A planar material can be modeled as 1-dimensional with thickness L = 2m. On one boundary...
A planar material can be modeled as 1-dimensional with thickness L = 2m. On one boundary (x=0), the surface is held at a fixed temperature Ts = 20°C. the other boundary is perfectly insulated. There is a constant thermal conductivity k = 40 W/mK and the material is being heated internally. The system is at steady state.
a) write an expression for each of the two boundary conditions
b) If the volumetric heat generation is equal to q.= 10 W/m3.
i) Evaluate the heat flux in the positive x direction at the constant temperature boundary (x=0).
ii) Evaluate the temperature on the perfectly insulated boundary.
iii) Sketch the temperature distribution within the material (i.e roughly plot T(x) noting the position of the boundaries)
c) If the heat generation varies with location following the expression q.=αx2, where α = 6 W/m5. Evaluate the heat flux in the positive x direction at the constant temperature boundary (x=0).
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A planar material can be modeled as 1-dimensional with thickness
L = 2m. On one boundary...
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3/5 25 pts.J A slab of thickness L, made of material with constant thermal conductivity k, is undergoing a 1-D, steady heat transfer. Its boundary surface at x 0 is insulated while the boundary surface at x= 1 is kept at constant temperature T= oc. Heat energy is generated within the slab at a rate of 2. qx)o cos(rx/2L) is the energy generation rate per unit volume (Wm) at x= 0. where qo a. Develop an expression for the steady-state...
ent material has the thermal conductivity k and thickness L. The temperature the material is of the form: distribution along the x-direction, T(x) in + Bx2 + C, where A, a, B, and C are constants...
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Problem 2: Consider a large plane slab of semi-thickness L = 0.3 m, thermal conductivity k...
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A plane wall of thickness L has constant thermal conductivity, k, uniform generation throughout, q, and...
A plane wall of thickness L has constant thermal conductivity, k, uniform generation throughout, q, and is insulated on one side, at x-0. Only the outer surface temperature (Ts) is known. (a) Derive an equation describing the steady-state wall temperature at any point (x), when given the outer wall surface temperature, Tsi. (b) If L-15 cm, k: 3.4 W/m"K, q-10 kW/m3, and Ts1-300 K, what is the steady-state temperature at x - 6 cm (in K)? S1
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Problem 2 Heat Diffusion: A tall wall has a thickness of L = 400 mm and a thermal conductivity of 0.25 W/m-K. One side of the wall is maintained at Ts 80°C. The temperature in the wall varies as a function of position due to internal heat generation. The temperature variation is given as, goL2 where go 10 W/m3. Use this expression to answer the following questions. Assume that the wall temperature is at steady state. A) Find the temperature...
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