Heal generation thermal energy

A medium through which heat is conducted may involve the conversion of mechanical, electrical, nuclear, or chemical energy into heat (or thermal energy). In heal conduction analysis, such conversion processes are characterized as heal (or thermal energy) generation. 

Starting with an energy balance on a spherical shell volume clement, derive the one-dimensional transient heat conduction equation for a sphere with constant thermal conductivity and no heal generation. 

Consider steady one-dimensional heat conduction through a plane wall, a cylindrical shell, and a spherical shell of unifonn thickness with constant thcimophysical propenies and no thermal energy generation. The geometry in which the variation of temperature in the direction of heal transfer will be linear is... 

Consider transient heat conduction in a plane wall with variable heal generation and constant thermal conductivity. The nodal network of (he medium consists of nodes 0, 1, 2, 3, and 4 with a uniform nodal spacing of A.r. The wall is initially at a specified temperaWre. The temperature at the right bound ary (node 4) is specified. Using the energy balance approach, obtain the explicit finite difference formulation of the boundary... 

Consider a small hot metal object of mass m and specific heal c lliat is initially at a temperature of 7j. Now the object is allowed to cool in an environment at T by convection with a heat transfer coefficient of /r. The (emperanire of the metal object is observed to vary uniformly with time during cooling. Writing an energy balance on the entire metal object, derive the differential equation that describes the variation of temperature of the ball with time, T(/). Assume constant thermal conductivity and no heat generation in the object. Do not solve. 

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