JNTU B.Tech II PROCESS HEAT TRANSFER Previous Question Paper (March 2022 - R16)

Conduction is the transfer of thermal energy through a material medium without the bulk movement of matter. At the microscopic level, it occurs via lattice vibrations (phonons) in solids and collisions between free electrons and atoms. The rate of heat transfer is governed by Fourier's Law:

where k is thermal conductivity, A is area, and dT/dx is the temperature gradient.

Radiation is the transfer of energy through electromagnetic waves, requiring no medium. It involves the emission of photons from the surface of a body due to its temperature. The maximum theoretical emission from a black body is defined by the Stefan-Boltzmann Law:

where σ is the Stefan-Boltzmann constant and T is the absolute temperature. Real surfaces emit less, characterized by emissivity (ε).

A semi-infinite solid is an idealized body that has a single plane surface and extends to infinity in all other directions. When the surface is subjected to a sudden change in temperature or heat flux, the temperature distribution T(x, t) depends on depth x and time t.

For a constant surface temperature T_s applied to a solid initially at uniform temperature T_i, the solution to the one-dimensional transient heat conduction equation is expressed using the Gaussian error function (erf):

Key characteristics of this distribution include:

• The temperature profile penetrates deeper into the solid as time progresses.
• The term sqrt(α * t) represents the characteristic thermal diffusion length, where α is thermal diffusivity.
• At x = 0, the temperature is always T_s.
• As x approaches infinity, the temperature remains at the initial value T_i.
• The error function values range from 0 to 1, indicating that the temperature change is confined to a finite thermal boundary layer that grows over time.