The ends A and B of a rod of length 10cm long have their temperature distribution kept at 20 deg C and 70 deg C. Find the steady state tempe

Question

The ends A and B of a rod of length 10cm long have their temperature distribution kept at 20 deg C and 70 deg C. Find the steady state temperature distribution of the rod. *

1 point

u(x)=5x+20

u(X)=2X+50

u(x)=5x+2

u(X)=2X+5​

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Ximena 1 month 2021-08-13T16:19:49+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-08-13T16:21:02+00:00

    SOLUTION

    GIVEN

    The ends A and B of a rod of length 10cm long have their temperature distribution kept at 20° C and 70° C.

    TO DETERMINE

    The steady state temperature distribution of the rod. 

    • u(x)=5x+20
    • u(X)=2X+50
    • u(x)=5x+2
    • u(X)=2X+5

    EVALUATION

    The equation for heat flow is given by

     \displaystyle \sf{  \frac{ \partial u}{  \partial t}  =  { \alpha }^{2}   \:  \frac{ {\partial}^{2}  u}{  \partial  {x}^{2} }   \:  \: }

    In steady state temperature the above equation reduces to

     \displaystyle \sf{   \frac{ {\partial}^{2}  u}{  \partial  {x}^{2} }  = 0  \:  \: }

    The solution is given by

     \sf{u = ax + b \:  \: } \:  \: ....(1)

    where a and b constants

    Now it is given that

    At x = 0, u = 20 and at x = 10, x = 70

    Using x = 0, u = 20 we get from (1)

     \sf{20 = 0 + b}

     \implies \sf{b = 20 \: }

    Again Using x = 10, u = 70 we get from (1)

     \sf{70 = 10a + b \: }

     \implies  \sf{70 = 10a + 20 \: }

     \implies  \sf{10a  = 50}

     \implies  \sf{a  = 5}

    From Equation (1) we get by putting the value of a and b

     \sf{u = 5x + 20 \: }

    FINAL ANSWER

    In steady state temperature distribution of the rod

     \boxed{ \sf{ \:  \: u (x)= 5x + 20 \: \:  \:  }}

    ━━━━━━━━━━━━━━━━

    LEARN MORE FROM BRAINLY

    Divergence of r / r^3 is

    (a) zero at the origin

    (b) zero everywhere

    (c) zero everywhere except the origin

    (d) nonzero

    https://brainly.in/question/22316220

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