Question

Q. 1 1. A thin bar of length \( \pi \) units is placed in boiling water (temperature \( 100^{\circ} \mathrm{C} \) i.e. \( f(x)=100) \). After reaching \( 100^{\circ} \mathrm{C} \) throughout, the bar is moved from the boiling water. With the lateral sides kept insulated, suddenly at \( \mathrm{t}=0 \), the ends are immersed in a medium with constant freezing temperature \( 0^{\circ} \mathrm{C} \). Taking \( C=a=1 \) find the temperature \( u(x, t) \) for \( t>0 \).

          Q. 1
1. A thin bar of length \( \pi \) units is placed in boiling water (temperature \( 100^{\circ} \mathrm{C} \) i.e. \( f(x)=100) \). After reaching \( 100^{\circ} \mathrm{C} \) throughout, the bar is moved from the boiling water. With the lateral sides kept insulated, suddenly at \( \mathrm{t}=0 \), the ends are immersed in a medium with constant freezing temperature \( 0^{\circ} \mathrm{C} \). Taking \( C=a=1 \) find the temperature \( u(x, t) \) for \( t>0 \).

Q. 1
1. A thin bar of length π units is placed in boiling water (temperature 100^∘C i.e. f(x)=100). After reaching 100^∘C throughout, the bar is moved from the boiling water. With the lateral sides kept insulated, suddenly at t=0, the ends are immersed in a medium with constant freezing temperature 0^∘C. Taking C=a=1 find the temperature u(x, t) for t>0.

Added by Elaine P.

Advanced Engineering Mathematics

Erwin Kreyszig 9th Edition

Chapter 12

Instant Answer

Solved by Expert Sachin Rao

Step 1

We are given a heat conduction problem where a bar of length \( \pi \) units, initially at \( 100^{\circ} \mathrm{C} \), has its ends suddenly exposed to \( 0^{\circ} \mathrm{C} \) while the sides are insulated. We need to find the temperature distribution \( u(x, Show more…

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Q. 1 1. A thin bar of length \( \pi \) units is placed in boiling water (temperature \( 100^{\circ} \mathrm{C} \) i.e. \( f(x)=100) \). After reaching \( 100^{\circ} \mathrm{C} \) throughout, the bar is moved from the boiling water. With the lateral sides kept insulated, suddenly at \( \mathrm{t}=0 \), the ends are immersed in a medium with constant freezing temperature \( 0^{\circ} \mathrm{C} \). Taking \( C=a=1 \) find the temperature \( u(x, t) \) for \( t>0 \).