a fluid?
Chapter 6: Problem 7
When is heat transfer through a fluid conduction and when is it convection? For what case is the rate of heat transfer higher? How does the convection heat transfer coefficient differ from the thermal conductivity of a fluid?
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determined experimentally as a function of air velocity to be $h=17.9
V^{0.54}\( for \)0.5
Air at \(5^{\circ} \mathrm{C}\), with a convection heat transfer coefficient of \(30 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), is used for cooling metal plates coming out of a heat treatment oven at an initial temperature of \(300^{\circ} \mathrm{C}\). The plates $\left(k=180 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \rho=2800 \mathrm{~kg} / \mathrm{m}^{3}\right.$, and \(\left.c_{p}=880 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\right)\) have a thickness of \(10 \mathrm{~mm}\). Using appropriate software, determine the effect of cooling time on the temperature gradient in the metal plates at the surface. By varying the cooling time from 0 to \(3000 \mathrm{~s}\), plot the temperature gradient in the plates at the surface as a function of cooling time. 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 steady, laminar, two-dimensional, incompressible flow with constant properties and a Prandtl number of unity. For a given geometry, is it correct to say that both the average friction and heat transfer coefficients depend on the Reynolds number only?
What does the friction coefficient represent in flow over a flat plate? How is it related to the drag force acting on the plate?
Two metal plates are connected by a long ASTM B 98 copper-silicon bolt. A hot gas at \(200^{\circ} \mathrm{C}\) flows between the plates and across the cylindrical bolt. The diameter of the bolt is \(9.5 \mathrm{~mm}\), and the length of the bolt exposed to the hot gas is \(10 \mathrm{~cm}\). The average convection heat transfer coefficient for the bolt in crossflow is correlated with the gas velocity as \(h=24.6 \mathrm{~V}^{0.62}\), where \(h\) and \(V\) have the units \(\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and $\mathrm{m} / \mathrm{s}$, respectively. The maximum use temperature for the ASTM B98 bolt is \(149^{\circ} \mathrm{C}\) (ASME Code for Process Piping, ASME B31.3-2014, Table A-2M). If the gas velocity is \(10.4 \mathrm{~m} / \mathrm{s}\), determine the minimum heat removal rate required to keep the bolt surface from going above the maximum use temperature.
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