How to calculate the refractory wall temperature?

In summary, the gas-fired tube heater has specific dimensions and consists of 90 tubes arranged in a single row, with 6 of them being shield tubes. The fuel is a mixture of methane and ethane with a given heat value, and preheated air and fuel gas are used. The desired radiant heat flux and net heating value are also given. The four calculations to be made are the average flue gas temperature in the firebox, the effect of reducing excess air to 10% on fuel requirements, the effect of introducing combustion air at 60℉ on fuel requirements, and the refractory average temperature. To calculate the average flue gas temperature, the total heat release rate needs to be computed. For the fuel requirements
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Homework Statement



A gas-fired tube heater has the following data:

Dimensions of the combustion chamber: 15 * 20 * 40 ft

Tube outside diameter: 5 in

Temperature of the tube=800° F

Center to center spacing: 8 in

Number of tubes (arranged in a single row of which 6 tubes are shield tubes) : 90

Tube length: 40 ft

Preheated air enters at 400℉ and fuel gas enters at 60℉.The fuel gas consists of methane and ethane and has the empirical formula C40Hn. The rate of heat liberated by the fuel is 91200000 Btu/h. Thirty percent excess air is used. The desired radiant heat flux is 12,000 Btu h.ft2℉ of circumferential tube area. The net heating value of methane is 21496 Btu/lb and that of ethane is 20550 Btu/lb. Calculate:

(i) The average flue gas temperature in the firebox.

(ii) The effect of reducing the excess air to 10% on the fuel requirements.

(iii) The effect of introducing combustion air at 60℉ on the fuel requirements.

(iv) The refractory average temperature

Given n=159 and the specific heat of flue gas, air, and fuel = 0.24 Btu/lbmoF

Homework Equations


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The Attempt at a Solution


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iv) I estimated the total area of the chamber by arranging 90 tubes of the radiant zone along the perimeter of the heater section. Given the tube separations, I computed the necessary dimensions. Then I calculated the area of the equivalent plane which will be the sum of the area of the radiant tube planes and the shield tube plane, the equivalent plane efficiency from the graph of the equivalent plane efficiency vs distance between centers/ tube diameter ratio graph, view factor, and equivalent hemispherical beam length. How can I proceed further after determining the emissivity of the flue gas?
 

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  • #2
(i) I am confused as to how to calculate the average flue gas temperature. I have computed the total heat release rate, but I don't know how to proceed further. (ii) For the fuel requirements, I need to calculate the mass flow rate of air and fuel. I have calculated the air/fuel ratio. How can I calculate the mass flow rate? (iii) I am not sure how to calculate the effect of introducing combustion air at 60F on the fuel requirements. Any help would be much appreciated!
 

1. What is the formula for calculating the refractory wall temperature?

The formula for calculating the refractory wall temperature is T = (Q/A) + Tamb, where T is the refractory wall temperature, Q is the heat input, A is the surface area, and Tamb is the ambient temperature.

2. How is the heat input determined in the calculation?

The heat input can be determined by using the following equation: Q = mCpΔT, where Q is the heat input, m is the mass of the refractory material, Cp is the specific heat capacity, and ΔT is the change in temperature.

3. What units should be used in the calculation?

The units used in the calculation should be consistent. The most commonly used units are Joules (J) for heat input, square meters (m2) for surface area, and degrees Celsius (°C) for temperature.

4. How do I determine the surface area of the refractory material?

The surface area can be determined by measuring the length, width, and height of the refractory material and using the formula A = 2lw + 2lh + 2wh, where A is the surface area, l is the length, w is the width, and h is the height.

5. Is there a specific method for calculating the refractory wall temperature?

Yes, there are different methods for calculating the refractory wall temperature, such as the heat balance method, the heat transfer coefficient method, and the finite difference method. Each method has its own advantages and limitations, so it is important to choose the most appropriate method for your specific situation.

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