packed bed dryer

[billbill20002000]

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. Now 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

 

[m777182]

Both left sides of equations involve terms that are specific for a selected material.To a first approximation you can operate with constant coefficients in the interval of constant drying rate and in the second interval with some declining ramp function of the coefficients.The intercept of both lines could be theoreticaly estimated by experiments so that you use model values for the coefficients. Practically it works better if you put into the dryer T or H sensors at different levels of z and repeatedly calculate actual values of them.
There are many books on numerical methods - personally I would recommend The Applied Numerical Methods by Brice Carnahan and The Handbook of Numerical Analysis Application With Programs For Engineers And Scientists by Jaroslav Pachner,Mc Graw Hill, where you can find a piece of Basic code for each problem, but as I say, there are many.
regards
m777182