Lecture Notes for CO1 (Part 2)INTRODUCTION TO HEAT TRANSFERRizalman MamatUniversiti Malaysia PahangWeek 2

Course Outcome 1 (CO1)Students should be able to understand and analyse the concept of conduction, convection and radiation heat transfer.*Lesson Outcomes from CO1 (Part 2)

To explain the mechanism of various modes and equations for the estimation of heat transferTo derive the generalize 3-dimensional heat conduction equationTo develop the one-dimensional heat conduction form from the generalize 3-dimensional equation for various geometries

*INTRODUCTIONHeat transfer has direction as well as magnitude. It is a vector quantity.

The driving force for any form of heat transfer is the temperature difference.

*Three prime coordinate systems:rectangular T(x, y, z, t)cylindrical T(r, , z, t)spherical T(r, , , t).

*The rate of heat conduction through a medium in a specified direction is expressed by Fouriers law of heat conduction for one-dimensional heat conduction as:

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.

*If n is the normal of the isothermal surface at point P (heat flux vector), the rate of heat conduction at that point can be expressed by Fouriers law as

*ONE-DIMENSIONAL HEAT CONDUCTION EQUATION

*Heat Conduction Equation in a Large Plane Wall

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*Heat Conduction Equation in a Long Cylinder

*Heat Conduction Equation in a Long Cylinder

*thermal diffusivity

*Heat Conduction Equation in a Sphere

*Combined One-Dimensional Heat Conduction EquationOverall, the one-dimensional transient heat conduction equations for the plane wall, cylinder, and sphere can be expressed asn = 0 for a plane wall n = 1 for a cylinder n = 2 for a sphere In the case of a plane wall, replace r by x. This equation can be simplified for steady-state or no heat generation cases as described before.

*GENERAL HEAT CONDUCTION EQUATIONBefore, we considered one-dimensional heat conduction and assumed heat conduction in other directions to be negligible. However, sometimes we need to consider heat transfer in other directions as well. In such cases heat conduction is said to be multidimensional, and in this section we develop the governing differential equation in such systems in rectangular, cylindrical, and spherical.

*Rectangular Coordinates

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*Cylindrical CoordinatesRelations between the coordinates of a point in rectangular and cylindrical coordinate systems:

*Spherical CoordinatesRelations between the coordinates of a point in rectangular and spherical coordinate systems:

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