Calculating optimum thickness of the insulation for composite wall

In summary, the problem is to determine the minimum heat leak into a room when a wall is required to be insulated by embedding wood within concrete, with a total thickness of 10cm for concrete and 1cm for wood. The location of the wood within the concrete can be changed and the thermal conductivity of wood and concrete are given. The solution involves using the concept of thermal resistance and ignoring other ways for heat to enter the room.
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Homework Statement



A wall is required to be insulated by embedding wood within concrete. the total thickness of the concrete and wood are 10cm and 1 cm respectively and are fixed due to structural constraints. determine the minimum heat leak into the room if the location of the wood can be changed within the concrete. Take K for wood as 0.1w/mk and for concrete 1.0w/mk




Please help.

Homework Equations



thermal resistance

The Attempt at a Solution



I tried solving using thermal resistance concept by equating derivative of the total thermal resistance to 0, but not able to get the answer.
 
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  • #2
I don't believe they are asking you to find the minimium of an equation (eg I don't think you need to use derivatives). When they use the word minimium I think they are just referring to the fact that their might be other ways for heat to get into the room other than by conduction but these are to be ignored.
 

1. How do you calculate the optimum thickness of insulation for a composite wall?

The optimum thickness of insulation for a composite wall can be calculated by using the formula: t = (k x (Ti - To)) / (h x A x (Ri + Ro))Where:t = optimum thickness of insulationk = thermal conductivity of insulation materialTi = desired indoor temperatureTo = outdoor temperatureh = heat transfer coefficientA = surface area of the wallRi = thermal resistance of the inner layer of the wallRo = thermal resistance of the outer layer of the wallThe value of t calculated from this formula will be the optimum thickness of insulation that will provide the most efficient thermal insulation for the composite wall.

2. What factors should be considered when calculating the optimum thickness of insulation for a composite wall?

Some important factors that should be considered when calculating the optimum thickness of insulation for a composite wall include the desired indoor temperature, outdoor temperature, thermal conductivity of the insulation material, heat transfer coefficient, and thermal resistance of the inner and outer layers of the wall. Other factors such as cost, availability and environmental impact of the insulation material may also be taken into consideration.

3. Can the optimum thickness of insulation for a composite wall vary for different types of insulation materials?

Yes, the optimum thickness of insulation for a composite wall can vary for different types of insulation materials. This is because different insulation materials have different thermal conductivities, which affect the amount of insulation needed to achieve the same level of thermal insulation. Therefore, the formula for calculating the optimum thickness may need to be adjusted for different insulation materials.

4. Is it necessary to consider the thickness of each layer of the composite wall when calculating the optimum thickness of insulation?

Yes, it is necessary to consider the thickness of each layer of the composite wall when calculating the optimum thickness of insulation. This is because the thickness of each layer affects the overall thermal resistance of the wall, which is an important factor in the calculation. The thickness of the insulation layer itself will also impact the heat transfer coefficient, which is another factor in the formula.

5. Can the optimum thickness of insulation for a composite wall change over time?

Yes, the optimum thickness of insulation for a composite wall can change over time. This is because factors such as weather conditions, changes in indoor temperature, and wear and tear of the insulation material can affect its thermal properties. It is important to regularly monitor and adjust the insulation thickness as needed to maintain its optimum effectiveness.

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