Passage of an electric current through a long conducting rod of radius r; and thermal conductivity kr, esults in uniform volumetric heating at a rate of q.. The conduction rod is wrapped in an electrically non-conducting cladding material of radius ro and thermal conductivity ke and convection cooling is provided by an adjoining fluid. For steady-state conditions, a) Determine an expression for the heat transfer per unit length q', passing through the cladding in terms of 9, and ri. b) Determine an expression for T, the temperature of the cladding at 7; and also for To at ro. c) Calculate these cladding temperatures in °C when r and ro are 3 mm and 5 mm, ġ. = 200 kW/m³, ke = 0.15 W/m/K, T = 20°C and h = 20 W/m²/K. Conducting rod, å, k, Cladding, k d) Calculate the critical radius. To decrease the internal cladding temperature would it be necessary to increase or decrease ro; or should it remain unchanged? Explain. Th 201

Passage of an electric current through a long conducting rod of radius r; and thermal conductivity kr, esults in uniform volumetric heating at a rate of q.. The conduction rod is wrapped in an electrically non-conducting cladding material of radius ro and thermal conductivity ke and convection cooling is provided by an adjoining fluid. For steady-state conditions, a) Determine an expression for the heat transfer per unit length q', passing through the cladding in terms of 9, and ri. b) Determine an expression for T, the temperature of the cladding at 7; and also for To at ro. c) Calculate these cladding temperatures in °C when r and ro are 3 mm and 5 mm, ġ. = 200 kW/m³, ke = 0.15 W/m/K, T = 20°C and h = 20 W/m²/K. Conducting rod, å, k, Cladding, k d) Calculate the critical radius. To decrease the internal cladding temperature would it be necessary to increase or decrease ro; or should it remain unchanged? Explain. Th 201

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.23P

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Q1 Passage of an electric current through a long conducting rod of radius r; and thermal conductivity k, results in uniform volumetric heating at a rate of ġ. The conduct- ing rod is wrapped in an electrically nonconducting cladding material of outer radius r, and thermal conduc- tivity k, and convection cooling is provided by an adjoining fluid. Conducting rod, ġ, k, 11 To Čladding, ke For steady-state conditions, write appropriate forms of the heat equations for the rod and cladding. Express ap- propriate boundary conditions for the solution of these equations.
Drive an expression for heat transfer and temperature distribution for steady state one dimensional heat conduction in a plan wall. The temperature is maintained at a temperature Ti at x=0, while the other face X-L is maintained at temperature T2, the thickness of the wall may be taken as L and the energy equation is given by: d²T/dx² = 0. : Sketch a simple diagram for the temperature distribution in plane wall for a steady state one dimensional heat conduction, with heat generation. The surface temperature of the walls Ti and T2, for the cases Ti>T2, T1-T2, and T2>T1. The thickness of the wall may be taken as 2L
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