Answered: What does the logarithmic mean…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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This is a complete question I am stuck in. Kindly answer as soon as possible.
Air at atmospheric pressure flowing through a tube of 10 cm diameter at a rate of 0.1 kg/s is to be cooled from 400K to 300K with uniform wall temperature of 250K. Determine the length of the tube. Justify any assumptions that you have made.
Local Nusselt number for fully developed (hydrodynamically and thermally) turbulent flow in a smooth circular tube is defined by Nup-hD/kr, where h, D, and kr are the convective heat transfer coefficient, tube diameter, and fluid thermal conductivity, respectively. The friction factor for the smooth circular tube is given by the Blasius correlation, f-0.316Red ¹/4. The Reynolds number is defined by Rep-prviD/μr, where pr, vr, and ur are the fluid density, fluid velocity, and fluid viscosity, respectively. The Blasius correlation is applicable to Rep<2×10¹. Considering the analogy between velocity and thermal boundary layers and using the Blasius correlation, express the local Nusselt number using Reynolds and Prandtl numbers in the form of NuD-A-ReDxPr. The Prandtl number is defined by Pr-war, where and ar are the fluid kinematic viscosity and fluid thermal diffusivity, respectively. Note that the local Nusselt number formula should be applicable to Rep<2×10 and 0.6

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What does the logarithmic mean temperature difference represent for flow in a tube whose surface temperature is constant? Why do we use the logarithmic mean temperature instead of the arithmetic mean temperature?