STEADY HEAT CONDUCTION AZIZUL BIN MOHAMAD ENT255 HEAT TRANSFER

Steady State 1-D Conduction Assumptions Temperature varies in only one coordinate directions Energy Balance still applies but time term goes to zero Soln’s dependent on coordinate systems Plane Wall Linear T Constant heat flux and rate Cylinder Logarithmic T Constant heat rate ENT255 HEAT TRANSFER

1-D HEAT CONDUCTION 1-D heat transfer through a simple or composite body exposed to convection from both sides to mediums at temperatures Ts,1 and Ts,2 can be expressed as Where Rtotal is the total thermal resistance between the two mediums. ENT255 HEAT TRANSFER

Thermal Resistance Will utilize circuit analysis methods making analogy between heat flux and electric current. Electricity Thermal Conduction ENT255 HEAT TRANSFER

Convection Resistance Thermal Circuit Planar Wall Constant q throughout the circuit ENT255 HEAT TRANSFER

ENT255 HEAT TRANSFER

For a plane wall exposed to convection on both sides, the total resistance is expressed as: This relation can be extended to plane walls that consist of two or more layers by adding an additional resistance for each additional layer. ENT255 HEAT TRANSFER

Conduction resistance (plane wall): The elementary thermal resistance relations can be expressed as follows: Conduction resistance (plane wall): Conduction resistance (cylinder): Conduction resistance (sphere): ENT255 HEAT TRANSFER

Convection resistance Interface resistance Radiation resistance Rc = thermal contact resistance hc = thermal contact conductance ENT255 HEAT TRANSFER

Composite Wall Heat rate still constant across. But Temperature gradient changes Can use to find internal temperature distributions ENT255 HEAT TRANSFER

Parallel Walls Uniform Temperature at 1 and 2 Heat flux split between sections Thermal Resistance based on local areas Set up system of equations based upon energy balance into nodes ENT255 HEAT TRANSFER

A 3-m-high and 5-m-wide wall consists of long 16-cm x 22-cm cross section horizontal bricks (k = 0.72 W/m.°C) separated by 3-cm thick plaster layers (k = 0.22 W/m.°C). There are also 2-cm- thick plaster layers on each side of the brick and a 3-cm-thick rigid foam (k = 0.026 W/m.°C) on the inner side of the wall. The indoor and the outdoor temperatures are 20°C and -10°C, and the convection heat transfer coefficients on the inner and the outer sides are h1=10W/m2.°C and h2=25W/m2.°C, respectively. Assuming one-dimensional heat transfer and disregarding radiation, determine the rate of heat transfer through the wall. Ans: q = 4.38 W Qtotal = 263 W ENT255 HEAT TRANSFER

Radial Steady State Conduction ENT255 HEAT TRANSFER

ENT255 HEAT TRANSFER

Derivation of Cylindrical Conduction ENT255 HEAT TRANSFER

Composite Radial Wall Similar concept to the planar wall Apply thermal circuit to each wall Add the resistances that are in series ENT255 HEAT TRANSFER

The radial heat rate is constant across the circuit Can analyze in sections or across complete circuit depending on problem ENT255 HEAT TRANSFER

Spherical Coordinates ENT255 HEAT TRANSFER

Conduction with generation ENT255 HEAT TRANSFER

With equal wall temps Becomes parabolic ENT255 HEAT TRANSFER

Once the rate of heat transfer is available, the temperature drop across any layer can be determined from: The thermal resistance concept can also be used to solve steady heat transfer problems involving parallel layers or combined series-parallel arrangement ENT255 HEAT TRANSFER

Radial Generation Typical in electrical heating elements (wires) ENT255 HEAT TRANSFER