The nozzle of an experimental rocket motor is fabricated from 5 mm-thick alloy steel. The combu

step 1 So, here in this question, first we need to find the gas constant for the gas. We know that univ

The nozzle of an experimental rocket motor is fabricated...

The nozzle of an experimental rocket motor is fabricated from $5 \mathrm{~mm}$-thick alloy steel. The combustion gases are at $2100 \mathrm{~K}$, and the effective heat transfer coefficient is $6000 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}$. If the nozzle is initially at $300 \mathrm{~K}$ and the maximum allowable operating temperature for the steel is specified as $1300 \mathrm{~K}$, what is the allowable duration of firing? To obtain a conservative estimate, neglect the heat loss from the outer surface of the nozzle. Take $k=43 \mathrm{~W} / \mathrm{m} \mathrm{K}, \alpha=12.0 \times 10^{-6}$ $\mathrm{m}^{2} / \mathrm{s}$ for the steel.

Key Concepts

Thermal Diffusivity

Thermal diffusivity is a material property that characterizes how quickly heat diffuses through a material. It is defined as the thermal conductivity divided by the product of density and specific heat capacity. High thermal diffusivity indicates that a material quickly responds to changes in thermal energy, which is essential for predicting transient thermal responses.

Transient Heat Conduction

Transient heat conduction deals with how temperature within a material changes over time when subjected to thermal gradients. It involves solving the heat equation, which describes the spatial and temporal evolution of temperature in solids, allowing engineers to predict how quickly a material heats up or cools down under given conditions.

Convection Heat Transfer

Convection heat transfer is the process by which heat is transferred from a surface to a fluid (or vice versa) as a result of the fluid motion. This concept is critical when a solid surface is in contact with a fluid at a different temperature, influencing how rapidly the surface temperature can change.

Boundary Conditions in Heat Transfer

Boundary conditions define the behavior of temperature and heat flux at the interfaces of a material. In problems involving both conduction and convection, setting appropriate boundary conditions—such as a convective boundary on one side of a solid and an insulated boundary on the other—is crucial for accurately determining the temperature evolution within the material during transient processes.

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