• Middle East Technical University

• ME 311

ME 311 – Heat Transfer Fall 2013 Homework 4 1) Consider the one-dimensional wall shown in the sketch which is initially at a uniform temperature Ti and is suddenly subjected to the convection boundary condition with a fluid at T∞. For a particular wall, case 1, the temperature at x=L1 after t1=100s is T1(L1,t1) = 340˚C. Another wall, case 2 has different thickness and thermal conditions as shown below. L α k Ti T∞ h Case (m) (m 2 /s) (W/m∙K) (˚C) (˚C) (W/m2 ∙K) 1 0.15 14x10-6 30 250 350 150 2 0.40 27x10-6 24 125 18 45 How long will it take for the second wall to reach 28.7˚C at the position x=L2? Use as the basis for analysis, the dimensionless functional dependence for the transient temperature distribution expressed in Equation 5.38. SOLUTION: Assumptions: - One dimensional conduction - Constant properties The dimensionless functional dependence for the one-dimensional, transient temperature distribution, Equation 5.38, is: where x* = x/L Bi = hL/k Fo = αt/L2 If the parameters x*, Bi, and θ* are the same for both walls, then Fo must be the same. Evaluate these parameters: Wall, T(x,0)= Ti , k, α Insulation T∞, h This study source was downloaded by 100000899606070 from CourseH