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Please provide very detailed steps Find the temperature u(x, t) in a bar of length T...
please solve 17 for me thanks~~ :) ! temperature f(x) °C, where 5. f(x) = sin 0.1 x 6 f(x) = 4 - 08 |x - 5 7. fix) =x(1...
please solve 17 for me thanks~~ :) !
temperature f(x) °C, where 5. f(x) = sin 0.1 x 6 f(x) = 4 - 08 |x - 5 7. fix) =x(10 - x) 8 Arbitrarytemperatures at ends. If the ends x = 0 and x= Lof the bar in the text are kept at constant 20. CAS PROJECT. Isotherms. Fim solutions (tempe rature s) in the squa with a 2 satisfying the followin tions. Graph isotherms. (a) u80 sin Tx on...
A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x...
A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x and its two ends are held at temperature zero for all time t>O The heat equation is given as: ди au 4 for 0 < x < it and t > 0 at @x? Boundary conditions: u(0,t) = u(1,t)=0, Initial conditions: u(x,0) = 2 sin 3x By using the method of separation of variables, calculate the general temperature u(x,t) for all cases, k =...
A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x...
A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x and its two ends are held at temperature zero for all time t>O The heat equation is given as: ди au 4 for 0 < x < it and t > 0 at @x? Boundary conditions: u(0,t) = u(1,t)=0, Initial conditions: u(x,0) = 2 sin 3x By using the method of separation of variables, calculate the general temperature u(x,t) for all cases, k =...
(a) The heat flux through the faces at the ends of bar is found to be...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
Problem 3. Consider the following problem which governs the evolution of tem- perature in a bar...
Problem 3. Consider the following problem which governs the evolution of tem- perature in a bar of length l: du du 0<x<l, t>0, ot =^22+Yºu), og (0, ) = 0, de 10 , 1) = 0, u(x,0) = f(x) = A + 2 cos(") + 3 cos(477), where A, k and y are fixed positve constants. Recall that Neumann boundary con- ditions correspond to no heat flux through the boundaries (i.e. perfect insulation) and the term yều corresponds to internal...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...
A cylindrical carrot of radius R and length L with an initial temperature of T0 is...
A cylindrical carrot of radius R and length L with an initial temperature of T0 is placed into boiling water (TH). Note that the initial temperature is lower than the boiling water. The radius of the carrot is equal to that of half the length. The boiling water has a surface average heat transfer coefficient of h across the entire surface of the carrot. Use the center of the carrot to represent z = 0 and r = 0. 1....
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional he...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
(a) The temperature distribution u(x, t) of the one- dimensional silver rod is governed by the...
(a) The temperature distribution u(x, t) of the one- dimensional silver rod is governed by the heat equation as follows. du a²u at ar? Given the boundary conditions u(0,t) = t?, u(0.6, t) = 5t, for Osts 0.02s and the initial condition u(x,0) = x(0.6 – x) for 0 SX s 0.6mm, analyze the temperature distribution of the rod with Ax = 0.2mm and At = 0.01s in 4 decimal places. (10 marks)
please solve 17 for me thanks~~ :) !
temperature f(x) °C, where 5. f(x) = sin 0.1 x 6 f(x) = 4 - 08 |x - 5 7. fix) =x(10 - x) 8 Arbitrarytemperatures at ends. If the ends x = 0 and x= Lof the bar in the text are kept at constant 20. CAS PROJECT. Isotherms. Fim solutions (tempe rature s) in the squa with a 2 satisfying the followin tions. Graph isotherms. (a) u80 sin Tx on...
A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x and its two ends are held at temperature zero for all time t>O The heat equation is given as: ди au 4 for 0 < x < it and t > 0 at @x? Boundary conditions: u(0,t) = u(1,t)=0, Initial conditions: u(x,0) = 2 sin 3x By using the method of separation of variables, calculate the general temperature u(x,t) for all cases, k =...
A metal rod of length a cm has initial temperature function f(x) = 2 sin 3x and its two ends are held at temperature zero for all time t>O The heat equation is given as: ди au 4 for 0 < x < it and t > 0 at @x? Boundary conditions: u(0,t) = u(1,t)=0, Initial conditions: u(x,0) = 2 sin 3x By using the method of separation of variables, calculate the general temperature u(x,t) for all cases, k =...
(a) The heat flux through the faces at the ends of bar is found to be proportional to un au/an at the ends. If the bar is perfectly insulated, also at the ends x 0 and x L are adiabatic conditions, Q1 ux(0, t) = 0 0 (2'7)*n prove that the solution of the heat transfer problem above (adiabatic conditions at both ends) gives as, 2 an: nnx u(x, t) Ao t An cos n-1 where Ao and An are...
Problem 3. Consider the following problem which governs the evolution of tem- perature in a bar of length l: du du 0<x<l, t>0, ot =^22+Yºu), og (0, ) = 0, de 10 , 1) = 0, u(x,0) = f(x) = A + 2 cos(") + 3 cos(477), where A, k and y are fixed positve constants. Recall that Neumann boundary con- ditions correspond to no heat flux through the boundaries (i.e. perfect insulation) and the term yều corresponds to internal...
(a) Consider the one-dimensional heat equation for the temperature u(x, t), Ou,02u where c is the diffusivity (i) Show that a solution of the form u(x,t)-F )G(t) satisfies the heat equation, provided that 护F and where p is a real constant (ii) Show that u(x,t) has a solution of the form (,t)A cos(pr)+ Bsin(p)le -P2e2 where A and B are constants (b) Consider heat flow in a metal rod of length L = π. The ends of the rod, at...
Consider a uniform bar of length L having an initial temperature distribution given by f(x), 0 < x < L. Assume that the temperature at the end x=0 is held at 0°C, while the end x=L is thermally insulated. Heat is lost from the lateral surface of the bar into a surrounding medium. The temperature u(x, t) satisfies the following partial differential equation and boundary conditions aluxx – Bu = Ut, 0<x<l, t> 0 u(0,t) = 0, uz (L, t)...
Question 1: The separated solutions of the o fom u(x.t) -X(x)T(t), with the following solutions: ne-dimensional heat equation dtt lu solutions of are - X(x)-Ax +B and T(t) E X(x) = A cos kx + B sin kx and T(t)=Ee-Det The boundary conditions for a metal rod insulated from both sides arex aum = 0 when x =0, and dx (e) Using the boundary conditions for u(x.t) wrie the boundary conditions for XCx), explain for full marks. (b) Find the...
(a) The temperature distribution u(x, t) of the one- dimensional silver rod is governed by the heat equation as follows. du a²u at ar? Given the boundary conditions u(0,t) = t?, u(0.6, t) = 5t, for Osts 0.02s and the initial condition u(x,0) = x(0.6 – x) for 0 SX s 0.6mm, analyze the temperature distribution of the rod with Ax = 0.2mm and At = 0.01s in 4 decimal places. (10 marks)
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