The governing equations for heat transfer and fluid flow are often formulated in a general form for the simplification of discretization and programming, which has achieved great success in thermal science and engineering. Based on the analysis of the popular general form of governing equations, we found that energy conservation cannot be guaranteed when specific heat capacity is not constant, which may lead to unreliable results. A new concept of generalized density is put forward, based on which a new general form of governing equations is proposed to guarantee energy conservation. A number of calculation examples have been employed to verify validation and feasibility.

It is shown that a simple deduction engine can be developed for a propositional logic that follows the normal rules of classical logic in symbolic form, but the description of what is known about a proposition uses two numeric state variables that conveniently describe unknown and inconsistent, as well as true and false. Partly true and partly false can be included in deductions. The multi-valued logic is easily understood as the state variables relate directly to true and false. The deduction engine provides a convenient standard method for handling multiple or complicated logical relations. It is particularly convenient when the deduction can start with different propositions being given initial values of true or false. It extends Horn clause based deduction for propositional logic to arbitrary clauses. The logic system used has potential applications in many areas. A comparison with propositional logic makes the paper self-contained.