Chapter 4: Problem 129
How does \((a)\) the air motion and \((b)\) the relative humidity of the environment affect the growth of microorganisms in foods?
Chapter 4: Problem 129
How does \((a)\) the air motion and \((b)\) the relative humidity of the environment affect the growth of microorganisms in foods?
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Get started for freeThick slabs of stainless steel $(k=14.9 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\( and \)\left.\alpha=3.95 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\right)\( and copper \)(k=401 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\( and \)\left.\alpha=117 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\right)$ are placed under an array of laser diodes, which supply an energy pulse of \(5 \times 10^{7} \mathrm{~J} / \mathrm{m}^{2}\) instantaneously at \(t=0\) to both materials. The two slabs have a uniform initial temperature of \(20^{\circ} \mathrm{C}\). Determine the temperatures of both slabs at $5 \mathrm{~cm}\( from the surface and \)60 \mathrm{~s}$ after receiving an energy pulse from the laser diodes.
Consider a cubic block whose sides are \(5 \mathrm{~cm}\) long and a cylindrical block whose height and diameter are also \(5 \mathrm{~cm}\). Both blocks are initially at \(20^{\circ} \mathrm{C}\) and are made of granite $\left(k=2.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\right.\( and \)\left.\alpha=1.15 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\right)$. Now both blocks are exposed to hot gases at \(500^{\circ} \mathrm{C}\) in a furnace on all of their surfaces with a heat transfer coefficient of $40 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. Determine the center temperature of each geometry after 10 , 20 , and \(60 \mathrm{~min}\). Solve this problem using the analytical oneterm approximation method.
Consider a 7.6-cm-long and 3-cm-diameter cylindrical lamb meat chunk $\left(\rho=1030 \mathrm{~kg} / \mathrm{m}^{3}, c_{p}=3.49 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}\right.\(, \)k=0.456 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \alpha=1.3 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}$ ). Fifteen such meat chunks initially at \(2^{\circ} \mathrm{C}\) are dropped into boiling water at \(95^{\circ} \mathrm{C}\) with a heat transfer coefficient of $1200 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. The amount of heat transfer during the first \(8 \mathrm{~min}\) of cooking is (a) \(71 \mathrm{~kJ}\) (b) \(227 \mathrm{~kJ}\) (c) \(238 \mathrm{~kJ}\) (d) \(269 \mathrm{~kJ}\) (e) \(307 \mathrm{~kJ}\)
It is claimed that beef can be stored for up to two years at $-23^{\circ} \mathrm{C}\( but no more than one year at \)-12^{\circ} \mathrm{C}$. Is this claim reasonable? Explain.
During a fire, the trunks of some dry oak trees $\left(k=0.17 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\right.\( and \)\left.\alpha=1.28 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\right)$ that are initially at a uniform temperature of \(30^{\circ} \mathrm{C}\) are exposed to hot gases at \(600^{\circ} \mathrm{C}\) for a period of \(4 \mathrm{~h}\), with a heat transfer coefficient of \(65 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\) on the surface. The ignition temperature of the trees is \(410^{\circ} \mathrm{C}\). Treating the trunks of the trees as long cylindrical rods of diameter $20 \mathrm{~cm}$, determine if these dry trees will ignite as the fire sweeps through them. Solve this problem using the analytical one-term approximation method.
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