Resistance in Rectangle

M.M. Yovanovich

RESRECT1.MWS

Dimensionless resistance in a rectangle of width , height , thermal conductivity . The left boundary at and the top boundary at are adiabatic. The right boundary at is isothermal at temperature excess . This system corresponds to the case where and .

The lower boundary at from to has uniform flux , and the remainder of that boundary from to is adiabatic. The dimensionless resistance depends on and in the following manner: .

> restart:

System parameters.

> nmax:= 100:

> pars:= (epsilon = 0.2, beta = 1/2);

> term:= 16/Pi^3/epsilon^2*sin((2*n-1)*Pi*epsilon/2)^2/tanh((2*n-1)*Pi*beta/2)/((2*n-1)^3);

> terms:= evalf([seq(subs(pars, term), n=1..nmax)]):

> psi:= add(terms[j], j=1..nmax);

Summary of input and output parameters.

> pars; nmax:= nmax; kR:= psi;