3.112 A metal rod of length 21, diameter D. and thermalconductivity is inserted into a perfectly insulatingwall, exposing one-half of its length to an air streamthat is of temperature and provides a convection co-efficient h at the surface of the rod. An electro-magnetic field induces volumetric energy generation ata uniform rate q within the embedded portion of the rod.T=20°Ch=100 W/m²KRod, D. &TL 50 mmD-5 mm25 W/m-Kq=1 x 100 W/m²(a) Derive an expression for the steady-state tempera-ture 7, at the base of the exposed half of the rod.The exposed region may be approximated as avery long fin.(b) Derive an expression for the steady-state tempera-ture T at the end of the embedded half of the rod.(c) Using numerical values provided in the schematicplot the temperature distribution in the rod and de-scribe key features of the distribution. Does the rodbehave as a very long fin?

Given : To find : Derive an expression

3.112 A metal rod of length 21, diameter D. and thermal conductivity is inserted into a perfectly insulating wall, exposing one-half of its length to an air stream that is of temperature T, and provides a convection co- efficient h at the surface of the rod. An electro- magnetic field induces volumetric energy generation at a uniform rate q within the embedded portion of the rod. T = 20°C h=100 W/m²K T Rod, D, k Lv 50 mm D=5 mm k=25 W/m-K 4-1 x 10⁰ W/m² (a) Derive an expression for the steady-state tempera- ture 7, at the base of the exposed half of the rod. The exposed region may be approximated as a very long fin. (b) Derive an expression for the steady-state tempera- ture 7, at the end of the embedded half of the rod. (c) Using numerical values provided in the schematic plot the temperature distribution in the rod and de- scribe key features of the distribution. Does the rod behave as a very long fin?

3.112 A metal rod of length 21, diameter D. and thermal conductivity is inserted into a perfectly insulating wall, exposing one-half of its length to an air stream that is of temperature T, and provides a convection co- efficient h at the surface of the rod. An electro- magnetic field induces volumetric energy generation at a uniform rate q within the embedded portion of the rod. T = 20°C h=100 W/m²K T Rod, D, k Lv 50 mm D=5 mm k=25 W/m-K 4-1 x 10⁰ W/m² (a) Derive an expression for the steady-state tempera- ture 7, at the base of the exposed half of the rod. The exposed region may be approximated as a very long fin. (b) Derive an expression for the steady-state tempera- ture 7, at the end of the embedded half of the rod. (c) Using numerical values provided in the schematic plot the temperature distribution in the rod and de- scribe key features of the distribution. Does the rod behave as a very long fin?

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.

Chapter1: Basic Modes Of Heat Transfer

Section: Chapter Questions

Problem 1.6P: A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in...

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A square silicon chip 7mm7mm in size and 0.5-mm thick is mounted on a plastic substrate as shown in the sketch below. The top surface of the chip is cooled by a synthetic liquid flowing over it. Electronic circuits on the bottom of the chip generate heat at a rate of 5 W that must be transferred through the chip. Estimate the steady-state temperature difference between the front and back surfaces of the chip. The thermal conductivity of silicon is 150 W/m K. Problem 1.6
Consider a flat plate or a plane wall with a thickness L and a long cylinder of radius r0. Both of these are made of materials such that they can be treated as lumped capacitances (Bi0.1). Show that in each case, the characteristic length lc, defined lc=(V/As), can be approximated as (L/2) and (ro/2), respectively.
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