10.7 Heat transfer analysis

Steady-State or Transient Heat Transfer Analysis is devoted to predicting the temperature distribution for an object exposed to heating, radiation, convection and conduction. Thermal Stress Analysis predicts stresses, displacements due to thermal expansion or contraction. To perform heat transfer analysis or static structural analysis the same types of elements can be used. There is no need to decrease the order of elements or to remesh the model. For three-dimensional (3D) brick elements there are 3 nodal displacements for static analysis. Nodal temperature is an additional variable. Therefore, there are 4 variables per node for the thermal stress analysis. The structural stiffness matrix does not depend on boundary conditions or nodal temperature. Temperature change causes thermal expansion or contraction. High temperature causes thermal expansion of a solid. Uniform heating results in deformation only, not thermal stress. High gradient of temperature causes distortion of the beam. Thermal stresses are caused by temperature gradient. The smaller the distance between nodes with different temperatures, the larger the distortion and thermal stresses. Cooling causes contraction and tensile stress s_z in most of the elements. The stress does not depend on the width of the plate. The stress at the left-hand side of the notched specimen is very small. There is a stress gradient in the net-section A - B. The stress is the largest in element A. Oil quenching of a steel structure can be modeled by transient heat transfer module. The results are transferred to static analysis to calculate the thermal stresses. Quenching causes contraction of external surfaces. The contraction causes the tensile stress on those surfaces. The intersection of thin and thick walls causes the highest thermal stresses. A pressure vessel with bimetal steel walls was heated till 400^oC. The coefficient of thermal expansion is larger for stainless steel. The stainless steel layer tries to expand but the titanium alloy layer does not have such a large deformation. There is a negative tangential thermal stress in the stainless steel. There is additional compressive thermal stress in the stainless steel near the layer's intersection. Uniform heating of the rigid ring will expand it mostly in the tangential direction. There is a smaller displacement in the radial direction. Thin walled dome-shape plate will have a larger radial displacement. It causes the central points to move upwards. A cold drop of water on a hot metal surface causes thermal cracking due to local tensile stress. The temperature distribution in the structure is used as the loading condition for a structural analysis to calculate thermal stress. The temperature can be calculated using the differential equation governing transient heat transfer with a heat source. In this case: k is the heat transfer coefficient; T is temperature; t is time; Q(t) is the heat source.