Chapter 6: Problem 4
In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
Chapter 6: Problem 4
In which mode of heat transfer is the convection heat transfer coefficient usually higher, natural convection or forced convection? Why?
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Get started for freeA 6-cm-diameter shaft rotates at \(3000 \mathrm{rpm}\) in a 20 -cm-long bearing with a uniform clearance of \(0.2 \mathrm{~mm}\). At steady operating conditions, both the bearing and the shaft in the vicinity of the oil gap are at \(50^{\circ} \mathrm{C}\), and the viscosity and thermal conductivity of lubricating oil are \(0.05 \mathrm{~N} \cdot \mathrm{s} / \mathrm{m}^{2}\) and \(0.17 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\). By simplifying and solving the continuity, momentum, and energy equations, determine \((a)\) the maximum temperature of oil, \((b)\) the rates of heat transfer to the bearing and the shaft, and \((c)\) the mechanical power wasted by the viscous dissipation in the oil.
During air cooling of steel balls, the convection heat transfer coefficient is
determined experimentally as a function of air velocity to be \(h=17.9
V^{0.54}\) for \(0.5
Air flowing over a \(1-\mathrm{m}\)-long flat plate at a velocity of \(7 \mathrm{~m} / \mathrm{s}\) has a friction coefficient given as \(C_{f}=0.664(V x / \nu)^{-0.5}\), where \(x\) is the location along the plate. Determine the wall shear stress and the air velocity gradient on the plate surface at mid-length of the plate. Evaluate the air properties at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\).
During air cooling of a flat plate \((k=1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\), the convection heat transfer coefficient is given as a function of air velocity to be \(h=27 V^{0.85}\), where \(h\) and \(V\) are in \(\mathrm{W} / \mathrm{m}^{2} \cdot \mathrm{K}\) and \(\mathrm{m} / \mathrm{s}\), respectively. At a given moment, the surface temperature of the plate is \(75^{\circ} \mathrm{C}\) and the air \((k=0.266 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K})\) temperature is \(5^{\circ} \mathrm{C}\). Using EES (or other) software, determine the effect of the air velocity \((V)\) on the air temperature gradient at the plate surface. By varying the air velocity from 0 to \(1.2 \mathrm{~m} / \mathrm{s}\) with increments of \(0.1 \mathrm{~m} / \mathrm{s}\), plot the air temperature gradient at the plate surface as a function of air velocity.
Express continuity equation for steady two-dimensional flow with constant properties, and explain what each term represents.
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