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# Packed bed dryer

## Packed bed dryer

(OP)
Hello group

I am currently designing spreadsheets applications for unit operations, I have ready a multiple evaporator, packed adsorption colum sheets, but now I am working on a packed bed dryer. I have set up cells to calculate mass transfer coefficient, difussion coeficients, and humidity content in the solid. No I am atempting to predict the change in temperature and humidity content across the column by using:

for heat transfer

(h*a/G*cs) Integral(dz) = integral (dT/(T-Tw))
(h*a/G*cs)*(z - zo) = ln[(T1-Tw)/(T2-Tw)]

where h,a, G, cs are heat transfer coeff, dimension factor, flow rate per area, specific heat.

for mass transfer

(ky*a*M/G) integral(dz) = integral(dH/(Hw-H))
(ky*a*M/G)*(z-zo) = ln [(Hw-H2)/(Hw-H1)]

Where ky is mass transfer coefficient, H is humidity in gas stream use for drying.

My question is that since I migth have drying from a constant rate of drying to a falling rate of drying, how could I include this effect in the previous equations? I heard that I could use finite difference to solve this problem, but I have neither experience nor knowledge of numerical methods. any sugestions? do any of you know of a really practical book for num methods? the ones I checked have too much math and few examples that it just makes my confusion even bigger. Can this problem be solved analitically?

thanks

Cheers

Will

### RE: Packed bed dryer

I am not familiar with your application but have used Excel to set up many time series analysis for hydrology work.  It looks like this is a time series analysis since you talk about the "rate of drying" falling (over time?).  So what do z and T represent in your equations, and how does time fit in to your analysis?

I will assume that z is a dimension and T is the temperature of the solid.  It seems to me that you would want to set up rows for time steps in the analysis, and put the paramaters is the transfer equations across the columns.  You might need to establish the intervals of z and have a column for each interval.  Then each row would represent say a xx-second time interval.  Then you compute the above equations for the heat transfer & drying that occurs during that time interval.  The next row would use the "ending" values (e.g. T2 or H2 from row 1) as its "starting" values ( e.g. T1 and H1 in row 2).  And you fill down as needed.

So, if you can use this approach to your analysis, if one of your coefficients or factors is changing with time, can you develop a table that computes what the drying rate is at each time interval?  Then when analyzing the heat transfer for the time interval in each row you could look up the drying rate for each timestep using a VLOOKUP.

Thus your constants/coefficients/factors that might change over time would be contained in columns along with the H and T parameters you are modeling, and rows set up for the time intervals you are considering.

Hope this helps,

BT

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