MULTIDIMENSIONAL HEAT TRANSFER                

1) Heat transfer problems are also classified as being one-dimensional, two dimensional, or three dimensional, depending on the relative magnitudes of heat transfer rates in different directions and the level of accuracy desired.

a) A heat transfer problem is said to be one-dimensional if the temperature in the medium varies in one direction only and thus heat is transferred in one direction, and the variation of temperature and thus heat transfer in other directions are negligible or zero.

2) Fourier’s law of heat conduction for one-dimensional heat conduction as

a) k is the thermal conductivity of the material, which is a measure of the ability of a material to conduct heat

b) dT/dx is the temperature gradient, which is the slope of the temperature curve on a T-x diagram

c) Heat is conducted in the direction of decreasing temperature, and thus the temperature gradient is negative when heat is conducted in the positive x-direction. The negative sign in equation ensures that heat transfer in the positive x-direction is a positive quantity.

3) General relation for Fourier’s law of heat conduction

Figure The heat transfer vector is always normal to an isothermal surface and can be resolved into its components like any other vector.