# Modes of Heat Transfer

**Conduction: **An energy transfer across a system boundary due to a temperature difference by the mechanism of inter-molecular interactions. Conduction needs matter and does not require any bulk motion of matter.

Conduction rate equation is described by the Fourier Law:

q = −k*A*∇*T*

where: q = heat flow vector, (W)

k = thermal conductivity, a thermodynamic property of the material.

(W/m K)

A = Cross sectional area in direction of heat flow. (m^{2})

∇T = Gradient of temperature (K/m) = ∂T/∂x **i** + ∂T/∂y **j** + ∂T/∂z **k**

Note: Since this is a vector equation, it is often convenient to work with one component of the vector. For example, in the x direction:

qx = – k Ax dT/dx

In circular coordinates it may convenient to work in the radial direction:

qr = – k Ar dT/dr

**Convection: **An energy transfer across a system boundary due to a temperature difference by the combined mechanisms of intermolecular interactions and bulk transport. Convection needs fluid matter.

Newton’s Law of Cooling:

q = h As ΔT

where: q = heat flow from surface, a scalar, (W)

h = heat transfer coefficient (which is not a thermodynamic property of the material, but may depend on geometry of surface, flow characteristics, thermodynamic properties of the fluid, etc. (W/m^{2} K)

As = Surface area from which convection is occurring. (m^{2})

ΔT = T∞ – TS = Temperature Difference between surface and coolant. (K)

Table 1. Typical values of h (W/m^{2}K)

Free convection gases: 2 – 25

liquid: 50 – 100

Forced convection gases: 25 – 250

liquid: 50 – 20,000

Boiling/Condensation 2500 -100,000

**Radiation:** Radiation heat transfer involves the transfer of heat by electromagnetic radiation that arises due to the temperature of the body. Radiation does not need matter.

Emissive power of a surface:

E=σεTs^{4} (W/ m^{2})

where: ε = emissivity, which is a surface property (ε = 1 is black body)

σ = Steffan Boltzman constant = 5.67 x 10^{-8} W/m^{2} K4.

Ts = Absolute temperature of the surface (K)

The above equation is derived from Stefan Boltzman law, which describes a gross heat emission rather than heat transfer. The expression for the actual radiation heat transfer rate between surfaces having arbitrary orientations can be quite complex, and will be dealt with in Module 9. However, the rate of radiation heat exchange between a small surface and a large surrounding is given by the following expression:

q = ε·σ·A·(Ts^{4} – T_{sur}^{4})

where: ε = Surface Emissivity

A= Surface Area

Ts = Absolute temperature of surface. (K)

T_{sur} = Absolute temperature of surroundings.(K)

**Summary **