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Homework problems require the use of the template and require some effort on the part of the student

Hi all, I have a unique problem that I need help with

A company's curing oven's exposed surface temperature is measured at 80°c when the surrounding air is 23°c. You think it should be insulated and wager to pay for the cost of this yourself if you can keep the savings incurred. Is this a smart move? the oven is 3.7m long and 2.4m diameter. The plant operates 16 hours/day 365 days/year. The insulation to be used is fiberglass (Kins = 0.08 W/m/°c, assumed constant) which costs $2.5/m2 per cm thickness plus $21.5/m2 for labour regardless of tthickness. Convective heat transfer coefficient on the outer surfaced is estimated to be h0= 20W/m2/K. The oven uses natural gas, whose unit cost is £7.1/GJ input and the oven's efficiency is 80%.

Ignoring radiation heat loss from the outer surface, determine

A) how much money you will make out of this venture, by installing one inch (1 inch = 2.54 cm) of insulation, if any, and

B) the thickness of insulation (to nearest inches) that will maximise your earnings

My thinking for part A is to:

calculate the area of the oven exposed to the air,

use q = hA (T2-T1) to obtain the heat transfer rate of the system with no insulation

Use Rcond = ln(r2-r1)/(2*pi*L*K) to find the heat transfer rate *with* 1" insulation

find Rconv ( 1/(h*A)

use Rconv and Rcond to find Q

calculate loss per year versus installation cost.

This comes out to be a saving of $3432.67 for the year for me, but given the long answer nature of this question I've undoubtedly gone wrong somewhere and would appreciate other peoples' working if possible :)

Any input would be greatly appreciated as I'm well and truly stuck

A company's curing oven's exposed surface temperature is measured at 80°c when the surrounding air is 23°c. You think it should be insulated and wager to pay for the cost of this yourself if you can keep the savings incurred. Is this a smart move? the oven is 3.7m long and 2.4m diameter. The plant operates 16 hours/day 365 days/year. The insulation to be used is fiberglass (Kins = 0.08 W/m/°c, assumed constant) which costs $2.5/m2 per cm thickness plus $21.5/m2 for labour regardless of tthickness. Convective heat transfer coefficient on the outer surfaced is estimated to be h0= 20W/m2/K. The oven uses natural gas, whose unit cost is £7.1/GJ input and the oven's efficiency is 80%.

Ignoring radiation heat loss from the outer surface, determine

A) how much money you will make out of this venture, by installing one inch (1 inch = 2.54 cm) of insulation, if any, and

B) the thickness of insulation (to nearest inches) that will maximise your earnings

My thinking for part A is to:

calculate the area of the oven exposed to the air,

use q = hA (T2-T1) to obtain the heat transfer rate of the system with no insulation

Use Rcond = ln(r2-r1)/(2*pi*L*K) to find the heat transfer rate *with* 1" insulation

find Rconv ( 1/(h*A)

use Rconv and Rcond to find Q

calculate loss per year versus installation cost.

This comes out to be a saving of $3432.67 for the year for me, but given the long answer nature of this question I've undoubtedly gone wrong somewhere and would appreciate other peoples' working if possible :)

Any input would be greatly appreciated as I'm well and truly stuck

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