Example 14.5-3 Combined Radiation and Convection
> restart; > Qr := e1*A1*sigma*(Twater^4); Radiation loss of the water assuming the radiation is emitted to the sky where the temperature is very low. > Qconv := h*A1*(Tair-Twater); Convective heat absorbed by the water. > e1 := 0.95; sigma:=0.1712e-8*Btu/hr/ft^2/R^4; Twater := 492*R: h :=0.2*((Tair-Twater)/R)^(1/4)*Btu/hr/ft^2/R; Given in the problem. Note that we try to find Tair in the untis of R so (Tair-Twater)/R will be a pure number. > eq:=simplify((Qr-Qconv)/(A1*Btu/hr/ft^2)); Setting up the balance equation to be solved. > Tair:=x*R;eq:=simplify(eq,assume=positive); Deciding to use a numerical solution for the unitless number x. > eq:=unapply(eq,x); > plot(eq(x),x=492...700); There is obviously a root near 600R.
> x:='x'; > T:=fsolve(eq(x),x)*R; Without specifying the interval, Maple does not find a root. > T:=fsolve(eq(x),x,500....700)*R; This is better.