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Problem 3 • Compute the coefficient matrix and the right-hand side of the n-parameter Ritz approximation of the equation d du (1+x)· = 0 for 0 < x < 1 dx dx u (0) = 0, u(1) = 1 Use algebraic polynomials for the approximation functions. Specialize your result for n = 2 and compute the Ritz coefficients. Problem 4 • A steel rod of diameter d = 2 cm, length L = 25 cm, and thermal conductivity k =50 W/(m C) is exposed to ambient air T∞ = 20C with a heat-transfer coefficient ẞ= 64 W/(m2 C). Given that the left end of the rod is maintained at a temperature of T₁ = 120C and the other end is exposed to the ambient temperature, determine the temperature distribution in the rod using a two-parameter Ritz approximation with polynomial approximation functions. The equation governing the problem is given by: d20 dx2 +c=0 for 0 < x < 25 cm • Where = T - T∞, T is temperature and C= ВР Ak BπD 48 D²k kD • == 256 m² P being the perimeter and A the cross-sectional area of the rod. The boundary conditions are: de 0(0)=T(0) - T∞ = 100°C, k- + 30 dx ») | = 0 x=L

Problem 3 • Compute the coefficient matrix and the right-hand side of the n-parameter Ritz approximation of the equation d du (1+x)· = 0 for 0 < x < 1 dx dx u (0) = 0, u(1) = 1 Use algebraic polynomials for the approximation functions. Specialize your result for n = 2 and compute the Ritz coefficients. Problem 4 • A steel rod of diameter d = 2 cm, length L = 25 cm, and thermal conductivity k =50 W/(m C) is exposed to ambient air T∞ = 20C with a heat-transfer coefficient ẞ= 64 W/(m2 C). Given that the left end of the rod is maintained at a temperature of T₁ = 120C and the other end is exposed to the ambient temperature, determine the temperature distribution in the rod using a two-parameter Ritz approximation with polynomial approximation functions. The equation governing the problem is given by: d20 dx2 +c=0 for 0 < x < 25 cm • Where = T - T∞, T is temperature and C= ВР Ak BπD 48 D²k kD • == 256 m² P being the perimeter and A the cross-sectional area of the rod. The boundary conditions are: de 0(0)=T(0) - T∞ = 100°C, k- + 30 dx ») | = 0 x=L

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.7P
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Problem 3 • Compute the coefficient matrix and the right-hand side of the n-parameter Ritz approximation of the equation d du (1+x)· = 0 for 0 < x < 1 dx dx u (0) = 0, u(1) = 1 Use algebraic polynomials for the approximation functions. Specialize your result for n = 2 and compute the Ritz coefficients.
Transcribed Image Text:Problem 3 • Compute the coefficient matrix and the right-hand side of the n-parameter Ritz approximation of the equation d du (1+x)· = 0 for 0 < x < 1 dx dx u (0) = 0, u(1) = 1 Use algebraic polynomials for the approximation functions. Specialize your result for n = 2 and compute the Ritz coefficients.
Problem 4 • A steel rod of diameter d = 2 cm, length L = 25 cm, and thermal conductivity k =50 W/(m C) is exposed to ambient air T∞ = 20C with a heat-transfer coefficient ẞ= 64 W/(m2 C). Given that the left end of the rod is maintained at a temperature of T₁ = 120C and the other end is exposed to the ambient temperature, determine the temperature distribution in the rod using a two-parameter Ritz approximation with polynomial approximation functions. The equation governing the problem is given by: d20 dx2 +c=0 for 0 < x < 25 cm • Where = T - T∞, T is temperature and C= ВР Ak BπD 48 D²k kD • == 256 m² P being the perimeter and A the cross-sectional area of the rod. The boundary conditions are: de 0(0)=T(0) - T∞ = 100°C, k- + 30 dx ») | = 0 x=L
Transcribed Image Text:Problem 4 • A steel rod of diameter d = 2 cm, length L = 25 cm, and thermal conductivity k =50 W/(m C) is exposed to ambient air T∞ = 20C with a heat-transfer coefficient ẞ= 64 W/(m2 C). Given that the left end of the rod is maintained at a temperature of T₁ = 120C and the other end is exposed to the ambient temperature, determine the temperature distribution in the rod using a two-parameter Ritz approximation with polynomial approximation functions. The equation governing the problem is given by: d20 dx2 +c=0 for 0 < x < 25 cm • Where = T - T∞, T is temperature and C= ВР Ak BπD 48 D²k kD • == 256 m² P being the perimeter and A the cross-sectional area of the rod. The boundary conditions are: de 0(0)=T(0) - T∞ = 100°C, k- + 30 dx ») | = 0 x=L
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