Fourier law of heat conduction is essentially valid for heat flow under uni-directional and steady state conditions. However in many practical cases the temperature may be a function of space co-ordinate as well as time. 1. Heat Conduction Equation in Cartesian Co-Ordinates: Consider the flow of heat through an infinitesimal volume element oriented in a three- dimensional co-ordinate system. The [...]
In this article we will discuss about the conditions and mechanism of heat conduction. Conditions of Heat Conduction: The general heat conduction equation is of first order in time co-ordinates, and of second order in spatial co-ordinates. For the solution of single integration one constant is required, and for the solution of each double integration two constants are required. Obviously [...]
In this article we will discuss about:- 1. Heat Conduction through a Plane Wall 2. Heat Conduction through a Composite Wall 3. Effect of Variable Conductivity. Heat Conduction through a Plane Wall: Consider one-dimensional heat conduction through a homogeneous, isotropic wall of thickness 8 with constant thermal conductivity k and constant cross-sectional area A. The wall is insulated on its [...]
In this article we will discuss about the fourier equation and thermal conductivity of materials. Fourier Equation: Conduction is primarily a molecular phenomenon requiring temperature gradient as the driving force. Experimental evidence does indicate that steady-state one-dimensional flow of heat by conduction through a homogeneous material is given by the Fourier Law- Q = - k A dt/dx q = [...]
Consider heat conduction through a hollow sphere of inner radius r1, outer radius r2 and made of a material of constant thermal conductivity. The inner and outer surfaces are maintained at constant but different temperatures t1 and t2 respectively. Geometrical symmetry indicates that the heat flow is limited to radial direction only. Further if temperature t1 at the inner surface [...]
In this article we will discuss about the procedure for conduction of heat through a cylindrical wall and multi-layer cylindrical wall. Conduction of Heat through a Cylindrical Wall: Cylindrical metal tubes constitute an essential element of power stations, oil refineries and most process industries. The boilers have tubes in them, the condensers contain bank of tubes, the heat exchangers are [...]
In many situations of practical importance, heat is generated internally at uniform rate within the conducting medium itself. Notable examples are: (i) Resistance heating in electrical appliances; essentially it is the conversion of electrical energy into thermal energy in the current carrying medium (ii) Energy generated in the fuel element of a nuclear reactor (iii) Liberation of energy due to [...]
In this article we will discuss about transient conduction of heat in solids with infinite thermal conductivity and finite conduction. Transient Conduction of Heat in Solids with Infinite Thermal Conductivity K ā ā (Lumped Parameter Analysis): Solutions to the many of the transient heat flow problems are obtained by the lumped parameter analysis which presumes that the solid possesses infinitely [...]
In many situations of practical importance, heat is generated internally at uniform rate within the conducting medium itself. Notable examples are: (i) Resistance heating in electrical appliances; essentially it is the conversion of electrical energy into thermal energy in the current carrying medium (ii) Energy generated in the fuel element of a nuclear reactor (iii) Liberation of energy due to [...]
Contrary to the common belief that addition of insulating material on a surface always brings about a decrease in the heat transfer rate, there are instances when the addition of insulation to the outside surfaces of cylindrical or spherical walls (geometries which have non-constant cross-sectional areas) does not reduce the heat loss. In fact, under certain circumstances, it actually increases [...]