Analytical Heat Transfer by Je-Chin Han

By Je-Chin Han

Developed from the author’s 30 years of training a graduate-level intermediate warmth move direction, Analytical warmth Transfer explains the way to examine and clear up conduction, convection, and radiation warmth move difficulties. compatible for entry-level graduate scholars, the ebook fills the space among uncomplicated warmth move undergraduate classes and complex warmth move graduate courses.

The writer locations emphasis on modeling and fixing engineering warmth move difficulties analytically, instead of easily utilizing the equations and correlations for engineering challenge calculations. He describes many famous analytical tools and their recommendations, resembling Bessel capabilities, separation of variables, similarity technique, imperative strategy, and matrix inversion approach. He additionally provides step by step mathematical formulation derivations, analytical answer systems, and diverse demonstration examples of warmth move applications.

By supplying a powerful analytical heritage, the textual content permits scholars to take on advanced engineering warmth move difficulties encountered in perform. This analytical wisdom additionally is helping them to learn and comprehend warmth transfer-related study papers.

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Example text

The readers may note that zero and negative constants do not satisfy the BCs. 5) Then we have d2 X/dx2 + λ2 X = 0 ⇒ X = X(x), the equation for two homogeneous BCs, d2 Y/dy2 − λ2 Y = 0 ⇒ Y = Y(y), the equation for one homogeneous BC, X(x) = C1 cos λx + C2 sin λx, the solution for equation with two homogeneous BCs, Y(y) = C3 e−λy + C4 eλy or (Y(y) = C3 sinh λy + C4 cosh λy), the solution for equation with one homogeneous BC. Solve C1 and C2 for the x-direction equation at x = 0, T = 0, ⇒ X = 0, then C1 = 0, at x = a, T = 0, ⇒ X = 0, then C2 sin λa = 0 ⇒ λn a = nπ, n = 0, 1, 2, 3, .

The periphery at r = R is maintained at a uniform temperature TR by a heat source. a. Derive the steady-state heat conduction equation of disk. b. Determine the disk temperature distributions with the associated boundary conditions. Sketch the disk temperature profile T(r). c. If during the air cooling, the disk has also emitted a net uniform radiation flux qrad to the surrounding environment, derive the steady-state heat conduction equation of the disk and determine the disk temperature distributions.

The convection heat transfer coefficient h can be taken constant over the disk. The periphery at r = R is maintained at a uniform temperature TR . a. Derive the steady-state heat conduction equation of the disk. b. Propose a solution method and the associated boundary conditions that can be used to determine the disk temperature distributions. Sketch the disk temperature profile T(r). Do you think the disk temperature is hotter at the center or the periphery? Why? c. If during the air heating, the disk has also emitted a net uniform radiation flux qrad to the surrounding environment, derive the steady-state heat condition equation of the disk and propose a solution method to determine the disk temperature distributions.

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