1. HEAT CONDUCTION EQUATION
ENT 255 HEAT TRANSFER
SCHOOL OF MECHATRONIC ENGINEERING
UNIVERSITI MALAYSIA PERLIS

2. HEAT CONDUCTION EQUATION
STEADY => the temperature does not vary with time
TRANSIENT = UNSTEADY => temperature vary with time
HEAT GENERATION => conversion of electrical, chemical, or nuclear energy into heat (or thermal energy)

3. HEAT CONDUCTION EQUATION
ONE-DIMENSIONAL => the conduction is significant in one dimension only and negligible in the other two dimensions
TWO-DIMENSIONAL => when the conduction in third dimension is negligible
THREE-DIMENSIONAL => conduction in all dimensions is significant.

4. HEAT CONDUCTION EQUATION
Heat Conduction Equation can be derived by performing an energy balance on a differential volume element.
The 1-D heat transfer equation in rectangular coordinate system for the case of k=constant:

5. The 1-D heat transfer equation in cylindrical coordinate system for the case of k=constant:
The 1-D heat transfer equation in spherical coordinate system for the case of k=constant:
Where , the thermal diffusivity

6. SOLUTION OF A HEAT TRANSFER EQUATION
The solution of a heat conduction problem depends on the condition at the surfaces.
BOUNDARY CONDITIONS => mathematical expressions for the thermal conditions at the boundaries
INITIAL CONDITION => a mathematical expression for the temperature distribution of the medium initially, i.e. at time t = 0 or other start time. Applicable to transient heat conduction problems

7. TYPES OF BOUNDARY CONDITIONS

8. TYPES OF BOUNDARY CONDITIONS

9. HOMEWORK (due this Wednesday)
The temperature distribution across a wall 1 m thick at certain instant of time is given as
T(x) = a + bx + cx2
Where T is in degrees Celcius and x is in meters, while a = 1000°C,
b = -250°C/m, and c = -70°C/m2. A uniform heat generation, = 1300 W/m3, is present in the wall of area 15m2 having the properties =1700 kg/m3, k = 50 W/m.K, and cp = 6 kJ/kg.K
Determine the rate of heat transfer entering the wall (x=0) and leaving the wall (x = 1m)
Determine the rate of change of energy storage in the wall.
Determine the time rate of temperature change at x = 0, 0.03 and 0.7 m
Please draw the system schematic, list the assumptions, and perform the analysis
Hint: Part 1: Use Fourier’s Law
Part 2: Apply overall energy balance
Part 3: Apply heat conduction equation