FIND THE TEMPERATURE OF THE ROD u(x,t) at any point and at any time t. Obtain the expression for the coefficient by integrating the resulting half range expansion and include it in the final answer
Find The Temperature Of The Rod U X T At Any Point And At Any Time T Obtain The Expression For The Coefficient By Inte 1 (17.93 KiB) Viewed 22 times
Find The Temperature Of The Rod U X T At Any Point And At Any Time T Obtain The Expression For The Coefficient By Inte 2 (17.93 KiB) Viewed 22 times
Find The Temperature Of The Rod U X T At Any Point And At Any Time T Obtain The Expression For The Coefficient By Inte 3 (37.18 KiB) Viewed 22 times
) A slender rod of length L has its curved surface and left end perfectly insulated. The right-hand end is at 75 °C. Initially the temperature of the rod is 100 °C. Find the temperature of the rod u(x,t) at any point and at any time t. Obtain the expression for the coefficient by integrating the resulting half-range expansion and include it in the final answer.
=C- This is a problem of one dimension heat flow. Let u be the temperature of rod at time t and at x distance from left hand end. Thus its partial differential equation will be ди alu at [0 əx2 ( 052SL, t> 0) Әr2 Where c is diffusivity of rod material. Initial Condition: Initial Temperature: u(3,0) = 100 ди Initial end : 0,t ) = 0 : дх Boundary condition: Initial Temperature: u(L, t) = 75
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