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Consider the temperature distribution u(x, t) at time t at each point x of a bar of unit length sub- merged in ice at 0°C, with radiating heat at both ends. a. We assume that the thermal diffusivity and the heat convection coefficient are all equal to 1 and the initial temperature at each point x is given by the function f (x). Write down the initial boundary value problem that describes the temperature distribution u(x, t) in the bar. b. Determine the temperature in the bar at each point x and at time t, by solving the initial problem obtained in part a).

Consider the temperature distribution u(x, t) at time t at each point x of a bar of unit length sub- merged in ice at 0°C, with radiating heat at both ends. a. We assume that the thermal diffusivity and the heat convection coefficient are all equal to 1 and the initial temperature at each point x is given by the function f (x). Write down the initial boundary value problem that describes the temperature distribution u(x, t) in the bar. b. Determine the temperature in the bar at each point x and at time t, by solving the initial problem obtained in part a).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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No computer programs. Please solve the problem analytically. Also, finish the solution fully and not just partially.

Consider the temperature distribution u(x, t) at time t at each point x of a bar of unit length sub- merged in ice at 0°C, with radiating heat at both ends. a. We assume that the thermal diffusivity and the heat convection coefficient are all equal to 1 and the initial temperature at each point x is given by the function f (x). Write down the initial boundary value problem that describes the temperature distribution u(x, t) in the bar. b. Determine the temperature in the bar at each point x and at time t, by solving the initial problem obtained in part a).
Transcribed Image Text:Consider the temperature distribution u(x, t) at time t at each point x of a bar of unit length sub- merged in ice at 0°C, with radiating heat at both ends. a. We assume that the thermal diffusivity and the heat convection coefficient are all equal to 1 and the initial temperature at each point x is given by the function f (x). Write down the initial boundary value problem that describes the temperature distribution u(x, t) in the bar. b. Determine the temperature in the bar at each point x and at time t, by solving the initial problem obtained in part a).
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