Ethylene glycol-distilled water mixture with a mass fraction of \(0.72\) and a flow rate of \(2.05 \times 10^{-4} \mathrm{~m}^{3} / \mathrm{s}\) flows inside a tube with an inside diameter of \(0.0158 \mathrm{~m}\) and a uniform wall heat flux boundary condition. For this flow, determine the Nusselt number at the location \(x / D=10\) for the inlet tube configuration of \((a)\) bell-mouth and \((b)\) re-entrant. Compare the results for parts \((a)\) and \((b)\). Assume the Grashof number is Gr \(=60,000\). The physical properties of ethylene glycol- distilled water mixture are \(\operatorname{Pr}=33.46, \nu=3.45 \times 10^{-6} \mathrm{~m}^{2} / \mathrm{s}\) and \(\mu_{v} / \mu_{s}=2.0\).

Short Answer

Expert verified
Question: Determine the difference in heat transfer performance between bell-mouth and re-entrant inlet configurations for a flow of ethylene glycol-distilled water mixture inside a tube with uniform wall heat flux boundary condition. Answer: To compare the heat transfer performance between bell-mouth and re-entrant inlet configurations, we need to calculate the Nusselt numbers for both cases using the given empirical correlations and the calculated Reynolds number. After finding the Nusselt numbers, we can analyze the difference in heat transfer performance by comparing these values. Higher Nusselt numbers indicate better heat transfer performance.

Step by step solution

01

Determine the Reynolds number

First, we need to find the Reynolds number (Re) using the given values for flow rate, diameter, and kinematic viscosity: \( Re = \frac{u D}{\nu} \) where \(u\) is the flow velocity, \(D\) is the inside diameter of the tube, and \(\nu\) is the kinematic viscosity of the mixture. We are given the flow rate \(Q = 2.05 \times 10^{-4} \mathrm{~m}^{3}/\mathrm{s}\), so we can find the flow velocity by dividing the flow rate by the cross-sectional area of the tube: \( u = \frac{Q}{A} = \frac{Q}{(1/4)\pi D^{2}} \) Plugging in the given values, we can now find the Reynolds number: \( Re = \frac{ u D }{ \nu } \)
02

Determine the Nusselt number for bell-mouth configuration

For the bell-mouth inlet configuration, we can use the following empirical correlation for the Nusselt number (Nu): \( Nu = 0.021 Re^{0.8} Pr^{n} \) where \(Re\) is the Reynolds number, \(Pr\) is the Prandtl number and \(n = 0.4\) for flow with the given Grashof number (Gr = 60,000). By plugging in the values of Reynolds number and Prandtl number, we can find the Nusselt number for the bell-mouth inlet configuration.
03

Determine the Nusselt number for re-entrant configuration

For the re-entrant inlet configuration, we can use a different empirical correlation for the Nusselt number: \( Nu = 0.021 Re^{0.8} Pr^{n} (\frac{\mu_{v}}{\mu_{s}})^{0.14} \) where \(Re\) is the Reynolds number, \(Pr\) is the Prandtl number, \(n = 0.4\), and the ratios of dynamic viscosities at the bulk mean (v) and wall (s) temperature are given as \(\frac{\mu_{v}}{\mu_{s}} = 2.0\). Using the given values, we can find the Nusselt number for the re-entrant inlet configuration.
04

Compare the results

After calculating the Nusselt numbers for both inlet configurations, we can compare the results to analyze how the heat transfer performance changes due to the inlet tube configuration. Higher Nusselt numbers indicate better heat transfer performance.

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Most popular questions from this chapter

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