A suspended membrane micro fluidic heat flux sensor that is able to measure the heat flow rate was designed and fabricated by a complementary-metal-oxide-semiconductor-compatible process. The combination of a thirty-junction gold and nickel thermoelectric sensor with an ultralow noise preamplifier, low pass filter, and lock-in amp has enabled the resolution of 50 nW power and provides the sensitivity of $11.4;mV/{mu}W$. The heater modulation method was used to eliminate low frequency noises from sensor output. It is measured with various heat flux fluid of DI-water to test as micro fluidic application. In order to estimate the heat generation of samples from the output measurement of a micro fluidic heat-flux sensor, a methodology for modeling and simulating electro-thermal behavior in the micro fluidic heat-flux sensor with integrated electronic circuit is presented and validated. The electro-thermal model was constructed by using system dynamics, particularly the bond graph. The electro-thermal system model in which the thermal and the electrical domain are coupled expresses the heat generation of samples converts thermal input to electrical output. The proposed electro-thermal system model shows good agreement with measured output voltage response in transient state and steady-state.