A solid cylinder of radius R and length L is made from material with thermal conductivity 2. Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time). (a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature distribution in the cylinder, given that the surface temperature is Ts. (b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat generation in the animal is 10-3 W/cm³, find the skin temperature (Ts) for the mouse. The external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along the axis of the mouse, as in part a.)

A solid cylinder of radius R and length L is made from material with thermal conductivity 2. Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time). (a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature distribution in the cylinder, given that the surface temperature is Ts. (b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat generation in the animal is 10-3 W/cm³, find the skin temperature (Ts) for the mouse. The external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along the axis of the mouse, as in part a.)

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.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.10P: 5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder...

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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

A solid cylinder of radius R and length L is made from material with thermal conductivity 2.
Heat is generated inside the cylinder at a rate S (energy per unit volume per unit time).
(a) Neglecting conduction along the axis of the cylinder, find the steady-state temperature
distribution in the cylinder, given that the surface temperature is Ts.
(b) Consider a crude approximation of a mouse modeled as a cylinder of radius 1 cm and
length 5 cm. If the ambient air temperature is 10°C and the internal rate of heat
generation in the animal is 10-³ W/cm³, find the skin temperature (Ts) for the mouse. The
external heat-transfer coefficient is h = 0.2 W/m².K. (You can neglect conduction along
the axis of the mouse, as in part a.)

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Step 1: Consider the general heat conduction equation in cylindrical coordinates.

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