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3013-11 Hw-6 Solution

3013-11 Hw-6 Solution - conduction equation using...

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1 of 1 CHE 3013 Rate Operations I Fall 2011 Homework 6 Due: Monday, October 3, 2011 3 Problems, 12 points total 1. (3 points) A thermocouple is embedded in a thick slab of solid 15 mm from the surface. The uniform initial temperature of the solid is 30 ° C and the surface is suddenly brought to 0 ° C by exposure to ice water. What is the temperature measured by the thermocouple after 2 minutes? Physical properties: k = 1.41 W/m K ρ = 2200 kg/m 3 C p = 700 J/kg K 2. (3 points) Consider the system in Problem 1. What is the measured temperature after 2 minutes if the surface is suddenly brought to 100 ° C by exposure to boiling water? 3. (6 points) An infinite plate 0.050 m thick has a thermal conductivity of 75 W/m K. Heat is heat is generated uniformly in the plate at a rate of 1.5x10 6 W/m 3 . Integrate the steady-state heat

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Unformatted text preview: conduction equation using finite-difference methods and plot the temperature profile ( ° C, m) through the plate for the following boundary conditions: (a) ( ) ∞ = − = ∂ ∂ − T T h x T k x with T ∞ = 50 ° C and h = 2,000 W/m 2 ⋅ K T = 30 ° C at x = 0.050 m (b) ( ) ∞ = − = ∂ ∂ − T T h x T k x with T = 50 ° C and h = 2,000 W/m 2 ⋅ K ( ) ∞ = − = ∂ ∂ − T T h x T k x 050 . with T = 30 ° C and h = 1,000 W/m 2 ⋅ K Use a spatial increment of Δ x = 0.005 m. Note: You can check your solutions by setting h to a large value, i.e. 10 9 W/m 2 ⋅ K. This is equivalent to specifying a zero resistance for convective heat transfer at the surface, and T s → T . You have the analytical solution for these boundary conditions....
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