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;