# Study of Laminar Heat Transfer in a Cone

## Document Type

Thesis - Open Access

1972

## Degree Name

Master of Science (MS)

## Department / School

Mechanical Engineering

## Abstract

When a fluid flows through a conduit of different temperature from itself, a heat exchange occurs between them. In studying the heat transfer of the fluid in the conduit we can obtain information about the rate of heat absorption and losses, the temperature distributions, etc. This information is important in design work and to aid in the correct selection of construction and insulation materials. Sometimes the conduit or a section of the conduit is conical, as for example the diffuser in hydro-turbo machines and air compressors, the nozzles of steam or gas turbines, and various heating or exhaust ducts. Usually in these conical sections, the temperatures are more critical, and the cooling and insulation problem is much more difficult, but, unlike the case of straight pipes or tubes, the heat transfer problem in these kind of sections has been studied less extensively. For the case of pipe flow various analytical and experimental methods exist to find the rate of heat transfer. For entrance region heat transfer in nozzle flow, analytical solutions are scarce because of the difficulty in solving the governing equation. In 1962, Cobble published his work of heat transfer of flow in a cone, based on the assumptions that the angle of the cone is small, the fluid properties are constant, the surf ace temperature is uniform at Tw, the flow is laminar, and heat transfer is due to conduction alone; also a slug velocity profile is assumed. In 1969, Lumsdaine solved the problem under the same assumptions except that the cone is no longer limited to small angles. The present study aims to analyze both works, make comparisons by computer calculation and check the results wi.th specially designed experiments. The objectives of this thesis are: 1. To compare and analyze some existing theoretical publications on heat transfer in nozzles and diffusers. 2. To provide numerical results in the form of graphs for engineering application. 3. To set quantitative limitations for the analytical solutions as a result of these numerical computations. 4. To compare the nozzle flow analysis with experimental results in order to test the validity of the assumptions made in the analysis.

## Library of Congress Subject Headings

Heat -- Transmission
Laminar flow

application/pdf

58

## Publisher

South Dakota State University

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