# Fundamentals of Heat and Mass Transfer

Language: English

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ISBN: 1118989171

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store excess energy for use during low-power generation periods are urgently needed. Emerging energy conversion devices such as fuel cells could be used to (1) combine excess electricity that is generated during the day (in a solar power station, for example) with liquid water to produce hydrogen, and (2) subsequently convert the stored hydrogen at night by recombining it with oxygen to produce electricity and water. Roadblocks hindering the widespread use of hydrogen fuel cells are their size,

to Conduction qz + dz rdφ qr qφ + dφ dz z r T(r,φ ,z) qφ qr + dr dr y r x φ qz FIGURE 2.12 Differential control volume, dr ⅐ r d ⅐ dz, for conduction analysis in cylindrical coordinates (r, , z). When the del operator ٌ of Equation 2.3 is expressed in cylindrical coordinates, the general form of the heat flux vector and hence of Fourier’s law is Cylindrical Coordinates ѨT ѨT ϩk ѨTѨr ϩ j 1r Ѩ Ѩz qЉ ϭ ϪkٌT ϭ Ϫk i (2.24) where ѨT Ѩr qЉr ϭ Ϫk ѨT qЉ ϭ Ϫ kr Ѩ qЉz ϭ Ϫk ѨT

and electrical energy, and the thermal circuit is used to quantify only the thermal energy transfer. 2. Because of the thermally insulated boundary condition, it is not necessary to include the solder or substrate layers in the analysis. This is because there is no conduction through these materials and, from Fourier’s law, there can be no temperature gradients within these materials. At steady state, Tsdr ϭ Tan ϭ Tsi. 3. As the convection coefficient increases, the temperature of the silicon

conservation of energy dictates that the rate at which heat is transferred by convection from the fin must equal the rate at which it is conducted through the base of the fin. Accordingly, the alternative formulation for qf is ͵ h[T(x) Ϫ T ] dA q ϭ ͵ h(x) dA qf ϭ f ϱ Af s s Af (3.78) where Af is the total, including the tip, nfi surface area. Substitution of Equation 3.75 into Equation 3.78 would yield Equation 3.77. The second tip condition, Case B, corresponds to the assumption that

thermal conductivity, aluminum alloys are the more common choice because of additional benefits related to lower cost and weight. Fin effectiveness is also enhanced by increasing the ratio of the perimeter to the cross-sectional area. For this reason, the use of thin, but closely spaced fins, is preferred, with the proviso that the fin gap not be reduced to a value for which flow between the fins is severely impeded, thereby reducing the convection coefficient. Equation 3.87 also suggests that