Resistance in Rectangle

M.M. Yovanovich

RESRECT2.MWS

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

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

> restart:

System parameters.

> nmax:= 100:

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

[Maple Math]

> 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);

[Maple Math]

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

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

[Maple Math]

Summary of input and output parameters.

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

[Maple Math]

[Maple Math]

[Maple Math]