# Heat transfer with changing boundary conditions

• Alex K
In summary, the conversation discusses the difficulties in setting up an experiment to determine the time dependence of temperature on the front surface of a plate assembly with a heater on one side and exposed to a gaseous environment on the other. The problem arises from the lack of existing equations or literature that describe the assembly with a changing temperature on one side. The conversation also mentions assumptions made for the experiment, such as homogeneous plates and perfect thermal contact. Suggestions for solving the problem include simplifying to one dimension and using nodal analysis with proper time steps. The experiment is not a homework problem, but a research project being conducted at a university lab.
Alex K
I am trying to set up for an experiment, and I need to know the time dependence of the temperature of the front surface of an assembly of plates. The assembly has a heater on one side and is exposed to a gaseous environment (of constant known pressure and temperature) on the other. I am interested in the temperature of the plate where it meets the gas. My problem is that no equations or literature I have yet found describe the assembly when the heated side is changing temperature. I am simplifying it to 1 dimension for my calculations. The temperature of the heated side follows an arbitrary function that is only known after I run the experiment.

Assumptions:
homogeneous plates of constant thermal conductivity
perfect thermal contact between plates
Th = f(t)

I am stuck here. What equations exist to describe this? Everything I have seen deals with materials at constant temperature exposed to a fluid and allowed to reach equilibrium, not a plate with one side forced to have a changing temperature.

Note: This is not a homework problem, but a research experiment I am conducting in a lab at my university.

#### Attachments

• heat transfer setup.jpg
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Okay, so the plates are semi-infinite in the vertical direction, but they have a finite thickness in the horizontal (vertical and horizontal wrt the sketch)? I would think you could do a kind of 1D nodal analysis with the wall temperature fluctuating over time. You would have to set all the boundary and initial conditions and determine the proper time step. It might take a bit of doing, but I believe it would work.

## 1. What is heat transfer with changing boundary conditions?

Heat transfer with changing boundary conditions refers to the transfer of thermal energy between two or more objects or substances with different temperatures, where the boundary conditions (such as temperature, pressure, or phase) of the system may change over time.

## 2. What are some examples of changing boundary conditions in heat transfer?

Some examples include an ice cube melting in a warm room, a pot of water boiling on a stove, or the cooling of a hot metal object in a cold environment.

## 3. How does changing boundary conditions affect heat transfer?

The rate of heat transfer is affected by the difference in temperature between the objects, the thermal conductivity of the materials, and the surface area of contact. Changing boundary conditions can alter these factors and therefore impact the overall rate of heat transfer.

## 4. What are the different types of heat transfer with changing boundary conditions?

The three main types are conduction, convection, and radiation. Conduction is the transfer of heat through direct contact between two objects, convection is the transfer of heat through the movement of fluids, and radiation is the transfer of heat through electromagnetic waves.

## 5. How can we control heat transfer with changing boundary conditions?

Heat transfer can be controlled through various methods such as insulation, regulating the temperature of the objects, or altering the surface area of contact. Additionally, understanding the principles of heat transfer can help in designing more efficient systems and processes.

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