Reconsider Prob. 11-25. Using EES (or other) software, investigate the effect of the initial tem

Reconsider Prob. 11-25. Using EES (or other) software,...

Key Concepts

Annealing Process

This concept involves the controlled heating and subsequent cooling of a material to alter its physical and sometimes chemical properties. Annealing is used to relieve internal stresses and modify the microstructure of the material, which can influence its mechanical and thermal properties. Understanding the annealing process is essential in materials science and engineering as it affects how materials respond to thermal treatment over time.

Transient Heat Transfer

Transient heat transfer deals with the change in temperature within a body with time, especially when initial conditions are not in equilibrium with the surrounding environment. Analyzing transient heat transfer allows one to understand how the temperature of a system evolves from an initial state to a steady state, and it is crucial when considering processes that depend on time-dependent heating or cooling, such as the annealing process.

Parametric Analysis

Parametric analysis involves systematically varying one or more parameters to determine their effect on the outcome of a process or system. In the context of thermal processes, it includes studying how changes in initial conditions, such as the starting temperature, affect critical results like annealing time and overall heat transfer. This method is an important tool for optimizing thermal treatment processes.

Simulation Software Application

Using simulation software like Engineering Equation Solver (EES) facilitates the modeling and analysis of complex thermal systems. Such tools help in solving the governing equations of heat transfer and energy balance, and they provide graphical outputs that illustrate trends and dependencies. This application is vital for accurately predicting how variations in initial conditions influence the system’s performance over time.

Transcript

00:01 In this problem, we have a sphere maintained at a constant temperature of 110 celsius in a room temperature room, and it is losing heat to the environment of the surrounding air and also given an input to maintain its temperature.

00:20 And we're asked to graph the heat transfer rate of the sphere against the convection transfer coefficient h.

00:30 For some different emissivity values.

00:34 So in this problem, our sphere being maintained at this constant temperature, we're going to have a heat transfer via two methods.

00:43 We're going to have convection and radiation.

00:47 So we'll find a total heat transfer rate as the sum of the convection and the radiation rates.

00:55 And then with that, we'll have a function of q.

01:01 Of the heat transfer rate as a function of both the convection coefficient and the emissivity, and then we can graph those for some values that we're given.

01:15 All right, so our q dot is going to be the sum of the q dots, the rates for convection, and for radiation.

01:31 And we have for our convection, it is h, the coefficient, convection coefficient a surface area times the differential between the surface and the air.

01:55 And for our radiation, our q dot is equal to epsilon, the emissivity times sigma our stuff and boltman constant times area times temperature of our surface to the fourth minus temperature of our air to the fourth and for this problem where we're given our temperature at our surface is 110 celsius our air temperature is 20 degrees celsius.

02:46 The radius of our sphere was 4 .5 centimeters.

02:58 And we'll want to use our stefan boltzmann constant r -sigma equals to 5 .67 times 10 to the minus 8 watts per meter squared.

03:17 Kilven to the fourth okay so we're going to vary so our unknowns are going to be h and epsilon and we can figure out our a is our surface area for our sphere and from the surface area of a sphere being equal to 4 pi r squared and that will give us 4 pi times 0 .0 .04 or 5 meters squared.

04:00 So our surface area is 0 .0 about 0 .25 meters squared...

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