# Help with Steady State Heat Transfer Problem

• Diego Saenz
In summary, the conversation is about a steady state heat transfer problem with a flux source of 400 W/m². The goal is to calculate the heat flux passing through a surface that is placed and oriented in space with air in between. The proposed method is to use ∫∫(-k∇T)*(n dS), but the person is unsure about what ∇T represents. The suggested solution is to find T by solving the heat equation with additional boundary conditions. If the geometry is simple, it can be solved analytically, but if not, software is needed. The conversation also mentions the use of energy conservation and a constant temperature distribution to find the heat flux. The person requests a simple example to better understand the

#### Diego Saenz

Hello everyone,

I have this setady state, heat transfer problem; I hope you can help me with it.
I have flux source of 400 W/m² (a lamp), and i want to calculate the heat flux passing through a surface arbitrarily placed and oriented in the space. There is air in between. How can i do this?

I thought that I could use ∫∫(-k∇T)*(n dS)
But i don't know what ∇T is...

Thanks.

That will give you the answer once you've found T. Finding T involves solving the heat equation with a local heat source. You'll need some more boundary conditions to do this, e.g. what are the temperatures of the walls?

If your geometry is simply you can solve for T analytically then differentiate to find your heat flux through a surface.

If not, you'll need some software.

Hi mikeph,

My surface is simple, is a square. Is it possible to use this information to solve for T? Can you explain how can I do this?

Thanks

If the heat source is inside the surface then it's just 400 W/m^2, this is from energy conservation using the steady state assumption.

If you have a constant temperature distribution then the heat being added inside the box (400) must equal the heat leaving through the walls, otherwise the temperature of the box would have to increase which would introduce a time variation.

1 person
I really appreciate your help mikeph.
But I have problems visualizing the solution, could you provide simple example?

## 1. How do I set up a steady state heat transfer problem?

To set up a steady state heat transfer problem, you will need to define the boundary conditions, material properties, and heat source/sink in your system. Additionally, you will need to create a mathematical model using governing equations like Fourier's Law of Heat Conduction.

## 2. What is the difference between steady state and transient heat transfer?

Steady state heat transfer refers to a condition where the temperature in a system remains constant over time. Transient heat transfer, on the other hand, occurs when there is a change in temperature over time. In other words, steady state heat transfer is a state of thermal equilibrium, while transient heat transfer is a dynamic process.

## 3. How do I solve a steady state heat transfer problem numerically?

To solve a steady state heat transfer problem numerically, you will need to use a numerical method such as the Finite Difference Method or Finite Element Method. These methods involve discretizing the system into smaller elements and solving the governing equations for each element. The results can then be combined to obtain a solution for the entire system.

## 4. What factors affect the steady state heat transfer rate?

The steady state heat transfer rate is affected by several factors, including the temperature difference between the hot and cold ends, the thermal conductivity of the material, the size and shape of the system, and the boundary conditions. The presence of insulation or heat sinks/sources can also affect the heat transfer rate.

## 5. How can I improve the efficiency of heat transfer in a steady state system?

To improve the efficiency of heat transfer in a steady state system, you can increase the temperature difference between the hot and cold ends, use materials with higher thermal conductivity, optimize the shape and size of the system, and minimize heat losses through insulation or other methods. Additionally, using advanced techniques like multi-physics simulations can help optimize the design for efficient heat transfer.