In a production facility, 3-cm-thick large brass plates (k=110 W / m · ^∘ C, ρ=8530 kg / m^3,

step 1 In this problem, we have large brass plates that are heated in an oven at a rate of 300 per minu

In a production facility, 3-cm-thick large brass plates...

In a production facility, 3-cm-thick large brass plates $\left(k=110 \mathrm{~W} / \mathrm{m} \cdot{ }^{\circ} \mathrm{C}, \rho=8530 \mathrm{~kg} / \mathrm{m}^3, c_p=380 \mathrm{~J} / \mathrm{kg} \cdot{ }^{\circ} \mathrm{C}\right.$, and $\alpha=33.9 \times 10^{-6} \mathrm{~m}^2 / \mathrm{s}$ ) that are initially at a uniform temperature of $25^{\circ} \mathrm{C}$ are heated by passing them through an oven maintained at $700^{\circ} \mathrm{C}$. The plates remain in the oven for a period of 10 min . Taking the convection heat transfer coefficient to be $h=80 \mathrm{~W} / \mathrm{m}^2 \cdot{ }^{\circ} \mathrm{C}$, determine the surface temperature of the plates when they come out of the oven.

Key Concepts

Transient Heat Conduction

This concept refers to the process in which the temperature of a solid changes with time due to heat transfer. In scenarios where an object is suddenly exposed to a different thermal environment, the temperature within the object evolves from its initial value towards a new steady state. Mathematical formulations, often involving differential equations, are used to describe this time-dependent process.

Convection Heat Transfer

Convection is the mode of heat transfer that occurs at the surface of a solid when it is in contact with a moving fluid, such as air. The rate of convective heat transfer is characterized by the convection heat transfer coefficient, which influences how quickly heat is transferred through the boundary between the solid and the fluid environment.

Biot Number

The Biot number is a dimensionless parameter that compares the internal resistance to heat conduction within a solid to the external resistance to heat convection at its surface. It is used to assess the validity of the lumped capacitance method; a small Biot number indicates uniform temperature inside the solid, while a large Biot number suggests significant internal temperature gradients.

Thermal Diffusivity

Thermal diffusivity is a property of the material that indicates how quickly heat diffuses through it. It combines the effects of thermal conductivity, density, and specific heat. A high thermal diffusivity means that the material will reach thermal equilibrium quickly, influencing the transient heat conduction behavior.

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