# Basic Heat Transfer Calculations: Conduction, Convection and Radiation

The following are the basic heat transfer calculation formulas for conduction, convection, and radiation:

## Conduction Heat Transfer

Conduction is the transfer of heat through a material due to a temperature gradient within the material itself.

### Fourier Law of Conduction

• The rate of heat transfer through conduction is given by Fourier’s Law:

Q =  KA (T1 -T2)/ΔX

• Q is the rate of  heat transferred  through the surface (W or J/S)
• K is the thermal conductivity of the material (W/m-K)
• A is an area of the surface (m^2) normal to heat transfer direction
• T2  is the temperature of the hot surface (K)
• T1 is the temperature of the cold surface (K)
• Δx  is the thickness of the material (m)

### Determination of Conduction Rate

•  For multilayer conduction heat transfer
• Thermal resistance, R = Δx/KA
• The total thermal resistance (RTotal) of a multilayer system is the sum of the individual thermal resistances. For a series arrangement of layers, the formula is:

Rtotal = R1 + R2 + R3 + ….. + Rn

• Where R1, R2, and R3 are the thermal resistances of the individual layers. Each layer’s thermal resistance (Ri)) can be calculated using the formula
• Determine the overall heat transfer rate (Q) through the multilayer system using:

Q  = Overall Temperature Difference/Total thermal resistance

Q =  ΔT /Rtotal

• Where ΔT  is the overall Temperature difference across the multilayer system.
• Please note that this method assumes
• and uniform material properties
• One-dimensional heat transfer through the layers.
• Real-world applications may involve more complex geometries and material properties that might require more sophisticated models or numerical methods for accurate analysis.

## Convection Heat Transfer

• Convection is the transfer of heat between a surface and a fluid (liquid or gas) flowing over it.
• The convective heat transfer rate is commonly calculated using Newton’s Law of Cooling
• Q  is the convective rate of  heat transfer (J/S)
• h  is the heat transfer coefficient (W/m^2-K)
• C  is the specific heat capacity of the fluid (J/kg-K)
• A is  area of the surface (m^2)
• Ts  is the surface temperature of the hot surface (K)
• Tf  is the  temperature of the flowing fluid (K)

## Calculation of Total Heat Transfer from Composite Wall

• Input Data
• Surface Area, A (m2)
• Thermal conductivities of materials, K (w/m-k)
• Heat Transfer coefficients of fluid on both sides of composite walls
• Temperature of fluids
• Calculate overall thermal resistance, Rth
• Calculate overall heat transfer coefficients, U (w/m2-k)
• Calculate heat transfer per unit area, heat flux  (q,w/m2)
• Calculate total heat
• Refer to the following spread for calculations

## <span data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" class="lazy lazy-hidden mce_SELRES_start">﻿</span><span data-mce-type="bookmark" style="display: inline-block; width: 0px; overflow: hidden; line-height: 0;" class="mce_SELRES_start">﻿</span>

• Radiation is the transfer of heat through electromagnetic waves.
• The rate of heat transfer through radiation between two surfaces is given by the Stefan-Boltzmann Law:

Q = σ A (T2^4     –  T1^4)

where

• Q is the radiative  heat transferred (W or J/S)
• σ is the constant of Stefan-Boltzmann  (5.67 x 10^-8 W/m^2-K^4)
• A is  area of the surface (m^2)
• T2 is the  temperature of the hot surface (K)
• T1 is the  temperature of the cold surface (K)

These formulas can be used to calculate the heat transfer rate between two surfaces or to calculate the temperature of a surface after a certain amount of time.