Heat Conduction Differential Equation and Its Solutions for Steady-State

Akhrorbek Abdunabiyev¹ , Bobur Mirzo Shakirov² , Xamidova Shohidaxon³

Section:Research Paper, Product Type: Journal-Paper
Vol.11 , Issue.3 , pp.11-16, Sep-2024

Online published on Sep 30, 2024

Copyright © Akhrorbek Abdunabiyev, Bobur Mirzo Shakirov, Xamidova Shohidaxon . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Objective. The study of any physical process is determined by finding the relationship between the quantities characterizing that process. For heat conduction, such a relationship is the heat conduction differential equation. To derive this equation, we consider the following: there are no internal heat sources, the body is homogeneous and isotropic. Methods. We consider the solutions of the differential equation for steady-state. For example, let`s consider heat conduction through a multi-layer flat wall. For this, we need to know the boundary conditions. In many heat exchange devices used in industry, we consider the process of heat transfer by heat conduction through a multi-layer flat wall made of materials with different thermal conductivities. Results. The heat conduction differential equation determines the relationship between the quantities involved in the transfer of heat by heat conduction Conclusion. In each layer of the wall, the temperature changes along a logarithmic curve. We consider the process of heat transfer through a multi-layer wall in a steady-state regime. Therefore, the amount of heat flux $Q$ passing through each layer of the wall is constant in magnitude and the same for all layers.

Key-Words / Index Term :
heat conduction, differential, heat exchange, curve, single-layer, multi-layer, flat wall, heat transfer.

References :
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[8] S. Todeka, S.L. Mewada, “Concentrate on Engineering Basics,” World Academics Journal of Engineering Sciences, Vol.6, Issue.3, pp.321-335, 1992.