How can I solve non-linear heat conduction with a variable thermal conductivity?

In summary, the conversation is about solving non-linear heat conduction with thermal conductivity as a function of temperature using the finite difference method. The equation for this process is given and the speaker is looking for new ideas to solve the problem.
  • #1
annie.1991
5
0
Hi everyone

I am trying to solve non linear heat conduction where thermal conductivity is function of temperature, I am solving it by finite difference method. this is my equation
∂2t/∂x2+∂2t/∂y2 *k(t)= -q (x,y)

i have solved the equation taking k(t)= a-b*t,and when i further solved the equation it gave an quadratic equation. where temparature is the root of the equation. a and b are variables, where a>>b . i just taught i can see the variations of temperature depending on the values of a and b.I just wanted to write down in the equation where tempearture is changing with some other variables.

If anybody is having any other idea to solve the " thermal conductivity is function of temperature " in different manner please do share with me kindly.
 
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  • #2
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  • #3
annie.1991 said:
Hi everyone

I am trying to solve non linear heat conduction where thermal conductivity is function of temperature, I am solving it by finite difference method. this is my equation
∂2t/∂x2+∂2t/∂y2 *k(t)= -q (x,y)
i am running out of ideas can anybody help me out in solving this .
 

FAQ: How can I solve non-linear heat conduction with a variable thermal conductivity?

What is nonlinear heat conduction?

Nonlinear heat conduction is the study of heat transfer in materials that exhibit non-linear thermal behavior, meaning that the relationship between temperature and heat flux is not a simple linear function.

What are some examples of materials that exhibit nonlinear heat conduction?

Examples of materials that exhibit nonlinear heat conduction include polymers, ceramics, and composite materials. These materials typically have complex structures and thermal properties that result in non-linear thermal behavior.

How is nonlinear heat conduction different from linear heat conduction?

The main difference between nonlinear and linear heat conduction is the relationship between temperature and heat flux. In linear heat conduction, this relationship is linear and can be described by Fourier's law. However, in nonlinear heat conduction, this relationship is non-linear and requires more complex mathematical models to accurately describe heat transfer.

What are some applications of nonlinear heat conduction?

Nonlinear heat conduction has many practical applications, including the design of thermal insulators, heat shields, and electronic cooling systems. It is also important in the study of materials processing and manufacturing, as well as in the analysis of thermal energy storage systems.

How is nonlinear heat conduction studied and analyzed?

Nonlinear heat conduction is typically studied through numerical simulations and experiments. Computational methods, such as finite element analysis, are often used to solve the complex equations that govern non-linear heat transfer. Experimental techniques, such as infrared thermography and thermocouple measurements, are also commonly used to validate these numerical models and study the thermal behavior of materials.

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