3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x, t) if the bar is made of cast iron. Material a (cm?/s) Silver 1.71 Copper Aluminum 1.14 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materials

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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please solve question 3.

3.
A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends
of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an
expression for the temperature u(x,t) if the bar is made of cast iron.
Material
a² (cm?/s)
Silver
1.71
1.14
Сopper
Aluminum
0.86
Cast iron
0.12
Granite
0.011
Brick
0.0038
Water
0.00144
Table 1: Thermal Diffusivity Constants for Common Materials
Transcribed Image Text:3. A metallic rod 20 cm long is heated to a uniform temperature of 100° C. At t = 0 the ends of the bar are plunged into an ice bath at 0° C and thereafter maintained at this temperature. Find an expression for the temperature u(x,t) if the bar is made of cast iron. Material a² (cm?/s) Silver 1.71 1.14 Сopper Aluminum 0.86 Cast iron 0.12 Granite 0.011 Brick 0.0038 Water 0.00144 Table 1: Thermal Diffusivity Constants for Common Materials
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