Resistance in Rectangle
M.M. Yovanovich
RESRECT3.MWS
Dimensionless resistance in a rectangle of width , height , thermal conductivity . The left boundary at and the right boundary at are adiabatic. The upper boundary at convectively cooled.
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 spreading resistance depends on , and in the following manner: . The dimensionless one-dimensional flow resistance is , and the dimensionless total resistance is the sum of the spreading resistance and the 1D flow resistance.
> restart:
System parameters.
> nmax:= 30:
> pars:= (epsilon = 0.2, beta = 1/2, Bie = 100);
> term:= 2/(Pi^3*epsilon^2)*sin(n*Pi*epsilon)^2/n^3*((n*Pi + Bie*tanh(n*Pi*beta))/(n*Pi*tanh(n*Pi*beta) + Bie));
> terms:= evalf([seq(subs(pars, term), n=1..nmax)]):
> psi:= add(terms[j], j=1..nmax);
> psi1D:= beta + beta/Bie;
> psi1D1:= evalf(subs(pars, psi1D));
> kR:= psi + psi1D1;
Summary of input and output parameters.
> pars; nmax:= nmax; kR:= kR;