# Temperature distribution two semi-infintie bodies

• Drokz
In summary, the conversation discusses a problem involving two semi-infinite bodies with different thermal properties and initial temperatures. The goal is to find the temperature in the second body at a given time. The equation \frac{\delta^2 T}{\delta x^2} = \frac{C \rho}{K}\frac{\delta T}{\delta t} is mentioned and the issue of determining the appropriate boundary conditions is brought up. The idea of treating the problem as two separate problems is considered, but there is uncertainty about the boundary condition T(\infty, t) = 0.
Drokz
Hi there, I have to solve the following problem:

A semi-infinite body x<0 has thermal conductivity $$K_1$$, density $$\rho_1$$, and specific heat $$C_1$$. It is initially at temperature $$T_0$$. At time t=0, it is placed in thermal contact with the semi-infinite body x>0, which has parameters $$K_2$$, $$\rho_2$$, $$C_2$$, and is initially at temperature T=0. Find $$T_2(x,t)$$, the temperature in the second body.

$$\frac{\delta^2 T}{\delta x^2} = \frac{C \rho}{K}\frac{\delta T}{\delta t}$$

Does someone know what boundary conditions I have to apply? Tried using the Heaviside step function, but that got difficult when Fourier transforming it.

Thought about considering it as two different problems, but then I have only one boundary condition $$T(\infty, t) = 0$$?

Drokz said:
Thought about considering it as two different problems, but then I have only one boundary condition $$T(\infty, t) = 0$$?
Is there something wrong with this? This is what I would assume.

## 1. What is temperature distribution in two semi-infinite bodies?

Temperature distribution in two semi-infinite bodies refers to the way in which heat is transferred and distributed within two bodies that are considered to be infinitely large in one direction and have a finite size in the other direction. This phenomenon is commonly studied in materials science and thermal engineering.

## 2. How is temperature distribution affected by the properties of the two bodies?

The properties of the two bodies, such as their thermal conductivity, specific heat capacity, and surface emissivity, can greatly influence the temperature distribution between them. Higher thermal conductivity and specific heat capacity allow for more efficient heat transfer, while a higher surface emissivity can lead to a more uniform temperature distribution.

## 3. What factors can cause variations in temperature distribution between two semi-infinite bodies?

Some factors that can cause variations in temperature distribution between two semi-infinite bodies include differences in their initial temperatures, heat sources or sinks at their boundaries, and differences in their thermal properties. These variations can result in temperature gradients and non-uniform heat transfer between the two bodies.

## 4. How is temperature distribution between two semi-infinite bodies typically calculated?

The temperature distribution between two semi-infinite bodies is typically calculated using mathematical models, such as the heat equation, which takes into account the thermal properties and boundary conditions of the two bodies. Numerical methods, such as finite difference or finite element methods, are often used to solve these equations and calculate the temperature distribution.

## 5. Why is understanding temperature distribution in two semi-infinite bodies important?

Understanding temperature distribution in two semi-infinite bodies is important in many practical applications, such as thermal insulation, heat transfer in buildings and industrial processes, and the design of electronic devices. By studying and controlling temperature distribution, we can optimize the efficiency and performance of these systems and materials.

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