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# Set up the mathematical formulation of the following heat conduction problems Formulation includes the simplified differential heat equation along with boundary and initial conditions Do not solve

Set up the mathematical formulation of the following heat conduction problems. Formulation includes the simplified differential heat equation along with boundary and initial conditions. Do not solve the problems.

a. A slab in 0 ≤×≤ L is initially at a temperature F(x). For times t > 0, the boundary at x = 0 is kept insulated, and the boundary at x = L dissipates heat by convection into a medium at zero temperature. b. A semi-infinite region 0 ≤ × < ∞ is initially at a temperature F(x). For times t > 0, heat is generated in the medium at a constant, uniform rate of g0 (W/m3), while the boundary at x = 0 is kept at zero temperature.

c. A hollow cylinder a ≤ r ≤ b is initially at a temperature F(r). For times t > 0, heat is generated within the medium at a rate of g(r), (W/m3), while both the inner boundary at r = a and outer boundary r = b dissipate heat by convection into mediums at fluid temperature T∞

d. A solid sphere 0 ≤ r ≤ b is initially at temperature F(r). For times t > 0, heat is generated in the medium at a rate of g(r) (W/m3), while the boundary at r = b is kept at a uniform temperature T0.

Aug 06 2020 View more View Less

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