Heat Transfer Problem - Alex's Solution

[alex-book]

Heat transfer problem--please help

Homework Statement

I have a heating mantle (180Watt) and i want to use it for heating a ceramics flask (thermal conductivity : 1.38 W/m*K), however, there is a stainless steel on top of the flask (at 10cm distance between the heating mantle and the stainless steel). The thermal conductivity of SS is 21.5 W/m*K. and i know the formula is

h = delta Q/ A* delta T* delta t

Homework Equations

If want to know what is the temperature on the stainless steel after it has been heated up for 1 hour, should i calculate the heat transfer between the heating mantle and the flask first? and then go along with the stainless stell or how?

The Attempt at a Solution

I know Q=(1/((1/h)+(t/k))*A*Delta T
and Q = 180 W
h = specific heat? how could i get this value?
t = 3mm = 0.003m (thickness of the wall)
k = 1.38 W/m*K (thermal conductivity of flask)
A = area of the wall = 17cm*15cm = 255cm^2 = 0.0255m^2
but i don't know what will be the temperature difference between them?

and i also confuse about how could i calculate the heat transfer with open system?

I just need to find what will be the temperature of the stainless steel above 10cm from the heating mantle...
I am wondering that since ceramic is not a good heat conductor, plus the fact that it is an non-isolated system , so the heat would probably not going to be that hot, but still i need to get the approximation...i have put an image of the illustration..

any help will be appreciated..i am really lost at this one..thank you so much!

Alex..

 

[KataKoniK]

Dear Alex,

Thank you for sharing your heat transfer problem with us. It seems like you are on the right track with your equations, but there are a few things that I would like to clarify and suggest.

Firstly, the specific heat (h) in your equation refers to the heat transfer coefficient which is a measure of how easily heat can be transferred between two materials. This value can be found in tables or calculated using empirical formulas, but it is not the same as specific heat capacity (c) which is a property of the material itself.

Secondly, in order to calculate the temperature of the stainless steel, you will need to consider the heat transfer between the heating mantle and the flask, as well as the heat transfer between the flask and the stainless steel. You can use the same equation that you have mentioned, but you will need to consider the thermal conductivity of both the flask and the stainless steel in your calculations.

Lastly, in an open system, heat transfer is also influenced by factors such as convection and radiation. In this case, you may need to consider the convective heat transfer coefficient and the emissivity of the materials in your calculations.

I would recommend seeking help from your instructor or a heat transfer expert to guide you through the calculations and ensure that all relevant factors are taken into account. Best of luck with your problem!

 

[Mene]

Hello Alex,

Thank you for reaching out for help with your heat transfer problem. I can provide some guidance and suggestions for solving this problem.

Firstly, it is important to note that the specific heat (h) in your equation refers to the heat transfer coefficient, which is a measure of how easily heat can be transferred between two materials. It is a property of the materials involved and can be found in tables or calculated using empirical equations.

In order to find the temperature of the stainless steel after 1 hour of heating, you will need to calculate the heat transfer between the heating mantle and the stainless steel. This can be done by first calculating the heat transfer between the heating mantle and the ceramic flask, and then using that value to calculate the heat transfer between the ceramic flask and the stainless steel.

To calculate the heat transfer between the heating mantle and the ceramic flask, you can use the equation you provided: Q=(1/((1/h)+(t/k))*A*Delta T. In this case, Q should be equal to 180W (the power of the heating mantle), h is the heat transfer coefficient between the heating mantle and the flask, t is the thickness of the flask wall, k is the thermal conductivity of the flask, and A is the area of the flask wall. You can also assume an initial temperature difference (Delta T) between the heating mantle and the flask, such as room temperature (25°C) and the desired temperature of the flask.

Once you have calculated the heat transfer between the heating mantle and the ceramic flask, you can use this value to calculate the heat transfer between the ceramic flask and the stainless steel. This can be done using a similar equation, where Q is equal to the value you calculated for the heat transfer between the heating mantle and the flask, h is now the heat transfer coefficient between the ceramic flask and the stainless steel, t is the thickness of the stainless steel layer (10cm in this case), k is the thermal conductivity of the stainless steel, and A is the area of the stainless steel layer (which you can calculate using the dimensions provided).

Using these calculations, you should be able to find the temperature of the stainless steel layer after 1 hour of heating. However, it is important to keep in mind that this is an approximation and may not be completely accurate due to factors such as heat loss to the surrounding environment and variations in heat transfer coefficients.

I hope this helps and good luck with