Product solutions for unsteady heat conduction in solids (a) In Example 12.1-2 the unsteady state heat conduction
Question:
Product solutions for unsteady heat conduction in solids
(a) In Example 12.1-2 the unsteady state heat conduction equation is solved for a slab of thickness 2b. Show that the solution to Eq. 12.1-2 for the analogous problem for a rectangular block of finite dimensions 2a, 2b, and 2c may be written as the product of the solutions for three slabs of corresponding dimensions in which Θ(y/b, at/b2) is the right side of Eq. 12.1-31.
(b) Prove a similar result for cylinders of finite length; then rework Problem 12A.4 without the assumption that the cylinder is infinitely long.
T - T(x, y, z, t) T - To at at a'
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Product solutions for unsteady heat conduction in solids a We begin by defining a dimensionless temp...View the full answer
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Conduction heat transfer is the transfer of heat through matter (i.e., solids, liquids, or gases) without bulk motion of the matter. In another ward, conduction is the transfer of energy from the more energetic to less energetic particles of a substance due to interaction between the particles. Conduction heat transfer in gases and liquids is due to the collisions and diffusion of the molecules during their random motion.
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