Question

Find the values of C&D form equation and given boundaries

Qₜ = 0(adiabatic)
Boundary conditions :
x = 0 T = T∘ or θ = θ∘
x = L Qₜ = - kA[dT/dx]ₓ₌ₗ = 0
θ = C eᵐˣ +D e⁻ᵐˣ
C = e⁻ᵐᴸ/(eᵐᴸ+e⁻ᵐᴸ) D= eᵐᴸ/(eᵐᴸ+e⁻ᵐᴸ)

Answer 1

The values of constants C and D for a temperature distribution equation in adiabatic conditions can be found using the given boundary conditions and formulas for the constants.

Step-by-step explanation:

The student's question relates to determining the values of constants C and D for a differential equation describing temperature distribution in a one-dimensional rod with adiabatic boundary conditions.

The given temperature profile equation is θ = C em x + D e-m x. The boundary condition at x = 0 is that the temperature T is equal to T°, and at x = L, the heat flux Qt is zero.

To find the constants C and D, we are provided with the equations C = e-m L/(em L+e-m L) and D= em L/(em L+e-m L). By applying these equations to the given boundary conditions, the values of C and D can be found ensuring that the temperature profile satisfies the adiabatic condition in a steady state. This scenario is commonly encountered in heat transfer problems involving thermal conductivity.