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Shackleford
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I'm taking an engineering heat transfer course as an elective.
1. Homework Statement
Copper tubing is joined to a solar collector plate of thickness t, and the working fluid maintains the temperature of the plate above the tubes at To. There is a uniform net radiation heat flux q”rad to the top surface of the plate, while the bottom surface is well insulated. The top surface is also exposed to a fluid at T∞ that provides for a uniform convection coefficient h.
(a) Derive the differential equation that governs the temperature distribution T(x) in the plate.
(b) Obtain a solution to the differential equation for appropriate boundary conditions.
Conduction, convection, and radiation
I want to first analyze a differential control volume.
Ac = yt
As = ydx
qcond + qrad = qconv + qcond, x + dr
-kAcdT/dx + εσ[T4(x) - T4∞] ydx = h[T(x) - T∞] ydx + -kAcdT/dx -kd/dx(AcdT/dx)
Of course, t is constant and we're assuming that temperature does not vary with the y-coordinate. However, I wanted to start with an actual volume and see where y factors out. Am I on the right track?
1. Homework Statement
Copper tubing is joined to a solar collector plate of thickness t, and the working fluid maintains the temperature of the plate above the tubes at To. There is a uniform net radiation heat flux q”rad to the top surface of the plate, while the bottom surface is well insulated. The top surface is also exposed to a fluid at T∞ that provides for a uniform convection coefficient h.
(a) Derive the differential equation that governs the temperature distribution T(x) in the plate.
(b) Obtain a solution to the differential equation for appropriate boundary conditions.
Homework Equations
Conduction, convection, and radiation
The Attempt at a Solution
I want to first analyze a differential control volume.
Ac = yt
As = ydx
qcond + qrad = qconv + qcond, x + dr
-kAcdT/dx + εσ[T4(x) - T4∞] ydx = h[T(x) - T∞] ydx + -kAcdT/dx -kd/dx(AcdT/dx)
Of course, t is constant and we're assuming that temperature does not vary with the y-coordinate. However, I wanted to start with an actual volume and see where y factors out. Am I on the right track?
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