One-Dimensional Steady-State Conduction

One-Dimensional Steady-State 

1. Conduction problems may involve multiple directions and time-dependent conditions
2. Inherently complex – Difficult to determine temperature distributions
3. One-dimensionalsteady-state models can represent accurately numerous  engineering systems 

The Plane Wall

        Consider a simple case of one-dimensional conduction in a plane wall, separating two fluids of different temperature, without energy generation

                •Temperature is a function of x

                •Heat is transferred in the  x-direction

Must consider

–Convection from hot fluid to wall

–Conduction through wall

–Convection from wall to cold fluid

 

Temperature Distribution

     •Heat diffusion equation in the x-direction for steady-state conditions, with no energy generation

 

        •Boundary Conditions:

 

        •Temperature profile, assuming constant k:

 

Temperature varies linearly with x