Chapter 2: Problem 4
From a heat transfer point of view, what is the difference between isotropic and anisotropic materials?
Chapter 2: Problem 4
From a heat transfer point of view, what is the difference between isotropic and anisotropic materials?
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Consider a medium in which the heat conduction equation is given in its simplest form as $$ \frac{1}{r} \frac{d}{d r}\left(r k \frac{d T}{d r}\right)+\dot{e}_{\text {gen }}=0 $$ (a) Is heat transfer steady or transient? (b) Is heat transfer one-, two-, or three-dimensional? (c) Is there heat generation in the medium? (d) Is the thermal conductivity of the medium constant or variable?
Consider a large 5 -cm-thick brass plate \((k=111\) $\mathrm{W} / \mathrm{m} \cdot \mathrm{K})\( in which heat is generated uniformly at a rate of \)2 \times 10^{5} \mathrm{~W} / \mathrm{m}^{3}$. One side of the plate is insulated, while the other side is exposed to an environment at \(25^{\circ} \mathrm{C}\) with a heat transfer coefficient of $44 \mathrm{~W} / \mathrm{m}^{2}, \mathrm{~K}$. Explain where in the plate the highest and the lowest temperatures will occur, and determine their values.
How is the order of a differential equation determined?
A pipe is used for transporting boiling water in which the inner surface is at \(100^{\circ} \mathrm{C}\). The pipe is situated where the ambient temperature is \(20^{\circ} \mathrm{C}\) and the convection heat transfer coefficient is $50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}$. The pipe has a wall thickness of \(3 \mathrm{~mm}\) and an inner diameter of \(25 \mathrm{~mm}\), and it has a variable thermal conductivity given as \(k(T)=k_{0}(1+\beta T)\), where $k_{0}=1.5 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, \beta=0.003 \mathrm{~K}^{-1}\(, and \)T\( is in \)\mathrm{K}$. Determine the outer surface temperature of the pipe.
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