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Write the heat equation for each of the following cases: a. A wall, steady state, stationary, one-dimensional, incompressible and no energy generation. b. A wall, transient, stationary, one-dimensional, incompressible, constant k with energy generation. c. A cylinder, steady state, stationary, two-dimensional (radial and axial), constant k, incompressible, with no energy generation. d. A wire moving through a furnace with constant velocity, steady state, one-dimensional (axial), incompressible, constant k and no energy generation. e. A sphere, transient, stationary, one-dimensional (radial), incompressible, constant k with energy generation.

1 Answer

+16 votes
by (100 points)
Explanation:a) the steady-state, 1-D incompressible and no energy generation equation can be expressed as follows:b) For a transient, 1-D, constant with energy generationsuppose T = f(x)Then; the equation can be expressed as:where; = heat generated per unit volume = Thermal diffusivity c) The heat equation for a cylinder steady-state with 2-D constant and no compressible energy generation is:where;The radial directional term = and the axial directional term is d) The heat equation for a wire going through a furnace is:since;the steady-state is zero, Then:'e) The heat equation for a sphere that is transient, 1-D, and incompressible with energy generation is:

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