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A model has been developed for predicting turbulent heat transfer coefficients and associated temperature profiles in rough pipes from a knowledge of the fluid mechanics. The proposed method employs the Lyon heat transfer equation together with the velocity profile equations of Rouse and von Karman. Nusselt numbers were calculated by the proposed method for the following range of variables: f = fs to 0.020 Re = 4 x 10³ to 10⁷ Pr = 0.001 to 1,000 Temperature profiles were calculated for all combinations of the above extreme conditions, as well as for Pr = 1.0. The validity of the proposed model was tested by comparison of the predicted results with the experimental data of Nunner, Smith and Epstein and Dipprey. A similar test was made of Nunner's theoretical equation. It is concluded that, except for fluids with very low Prandtl numbers, e.g. liquid metals, the proposed model gives no better prediction of Nusselt number than Nunner's equation, which is less cumbersome to apply. In the existing form, the proposed model is not adequate. Certain combinations of the independent variables give rise to a discontinuity in the predicted value of Nusselt number. This is inconceivable in the physically real situation. Beyond the discontinuity appears a predicted region of zero net flow in the pipe. Two limiting assumptions can be made regarding the method of heat transport through this layer - viz. by molecular conduction only, or by an infinite conductivity eddy mechanism. Both assumptions have been made, and values of Nu calculated for each, whenever the situation arose. The agreement between the predicted and the experimental temperature profiles is in general good. However, not enough experimental data are available to satisfactorily define the effect of Re and f, and to substantiate the calculated results. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

The problem solved in this thesis is one of transient linear heat conduction in a two layer, three-dimensional slab subjected to an arbitrary heat flux on one surface, where each layer is thermally orthotropic. The sides and bottom of the slab are either insulated (Bi = 0) or held at a constant temperature (Bi = infinity). The Biot number of the top surface varies from zero to infinity. The solution is developed by decomposing the problem into a number of simpler problems, each of which is solved using eigenfunction expansions. In the vertical direction, the eigenvalue problem is solved using the Krawczyk algorithm, and an orthogonality relationship is found by Vodicka's method.

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This study analyzes the thermo-mechanical response of a composite cylinder made up of two layers of linear isotropic viscoelastic materials that belong to the class of non-Thermorheologically Simple Material. The effect of time-varying temperature field due to unsteady heat conduction phenomenon is analyzed on the short term and long term material response in terms of stress, strain and displacement fields. The material properties of the two layers of the composite cylinder at any given location and time are assumed to depend on the temperature at that location at that given instant of time. Sequentially coupled analyses of heat conduction and deformation of viscoelastic composite cylinder is carried out to obtain the overall response. The stress and strain field developed in the composite cylinder is evaluated as the discontinuity in hoop stress and radial strain at the interface of the two layers caused due to mismatch in material properties may lead to delamination if it exceeds critical value. Analytical solution for the stress, strain and displacement fields of the viscoelastic composite cylinder is developed from the corresponding solution of linear elasticity problem by using the Correspondence Principle. The analytical solution for determining the temperature dependent stress, strain and displacement fields is further developed by incorporating the temperature dependence on the material properties and modeling the material as non-TSM. To analyze more complex geometry with general loading and boundary conditions, Finite Element(FE) analysis of the composite cylinder is performed and the results of analytical and FE method are found to be in good agreement. Parametric studies are carried out to understand the effect of change in material parameters namely the Prony coefficients in the transient creep compliance, characteristic of creep time in transient creep compliance and the instantaneous elastic compliance, on the overall response of the composite cylinder. The effect of different temperature dependent functions of the material properties, namely linear temperature variation and quadratic polynomial variation on the overall material response is also analyzed. It is observed that the effect of change in elastic properties significantly increases the jump in hoop stress and radial strain. It is also observed that when the materials are highly dependent on temperature the jump in radial strain and hoop stress increases significantly. The radial displacement also increases by a significant amount in both the cases.

This study analyzes the thermo-mechanical response of a composite cylinder made up of two layers of linear isotropic viscoelastic materials that belong to the class of non-Thermorheologically Simple Material. The effect of time-varying temperature field due to unsteady heat conduction phenomenon is analyzed on the short term and long term material response in terms of stress, strain and displacement fields. The material properties of the two layers of the composite cylinder at any given location and time are assumed to depend on the temperature at that location at that given instant of time. Sequentially coupled analyses of heat conduction and deformation of viscoelastic composite cylinder is carried out to obtain the overall response. The stress and strain field developed in the composite cylinder is evaluated as the discontinuity in hoop stress and radial strain at the interface of the two layers caused due to mismatch in material properties may lead to delamination if it exceeds critical value. Analytical solution for the stress, strain and displacement fields of the viscoelastic composite cylinder is developed from the corresponding solution of linear elasticity problem by using the Correspondence Principle. The analytical solution for determining the temperature dependent stress, strain and displacement fields is further developed by incorporating the temperature dependence on the material properties and modeling the material as non-TSM. To analyze more complex geometry with general loading and boundary conditions, Finite Element(FE) analysis of the composite cylinder is performed and the results of analytical and FE method are found to be in good agreement. Parametric studies are carried out to understand the effect of change in material parameters namely the Prony coefficients in the transient creep compliance, characteristic of creep time in transient creep compliance and the instantaneous elastic compliance, on the overall response of the composite cylinder. The effect of different temperature dependent functions of the material properties, namely linear temperature variation and quadratic polynomial variation on the overall material response is also analyzed. It is observed that the effect of change in elastic properties significantly increases the jump in hoop stress and radial strain. It is also observed that when the materials are highly dependent on temperature the jump in radial strain and hoop stress increases significantly. The radial displacement also increases by a significant amount in both the cases.

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No description available.

No description available.