In the design of a certain computer application, a heat flow simulation is required. In the simulation, the heat conductor, which is of length 10m, has a perfectly insulated surface. The temperature at both ends of the conductor is kept consistently at zero. The initial temperature at any point of the conductor is uniform at 25°C. The 1-dimensional heat equation is given as follows: for all 0< x 10 and t20 (a) Describe the initial and boundary conditions of the 1-dimension heat equation in the simulation. Hence, deduce the temperature function (x, t) of the conductor, subjected to the conditions in (a).

In the design of a certain computer application, a heat flow simulation is required. In the simulation, the heat conductor, which is of length 10m, has a perfectly insulated surface. The temperature at both ends of the conductor is kept consistently at zero. The initial temperature at any point of the conductor is uniform at 25°C. The 1-dimensional heat equation is given as follows: for all 0< x 10 and t20 (a) Describe the initial and boundary conditions of the 1-dimension heat equation in the simulation. Hence, deduce the temperature function (x, t) of the conductor, subjected to the conditions in (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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5.10 Experiments have been performed on the temperature distribution in a homogeneous long cylinder (0.1 m diameter, thermal conductivity of 0.2 W/m K) with uniform internal heat generation. By dimensional analysis, determine the relation between the steady-state temperature at the center of the cylinder , the diameter, the thermal conductivity, and the rate of heat generation. Take the temperature at the surface as your datum. What is the equation for the center temperature if the difference between center and surface temperature is when the heat generation is ?
2.3 The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of . Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially from a value of at the inner surface to a value of at a distance of 12.5 cm from the interior surface. If the exterior surface is kept at 38°C by forced convection, determine the temperature at the inner surface of the field. Hint: First set up the differential equation for a system in which the heat generation rate varies according to .
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