A fluid flows between two parallel plates held at temperature zero. At the inlet, fluidPage 1 of 2temperature is To and initially the fluid is at temperature T1. If V is the speed of thefluid in the x direction, a problem describing the temperature u(x, y, t) is:ng+VƏtди= kx > 0, 0< y < b, t> 0,u(г, 0, t) — 0, и(х, b, t) —D 0,u(0, у, t) — То, и (1, у, 0) — Tі.Make a separation of variables as above. State and solve the eigenvalue problem for YShow thatUn (T, Y, t) = ¢n(x – Vt)ek(z+Vt)2Vsin lnywhere An = u, for n =PDE and boundary conditions at y = 0 and ydifferentiability).1, 2, 3, ... are the eigen values for the Y problem, satisfies theb, without restrictions of on (except

Given:To find:Solve the eigenvalue problem.

A fluid flows between two parallel plates held at temperature zero. At the inlet, fluid temperature is To and initially the fluid is at temperature T₁. If V is the speed of the fluid in the x direction, a problem describing the temperature u(x, y, t) is: du Ət + V = = μ², for n ди J²u მყ2 k- Əx - x > 0, 0 0, u(x, 0, t) = 0, u(x, b, t) = 0, u(0, y, t) = To, u(x, y,0) = T₁. Make a separation of variables as above. State and solve the eigenvalue problem for Y. Show that Page 1 of 2 H²k(x+Vt) un (x, y, t) = n(x – Vt)e¯ where An = : 1, 2, 3,... are the eigen values for the Y problem, satisfies the PDE and boundary conditions at y = 0 and y = b, without restrictions of n (except differentiability). 2V sin ny

A fluid flows between two parallel plates held at temperature zero. At the inlet, fluid temperature is To and initially the fluid is at temperature T₁. If V is the speed of the fluid in the x direction, a problem describing the temperature u(x, y, t) is: du Ət + V = = μ², for n ди J²u მყ2 k- Əx - x > 0, 0 0, u(x, 0, t) = 0, u(x, b, t) = 0, u(0, y, t) = To, u(x, y,0) = T₁. Make a separation of variables as above. State and solve the eigenvalue problem for Y. Show that Page 1 of 2 H²k(x+Vt) un (x, y, t) = n(x – Vt)e¯ where An = : 1, 2, 3,... are the eigen values for the Y problem, satisfies the PDE and boundary conditions at y = 0 and y = b, without restrictions of n (except differentiability). 2V sin ny

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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