Re: Solving integral equations numerically

*To*: mathgroup at smc.vnet.net*Subject*: [mg100076] Re: Solving integral equations numerically*From*: antononcube at gmail.com*Date*: Fri, 22 May 2009 23:38:53 -0400 (EDT)*References*: <gv2jgr$977$1@smc.vnet.net>

The message NIntegrate::inumr is issued because Tlo does not have a numerical value. On May 20, 11:58 pm, viehhaus <g.viehhaus... at physics.ox.ac.uk> wrote: > Hi, > > I'm trying to solve a set of two integral equations, which don't have an analytic solution, so I'm using NIntegrate and FindRoot > > nodes = 11 (*number of nodes*) > RCOM = 2.17 (* common resistance *) > RS0 = 0.1 (*off-sensor resistance for sensor*) > RS = 1.1 (*sensor resistance pre node*) > Ph = 6 (*hybrid power in W*) > tcool = -25 (*coolant temperature (degC) *) > ta = 1.2/2/0.0000862 (*activation temperature (K) *) > l = 63.56/1000(*length of thermal path*) > w = 128.05/1000(*width of thermal path*) > T0 = 273 + tcool + Ph*RCOM > T = 4/3*(Tlo - T0^2/ta)*(x^2/l^2 - 2*x/l) + Tlo (*parabolic temperature function in sensor*) > I1 = (RCOM + RS0)*w*qref*Exp[ta/273]/273^2*NIntegrate[T^2*Exp[-ta/T], {x, 0, l}] > I2 = (RS/l)*w*qref*Exp[ta/273]/273^2*NIntegrate[T^2*Exp[-ta/T]*x, {x, 0, l/2}] > FindRoot[{Tlo == T0 + I1, T0^2/ta == Tlo + I2}, {{Tlo, 270}, {qref, 300}}] > > but I get errors like "... has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,0.06356}}..." and FindRoot does not move. Any idea what I'm doing wrong? > > Cheers, Georg